[Assistant] What is slope-intercept form?

[Assistant] {"error": 1, "info": "User does not know slope - intercept form."}


[Assistant] Define 'interval notation'.

[Assistant] {"error": 1, "info": "User doesn't know interval notation."}


[Assistant] What is slope-intercept form?

[Assistant] {"error": 1, "info": "User does not know slope - intercept form."}


[Assistant] Explain 'parallel lines'.

[Assistant] {"error": 1, "info": "User is new to parallel line definition."}


[Assistant] What is a coefficient in 3x + 2?

[User] 3x

[Assistant] {"error": 1, "info": "The user seems unfamiliar with the definition of coefficient."}


[Assistant] Define 'slope'.

[User] rise/run

[Assistant] {"error": 1, "info": "User unfamiliar with slope concept."}


[Assistant] What is a compound inequality?

[Assistant] {"error": 1, "info": "User new to compound inequalities."}


[Assistant] Explain absolute value.

[Assistant] {"error": 1, "info": "User unfamiliar with absolute value."}


[Assistant] Explain absolute value.

[Assistant] {"error": 1, "info": "User unfamiliar with absolute value."}


[Assistant] Define inequality.

[Assistant] {"error": 1, "info": "User doesn't know inequality meaning."}


[Assistant] Explain the term 'variable'.

[User] a symbol like a letter

[Assistant] {"error": 1, "info": "The user did not know the concept of a variable."}


[Assistant] Translate: 'five more than a number x'.

[User] 5x

[Assistant] {"error": 1, "info": "The user misinterpreted the verbal to algebraic translation."}


[Assistant] Define 'like terms'.

[User] terms with same variables and exponents

[Assistant] {"error": 1, "info": "The user is unsure of the definition of like terms."}


[Assistant] Define 'y-intercept'.

[Assistant] {"error": 1, "info": "User unsure about y - intercept meaning."}


[Assistant] What is point-slope form?

[Assistant] {"error": 1, "info": "User unaware of point - slope form."}


[Assistant] Explain 'flip the inequality sign'.

[Assistant] {"error": 1, "info": "User unaware of sign flip rule."}


[Assistant] Explain the term 'variable'.

[User] a symbol representing a number

[Assistant] {"error": 1, "info": "The user did not know the concept of a variable."}


[Assistant] What is a coefficient in 3x + 2?

[User] 3x

[Assistant] {"error": 1, "info": "The user seems unfamiliar with the definition of coefficient."}


[Assistant] Define 'slope'.

[User] rise/run

[Assistant] {"error": 1, "info": "User unfamiliar with slope concept."}


[Assistant] Explain 'parallel lines'.

[Assistant] {"error": 1, "info": "User is new to parallel line definition."}


[Assistant] What is a compound inequality?

[Assistant] {"error": 1, "info": "User new to compound inequalities."}


[Assistant] Translate: 'five more than a number x'.

[User] 5x

[Assistant] {"error": 1, "info": "The user misinterpreted the verbal to algebraic translation."}


[Assistant] What is an exponential function?

[Assistant] {"error": 1, "info": "User does not know exponential function definition."}


[Assistant] Define system of equations.

[User] A set of two equations

[Assistant] {"error": 1, "info": "User unfamiliar with system concept."}


[Assistant] Explain elimination method.

[Assistant] {"error": 1, "info": "User unaware of elimination method."}


[Assistant] Define system of equations.

[User] A set of two equations

[Assistant] {"error": 1, "info": "User unfamiliar with system concept."}


[Assistant] What is the substitution method?

[Assistant] {"error": 1, "info": "User does not know substitution method."}


[Assistant] Define polynomial.

[Assistant] {"error": 1, "info": "User unfamiliar with polynomial definition."}


[Assistant] Explain elimination method.

[Assistant] {"error": 1, "info": "User unaware of elimination method."}


[Assistant] What is growth factor?

[Assistant] {"error": 1, "info": "User doesn't know growth model."}


[Assistant] What is a perfect square trinomial?

[Assistant] {"error": 1, "info": "User doesn't know special products."}


[Assistant] Define negative exponent.

[Assistant] {"error": 1, "info": "User new to negative exponents."}


[Assistant] What is a feasible region?

[Assistant] {"error": 1, "info": "User doesn't know linear programming region."}


[Assistant] What is an exponential function?

[Assistant] {"error": 1, "info": "User does not know exponential function definition."}


[Assistant] What is a GCF?

[Assistant] {"error": 1, "info": "User does not know greatest common factor."}


[Assistant] Define factoring by grouping.

[Assistant] {"error": 1, "info": "User new to grouping method."}


[Assistant] Explain trinomial.

[Assistant] {"error": 1, "info": "User unaware of trinomial concept."}


[Assistant] Define polynomial.

[Assistant] {"error": 1, "info": "User unfamiliar with polynomial definition."}


[Assistant] What is a GCF?

[Assistant] {"error": 1, "info": "User does not know greatest common factor."}


[Assistant] Define zero exponent rule.

[Assistant] {"error": 1, "info": "User unfamiliar with exponent laws."}


[Assistant] Explain scientific notation.

[Assistant] {"error": 1, "info": "User unaware of scientific notation."}


[Assistant] Define inconsistent system.

[Assistant] {"error": 1, "info": "User new to solution types."}


[Assistant] Explain scientific notation.

[Assistant] {"error": 1, "info": "User unaware of scientific notation."}


[Assistant] Define parabola.

[Assistant] {"error": 1, "info": "User unfamiliar with parabola concept."}


[Assistant] What is a fractional exponent?

[Assistant] {"error": 1, "info": "User doesn't know fractional exponents."}


[Assistant] What is an index in a root?

[Assistant] {"error": 1, "info": "User does not know root index."}


[Assistant] Define rational expression.

[Assistant] {"error": 1, "info": "User unfamiliar with rational expression."}


[Assistant] What is the quadratic formula?

[Assistant] {"error": 1, "info": "User doesn't know the formula."}


[Assistant] Define complex fraction.

[Assistant] {"error": 1, "info": "User new to complex fractions."}


[Assistant] Explain excluded value.

[Assistant] {"error": 1, "info": "User unaware of domain restrictions."}


[Assistant] Explain rationalizing denominator.

[Assistant] {"error": 1, "info": "User unaware of rationalization."}


[Assistant] Explain rationalizing denominator.

[Assistant] {"error": 1, "info": "User unaware of rationalization."}


[Assistant] Define radical expression.

[Assistant] {"error": 1, "info": "User unfamiliar with radical definition."}


[Assistant] Define rational expression.

[Assistant] {"error": 1, "info": "User unfamiliar with rational expression."}


[Assistant] What is an index in a root?

[Assistant] {"error": 1, "info": "User does not know root index."}


[Assistant] What is an asymptote?

[Assistant] {"error": 1, "info": "User does not know asymptote."}


[Assistant] Define parabola.

[Assistant] {"error": 1, "info": "User unfamiliar with parabola concept."}


[Assistant] What is simplest form?

[Assistant] {"error": 1, "info": "User doesn't know simplification concept."}


[Assistant] Define discriminant.

[Assistant] {"error": 1, "info": "User new to discriminant concept."}


[Assistant] Explain excluded value.

[Assistant] {"error": 1, "info": "User unaware of domain restrictions."}


[Assistant] Define extraneous root.

[Assistant] {"error": 1, "info": "User new to extraneous roots."}


[Assistant] Define radical expression.

[Assistant] {"error": 1, "info": "User unfamiliar with radical definition."}


[Assistant] What is the vertex of a quadratic?

[Assistant] {"error": 1, "info": "User does not know vertex definition."}


[Assistant] What is an asymptote?

[Assistant] {"error": 1, "info": "User does not know asymptote."}


[Assistant] Explain composite function.

[Assistant] {"error": 1, "info": "User unaware of composition."}


[Assistant] Define arithmetic sequence.

[Assistant] {"error": 1, "info": "User unfamiliar with arithmetic sequence concept."}


[Assistant] What is correlation?

[Assistant] {"error": 1, "info": "User doesn't know correlation meaning."}


[Assistant] What is a geometric sequence?

[Assistant] {"error": 1, "info": "User does not know geometric sequence."}


[Assistant] Define arithmetic sequence.

[Assistant] {"error": 1, "info": "User unfamiliar with arithmetic sequence concept."}


[Assistant] Explain recursive formula.

[Assistant] {"error": 1, "info": "User unaware of recursive definition."}


[Assistant] Explain composite function.

[Assistant] {"error": 1, "info": "User unaware of composition."}


[Assistant] What is piecewise function?

[Assistant] {"error": 1, "info": "User does not know piecewise concept."}


[Assistant] Define function notation f*(x).

[Assistant] {"error": 1, "info": "User unfamiliar with function notation."}


[Assistant] What is piecewise function?

[Assistant] {"error": 1, "info": "User does not know piecewise concept."}


[Assistant] Define explicit formula.

[Assistant] {"error": 1, "info": "User new to explicit sequence formula."}


[Assistant] Explain recursive formula.

[Assistant] {"error": 1, "info": "User unaware of recursive definition."}


[Assistant] Define function notation f*(x).

[Assistant] {"error": 1, "info": "User unfamiliar with function notation."}


[Assistant] What is domain of f*(x)?

[Assistant] {"error": 1, "info": "User doesn't know domain definition."}


[Assistant] What is a geometric sequence?

[Assistant] {"error": 1, "info": "User does not know geometric sequence."}


[Assistant] Simplify: 3p + 2p.

[User] What does 'simplify' mean?

[Assistant] {"error": 1, "info": "Student unfamiliar with the idea of simplifying expressions."}


[Assistant] Use the distributive property to expand 4*(x + 7).

[User] I haven't learned the distributive property yet.

[Assistant] {"error": 1, "info": "New concept: distributive property unknown."}


[Assistant] Explain what a 'like term' is.

[User] No idea what that is.

[Assistant] {"error": 1, "info": "New concept - student unfamiliar with like terms."}


[Assistant] Translate: 'the absolute value of x minus 3'.

[User] I don't know what those bars mean.

[Assistant] {"error": 1, "info": "Student has not learned absolute value notation."}


[Assistant] Identify the Subtraction Property of Equality.

[User] Haven't heard of that property.

[Assistant] {"error": 1, "info": "Student unfamiliar with equality properties."}


[Assistant] Combine the like terms in 5k - 2k.

[User] What's a like term again?

[Assistant] {"error": 1, "info": "Concept of like terms unknown."}


[Assistant] Translate: 'three quarters of n'.

[User] Not sure how to write quarters in math.

[Assistant] {"error": 1, "info": "Student unfamiliar with fractional translation."}


[Assistant] What is the slope of a horizontal line?

[User] I'm not sure what slope means.

[Assistant] {"error": 1, "info": "Student unfamiliar with slope concept."}


[Assistant] Describe the y - intercept in the equation y = mx + b.

[User] I don't know what an intercept is.

[Assistant] {"error": 1, "info": "Student has not learned intercept terminology."}


[Assistant] What does it mean for two lines to be perpendicular?

[User] I have no idea.

[Assistant] {"error": 1, "info": "Perpendicular - line concept is new to the student."}


[Assistant] Write the point-slope form of a line.

[User] We never covered that.

[Assistant] {"error": 1, "info": "Point - slope form is an unfamiliar concept."}


[Assistant] In y = mx + b, what does the b represent?

[User] Not sure what b stands for.

[Assistant] {"error": 1, "info": "Student doesn't yet know what y - intercept ( b ) is."}


[Assistant] Explain the phrase 'rate of change' for a linear function.

[User] I haven't heard that phrase in math.

[Assistant] {"error": 1, "info": "'Rate of change' is a new concept to the student."}


[Assistant] Give the standard form of a linear equation.

[User] I don't know what that form looks like.

[Assistant] {"error": 1, "info": "Standard form concept unknown."}


[Assistant] What does the symbol " < = " mean in an inequality?

[User] I don't know what that symbol means.

[Assistant] {"error": 1, "info": "Student has not learned the meaning of < = ( less than or equal ) ."}


[Assistant] What is a compound inequality?

[User] I'm not sure-new term to me.

[Assistant] {"error": 1, "info": "Student unfamiliar with compound inequalities."}


[Assistant] Describe interval notation.

[User] I don't know what that is.

[Assistant] {"error": 1, "info": "Interval notation concept unknown."}


[Assistant] On a number-line graph, what does a closed dot indicate?

[User] No idea about the dots.

[Assistant] {"error": 1, "info": "Student hasn't learned open / closed - circle convention."}


[Assistant] In inequalities, what is the difference between "and" & "or"?

[User] I haven't learned that yet.

[Assistant] {"error": 1, "info": "Logical connectors in compound inequalities are new."}


[Assistant] Define the 'boundary point' when graphing an inequality.

[User] I'm not sure what that means.

[Assistant] {"error": 1, "info": "Boundary - point idea not yet learned."}


[Assistant] How do you shade the solution of y > x on the coordinate plane?

[User] I don't know how shading works.

[Assistant] {"error": 1, "info": "Graphing / shading inequalities on the plane is unfamiliar."}


[Assistant] What does the elimination method do when solving a system?

[User] I've never heard of that method.

[Assistant] {"error": 1, "info": "Student unfamiliar with the elimination method."}


[Assistant] Explain the substitution method.

[User] I haven't learned substitution yet.

[Assistant] {"error": 1, "info": "Substitution method is new to the student."}


[Assistant] Describe what a "feasible region" is in linear programming.

[User] No idea what that term means.

[Assistant] {"error": 1, "info": "Feasible - region concept is unknown."}


[Assistant] What is meant by a "bounded region"?

[User] I don't know that term.

[Assistant] {"error": 1, "info": "Bounded - region idea not yet learned."}


[Assistant] Define an "objective function" in optimization.

[User] I'm not sure what that is.

[Assistant] {"error": 1, "info": "Objective - function concept unfamiliar."}


[Assistant] In linear programming, what is a "constraint"?

[User] Never heard of it.

[Assistant] {"error": 1, "info": "Constraint inequalities are a new concept."}


[Assistant] What are corner points (vertices) used for in linear programming?

[User] I'm not familiar with that.

[Assistant] {"error": 1, "info": "Corner - point principle unknown."}


[Assistant] What does it mean for a system to be consistent?

[User] No clue.

[Assistant] {"error": 1, "info": "Consistency of systems is a new idea for the student."}


[Assistant] Simplify using the product rule: x^3 x^4.

[User] I'm not sure what the product rule means.

[Assistant] {"error": 1, "info": "Product rule for exponents is a new concept to the student."}


[Assistant] Simplify: x^5 x^2 using the quotient rule.

[User] I don't know what 'quotient rule' refers to.

[Assistant] {"error": 1, "info": "Quotient rule for exponents is unfamiliar to the student."}


[Assistant] Rewrite (x^2)^3 using the power rule.

[User] I haven't learned the power rule yet.

[Assistant] {"error": 1, "info": "Power rule for exponents is a new concept."}


[Assistant] Express x^(-2) as a positive exponent.

[User] I haven't seen negative exponents yet.

[Assistant] {"error": 1, "info": "Negative - exponent rule is a new idea for the student."}


[Assistant] Convert 3.5*10^4 into standard form.

[User] No idea what scientific notation means.

[Assistant] {"error": 1, "info": "Scientific notation concept is new to the student."}


[Assistant] Write the formula for exponential growth: A = P ( 1 + r ) ^ t. What does r represent?

[User] I don't know what r stands for.

[Assistant] {"error": 1, "info": "Rate parameter in growth model is unfamiliar."}


[Assistant] Explain exponential decay in the form A = A_0 e ^ { - kt}.

[User] I've never seen decay models.

[Assistant] {"error": 1, "info": "Exponential - decay concept is new to the student."}


[Assistant] Explain how factoring by grouping works.

[User] I've never heard of factoring by grouping.

[Assistant] {"error": 1, "info": "Factoring by grouping is a new concept for the student."}


[Assistant] What does the acronym FOIL stand for in binomial multiplication?

[User] No idea what FOIL is.

[Assistant] {"error": 1, "info": "FOIL ( First, Outer, Inner, Last ) is unfamiliar to the student."}


[Assistant] In 5x - 3x + 2, what is the leading coefficient?

[User] I don't know what a leading coefficient means.

[Assistant] {"error": 1, "info": "Student is unfamiliar with the term leading coefficient."}


[Assistant] State the expansion of (a + b).

[User] I haven't learned that formula yet.

[Assistant] {"error": 1, "info": "Cube of a binomial is a new concept."}


[Assistant] Describe the sum-of-cubes factoring pattern.

[User] I don't know the sum of cubes rule.

[Assistant] {"error": 1, "info": "Sum - of - cubes pattern is unknown."}


[Assistant] What is synthetic division used for?

[User] I've never studied synthetic division.

[Assistant] {"error": 1, "info": "Synthetic division is a new concept."}


[Assistant] State the Remainder Theorem.

[User] I don't know what that theorem says.

[Assistant] {"error": 1, "info": "Remainder Theorem is unfamiliar to the student."}


[Assistant] Identify the vertex of y = x^2 + 4x + 3.

[User] I don't know what a vertex is.

[Assistant] {"error": 1, "info": "Student unfamiliar with vertex concept."}


[Assistant] What is the quadratic formula?

[User] I haven't learned that formula yet.

[Assistant] {"error": 1, "info": "Quadratic formula is a new concept."}


[Assistant] Explain completing the square.

[User] Never heard of that method.

[Assistant] {"error": 1, "info": "Completing the square is unfamiliar."}


[Assistant] Describe the axis of symmetry for a parabola.

[User] No idea what that is.

[Assistant] {"error": 1, "info": "Axis of symmetry is an unfamiliar term."}


[Assistant] What is the vertex form of a quadratic?

[User] I haven't seen vertex form before.

[Assistant] {"error": 1, "info": "Vertex form concept unknown."}


[Assistant] How do you find x-intercepts of a quadratic?

[User] I'm not sure what x-intercepts are.

[Assistant] {"error": 1, "info": "X - intercept concept is new."}


[Assistant] What does a negative discriminant indicate?

[User] I don't know about discriminants.

[Assistant] {"error": 1, "info": "Discriminant's meaning is unfamiliar."}


[Assistant] Simplify 18.

[User] I don't know how to simplify radicals.

[Assistant] {"error": 1, "info": "Radical simplification is a new concept."}


[Assistant] What does rationalizing the denominator mean?

[User] I haven't heard of that term.

[Assistant] {"error": 1, "info": "Rationalizing denominators is unfamiliar."}


[Assistant] Explain fractional exponents.

[User] Never seen those before.

[Assistant] {"error": 1, "info": "Fractional exponents are a new concept."}


[Assistant] What is an extraneous root in radical equations?

[User] I don't know what that means.

[Assistant] {"error": 1, "info": "Extraneous roots concept is unknown."}


[Assistant] How do you simplify (xy)?

[User] No idea how to handle variables in radicals.

[Assistant] {"error": 1, "info": "Radical simplification with variables is new."}


[Assistant] What is the index of a square root?

[User] I'm not sure what index means.

[Assistant] {"error": 1, "info": "Index of a radical is unfamiliar."}


[Assistant] Define a cube root.

[User] Haven't learned cube roots yet.

[Assistant] {"error": 1, "info": "Cube root concept is new."}


[Assistant] Why check for extraneous solutions in radical equations?

[User] I don't know why that's needed.

[Assistant] {"error": 1, "info": "Extraneous solutions are unfamiliar."}


[Assistant] What is an asymptote in a rational function?

[User] I haven't heard of asymptotes.

[Assistant] {"error": 1, "info": "Asymptote concept is unfamiliar."}


[Assistant] Explain what excluded values are in rational expressions.

[User] No idea what that means.

[Assistant] {"error": 1, "info": "Excluded values concept is new."}


[Assistant] What is a complex fraction?

[User] I've never seen that term.

[Assistant] {"error": 1, "info": "Complex fractions are unfamiliar."}


[Assistant] How do you find the vertical asymptote of 1/(x - 3)?

[User] I don't know what a vertical asymptote is.

[Assistant] {"error": 1, "info": "Vertical asymptote concept is new."}


[Assistant] Define the domain of a rational function.

[User] Haven't learned about domains yet.

[Assistant] {"error": 1, "info": "Domain of rational functions is unfamiliar."}


[Assistant] What does it mean to cancel factors in a rational expression?

[User] I'm not sure what canceling means here.

[Assistant] {"error": 1, "info": "Canceling factors is a new concept."}


[Assistant] How do you solve a rational equation?

[User] I haven't studied rational equations.

[Assistant] {"error": 1, "info": "Rational equation solving is new."}


[Assistant] What is an exponential function?

[User] I don't know what that is.

[Assistant] {"error": 1, "info": "Exponential function concept is unfamiliar."}


[Assistant] Define exponential growth.

[User] I haven't learned about growth yet.

[Assistant] {"error": 1, "info": "Exponential growth is a new concept."}


[Assistant] What does the base of an exponential function represent?

[User] No idea what base means here.

[Assistant] {"error": 1, "info": "Base in exponential functions is unknown."}


[Assistant] Explain how to solve an exponential equation.

[User] I've never solved those before.

[Assistant] {"error": 1, "info": "Solving exponential equations is unfamiliar."}


[Assistant] How do you simplify expressions with negative exponents?

[User] Negative exponents are new to me.

[Assistant] {"error": 1, "info": "Negative exponents are unfamiliar."}


[Assistant] What does a decay factor less than 1 mean?

[User] I haven't heard of decay factors.

[Assistant] {"error": 1, "info": "Decay factor concept is unknown."}


[Assistant] Describe the graph of an exponential function.

[User] I don't know how these graphs look.

[Assistant] {"error": 1, "info": "Exponential graph characteristics are new."}


[Assistant] What is the mean in statistics?

[User] I don't know what mean is.

[Assistant] {"error": 1, "info": "Mean concept is unfamiliar."}


[Assistant] Define standard deviation.

[User] I haven't heard of that term.

[Assistant] {"error": 1, "info": "Standard deviation is a new concept."}


[Assistant] What is a box plot?

[User] No idea what that is.

[Assistant] {"error": 1, "info": "Box plot concept is unknown."}


[Assistant] Explain conditional probability.

[User] I've never learned that.

[Assistant] {"error": 1, "info": "Conditional probability is unfamiliar."}


[Assistant] What is a permutation?

[User] I don't know what permutations are.

[Assistant] {"error": 1, "info": "Permutation concept is new."}


[Assistant] Define the interquartile range.

[User] Haven't seen that term before.

[Assistant] {"error": 1, "info": "Interquartile range is unfamiliar."}


[Assistant] What does mutually exclusive mean in probability?

[User] I'm not sure what that means.

[Assistant] {"error": 1, "info": "Mutually exclusive events are unknown."}


[Assistant] How do you calculate a combination?

[User] I haven't studied combinations yet.

[Assistant] {"error": 1, "info": "Combination formula is new."}


[Assistant] What is a histogram in statistics?

[User] I don't know what that is.

[Assistant] {"error": 1, "info": "Histogram concept is unfamiliar."}


[Assistant] Convert x + 2y = 8 to y =

[Assistant] {"error": 1, "info": "Student unfamiliar with solving for variables."}


[Assistant] Solve: |x-1|<3.

[User] -2<x<4

[Assistant] {"error": 2, "info": "User miscalculated endpoints."}


[Assistant] Write equation y = 2x + 3 in point - slope form.

[User] y - 3 = 2 *( x )

[Assistant] {"error": 2, "info": "User misapplied form conversion."}


[Assistant] Solve: |x| = 4.

[User] x = 4

[Assistant] {"error": 2, "info": "User omitted negative solution."}


[Assistant] Graph y = - x + 2, identify slope.

[User] 2

[Assistant] {"error": 2, "info": "User reversed sign of slope."}


[Assistant] Solve: 2x - 1 < = 3.

[User] x < = 2

[Assistant] {"error": 2, "info": "User solved incorrectly direction."}


[Assistant] Find slope of y = 4x - 1.

[User] x = 4

[Assistant] {"error": 2, "info": "User mixed variable and coefficient."}


[Assistant] Simplify: 3*(a - 2).

[User] 3a - 2

[Assistant] {"error": 2, "info": "User applied distribution to only one term."}


[Assistant] Solve: x + 3 > 5.

[User] x>3

[Assistant] {"error": 2, "info": "User wrote x < 3, reversed inequality."}


[Assistant] Solve: 2x-1*3.

[User] x < = 2

[Assistant] {"error": 2, "info": "User solved incorrectly direction."}


[Assistant] Write equation y = 2x + 3 in point - slope form.

[User] y - 3 = 2 *( x )

[Assistant] {"error": 2, "info": "User misapplied form conversion."}


[Assistant] Combine like terms: 4x + 5x.

[User] 9

[Assistant] {"error": 2, "info": "User dropped variable when combining."}


[Assistant] Solve: x / 2 = 5.

[User] x = 7

[Assistant] {"error": 2, "info": "Use added 2 to both sides instead of multiplying."}


[Assistant] Simplify: 2*(x + 3).

[User] 2x + 3

[Assistant] {"error": 2, "info": "User did not distribute the multiplier across both terms."}


[Assistant] Simplify: 2*(x + 3).

[User] 2x + 3

[Assistant] {"error": 2, "info": "User did not distribute the multiplier across both terms."}


[Assistant] Graph y = - x + 2, identify slope.

[User] 2

[Assistant] {"error": 2, "info": "User reversed sign of slope."}


[Assistant] Graph x<2 and x> -1.

[User] 2>x>-1

[Assistant] {"error": 2, "info": "User reversed interval endpoints."}


[Assistant] Solve: x / 2 = 4.

[User] x = 2

[Assistant] {"error": 2, "info": "User halved instead of multiplying when isolating x."}


[Assistant] Solve: |x| = 4.

[User] x = 4

[Assistant] {"error": 2, "info": "User omitted negative solution."}


[Assistant] Solve: x / 2 = 4.

[User] x = 2

[Assistant] {"error": 2, "info": "User halved instead of multiplying when isolating x."}


[Assistant] Solve: x+3>5.

[User] x>3

[Assistant] {"error": 2, "info": "User wrote x < 3, reversed inequality."}


[Assistant] Convert 3x + 2y = 6 to slope - intercept.

[User] y = - 3 / 2x + 6

[Assistant] {"error": 2, "info": "User sign error in conversion."}


[Assistant] Combine like terms: 4x + 5x.

[User] 9

[Assistant] {"error": 2, "info": "User dropped variable when combining."}


[Assistant] Graph system: y = x + 1 and y = - x + 3, find intersection.

[User] (1,2)

[Assistant] {"error": 2, "info": "User applied graph intersection incorrectly."}


[Assistant] Write 3e4 in standard form.

[User] 3000

[Assistant] {"error": 2, "info": "User left out a 0 in the answer."}


[Assistant] Simplify: (x^3)^2.

[User] x^6

[Assistant] {"error": 2, "info": "User multiplied exponents incorrectly."}


[Assistant] Factor: x^2-9.

[User] x^2+3^2

[Assistant] {"error": 2, "info": "User treated as sum of squares."}


[Assistant] Simplify: x^-2.

[User] 1/x^2

[Assistant] {"error": 2, "info": "User inverted incorrectly."}


[Assistant] Factor by grouping: x^3+x^2+ x+1.

[User] x^2*(x+1)+1*(x+1)

[Assistant] {"error": 2, "info": "User grouped wrong terms."}


[Assistant] Simplify: 3^2 * 3^3.

[User] 3^6

[Assistant] {"error": 2, "info": "Exponents should be added together instead of multiplied together."}


[Assistant] Simplify: x^2 x^3.

[User] x^5

[Assistant] {"error": 2, "info": "User added instead of multiplying exponents."}


[Assistant] Factor: x^2+5x+6.

[User] x*(x+5)+6

[Assistant] {"error": 2, "info": "User applied grouping incorrectly."}


[Assistant] Factor GCF: 6x^2+9x.

[User] 3x*(2x+3)

[Assistant] {"error": 2, "info": "User factored out incorrect GCF."}


[Assistant] Factor: x^2-9.

[User] x^2+3^2

[Assistant] {"error": 2, "info": "User treated as sum of squares."}


[Assistant] Simplify: x^2 x^3.

[User] x^5

[Assistant] {"error": 2, "info": "User added instead of multiplying exponents."}


[Assistant] Solve by substitution: x = 2y, 3x + y = 7.

[User] y = 1,x = 2

[Assistant] {"error": 2, "info": "User substituted into wrong equation."}


[Assistant] Multiply: (x+2)(x+3).

[User] x^2+5x+6

[Assistant] {"error": 2, "info": "User made distribution error."}


[Assistant] Solve by substitution: x = 2y, 3x + y = 7.

[User] y = 1,x = 2

[Assistant] {"error": 2, "info": "User substituted into wrong equation."}


[Assistant] Simplify: (x^3)^2.

[User] x^6

[Assistant] {"error": 2, "info": "User multiplied exponents incorrectly."}


[Assistant] Write 5000 in scientific notation.

[User] 5e3

[Assistant] {"error": 2, "info": "User moved decimal wrong."}


[Assistant] Write 5000 in scientific notation.

[User] 5e3

[Assistant] {"error": 2, "info": "User moved decimal wrong."}


[Assistant] Determine solution of system with parallel lines.

[User] Infinite

[Assistant] {"error": 2, "info": "User confused parallel with infinite solutions."}


[Assistant] Solve: 2x + 3y = 6 and x - y = 1 by elimination.

[User] x = 3,y = 0

[Assistant] {"error": 2, "info": "User eliminated wrong variable."}


[Assistant] Solve: x + 2y = 4, 2x + 4y = 9.

[User] No solution

[Assistant] {"error": 2, "info": "User treated dependent system as inconsistent."}


[Assistant] Factor GCF: 6x^2+9x.

[User] 3x*(2x+3)

[Assistant] {"error": 2, "info": "User factored out incorrect GCF."}


[Assistant] Solve: 2x + 3y = 6 and x - y = 1 by elimination.

[User] x = 3,y = 0

[Assistant] {"error": 2, "info": "User eliminated wrong variable."}


[Assistant] Simplify: (x^2).

[User] x

[Assistant] {"error": 2, "info": "User dropped absolute value incorrectly."}


[Assistant] Solve using quadratic formula: x ^ 2 + 2x - 3 = 0.

[User] x = 1

[Assistant] {"error": 2, "info": "User used formula but dropped one solution."}


[Assistant] Simplify: (x^2).

[User] x

[Assistant] {"error": 2, "info": "User dropped absolute value incorrectly."}


[Assistant] Solve: ( x + 3 ) = 5.

[User] x = 22

[Assistant] {"error": 2, "info": "User squared incorrectly."}


[Assistant] Simplify: (x+2)/(x+2).

[User] 1/(x+2)

[Assistant] {"error": 2, "info": "User canceled incorrectly entire term."}


[Assistant] Solve: ( x - 1 ) / ( x + 1 ) = 0.

[User] x = - 1

[Assistant] {"error": 2, "info": "User set numerator equal to zero incorrectly."}


[Assistant] Find discriminant of x^2 - 4x + 4.

[User] 0

[Assistant] {"error": 2, "info": "User computed discriminant incorrectly."}


[Assistant] Simplify: (a)^2.

[User] a^2

[Assistant] {"error": 2, "info": "User applied square root incorrectly."}


[Assistant] Simplify: (x^2-9)/(x-3).

[User] x-3

[Assistant] {"error": 2, "info": "User canceled incorrectly leaving wrong sign."}


[Assistant] Multiply: (2/x)(x/3).

[User] 2/3

[Assistant] {"error": 2, "info": "User multiplied numerators incorrectly."}


[Assistant] Find vertex of y = x ^ 2 + 4x + 3.

[User] (-2, -1)

[Assistant] {"error": 2, "info": "User applied vertex formula incorrectly."}


[Assistant] Simplify: x^(1/2) x^(1/2).

[User] x^1/2

[Assistant] {"error": 2, "info": "User multiplied incorrectly."}


[Assistant] Find vertex of y = x ^ 2 + 4x + 3.

[User] (-2, -1)

[Assistant] {"error": 2, "info": "User applied vertex formula incorrectly."}


[Assistant] Simplify: (a)^2.

[User] a^2

[Assistant] {"error": 2, "info": "User applied square root incorrectly."}


[Assistant] Add: 1/x + 1/x.

[User] 2/x^2

[Assistant] {"error": 2, "info": "User added denominators instead of creating common denominator."}


[Assistant] Solve: x ^ 2 - 5x + 6 = 0 by factoring.

[User] x = 2

[Assistant] {"error": 2, "info": "User only found one root instead of both."}


[Assistant] Rationalize: 1/2.

[User] 2/2

[Assistant] {"error": 2, "info": "User did denominator rationalization wrong."}


[Assistant] Multiply: (2/x)(x/3).

[User] 2/3

[Assistant] {"error": 2, "info": "User multiplied numerators incorrectly."}


[Assistant] Graph y = - x ^ 2 + 2x + 3, find intercepts.

[User] y = 3,x = 1

[Assistant] {"error": 2, "info": "User mixed up intercept coordinates."}


[Assistant] Simplify: (x^2-9)/(x-3).

[User] x-3

[Assistant] {"error": 2, "info": "User canceled incorrectly leaving wrong sign."}


[Assistant] Solve: x ^ 2 - 5x + 6 = 0 by factoring.

[User] x = 2

[Assistant] {"error": 2, "info": "User only found one root instead of both."}


[Assistant] Find inverse of f *( x ) = x + 4.

[User] f ^ { - 1} ( x ) = x - 4

[Assistant] {"error": 2, "info": "User applied inverse incorrectly."}


[Assistant] Given recursive an = an - 1 + 2, a1 = 3, find a3.

[User] a3 = 5

[Assistant] {"error": 2, "info": "User applied recursion incorrectly."}


[Assistant] Compute mean of 2,4,6,8.

[User] mean = 10

[Assistant] {"error": 2, "info": "User summed incorrectly for mean."}


[Assistant] Evaluate g *( f *( x ) ) for f *( x ) = x + 2,g *( x ) = x ^ 2.

[User] g *( f *( x ) ) = ( x + 2 ) ^ 2

[Assistant] {"error": 2, "info": "User applied functions incorrectly."}


[Assistant] Given f *( x ) = 2x + 3, find f *( 2 ) .

[User] f *( 2 ) = 5

[Assistant] {"error": 2, "info": "User applied substitution incorrectly."}


[Assistant] Find 5th term of arithmetic sequence with a1 = 2,d = 3.

[User] a5 = 14

[Assistant] {"error": 2, "info": "User used wrong formula for term."}


[Assistant] Find correlation from scatter plot trend.

[User] positive

[Assistant] {"error": 2, "info": "User misread trend direction."}


[Assistant] Given f *( x ) = 2x + 3, find f *( 2 ) .

[User] f *( 2 ) = 5

[Assistant] {"error": 2, "info": "User applied substitution incorrectly."}


[Assistant] Write explicit formula for geometric sequence 2,6,18.

[User] an = 2 * 3 ^ ( n - 1 )

[Assistant] {"error": 2, "info": "User applied ratio incorrectly."}


[Assistant] Given recursive an = an - 1 + 2, a1 = 3, find a3.

[User] a3 = 5

[Assistant] {"error": 2, "info": "User applied recursion incorrectly."}


[Assistant] Write explicit formula for geometric sequence 2,6,18.

[User] an = 2 * 3 ^ ( n - 1 )

[Assistant] {"error": 2, "info": "User applied ratio incorrectly."}


[Assistant] Compose f *( x ) = x + 1 and g *( x ) = 2x.

[User] f *( g *( x ) ) = 2x + 1

[Assistant] {"error": 2, "info": "User reversed order."}


[Assistant] Find 5th term of arithmetic sequence with a1 = 2,d = 3.

[User] a5 = 14

[Assistant] {"error": 2, "info": "User used wrong formula for term."}


[Assistant] Compose f *( x ) = x + 1 and g *( x ) = 2x.

[User] f *( g *( x ) ) = 2x + 1

[Assistant] {"error": 2, "info": "User reversed order."}


[Assistant] Find inverse of f *( x ) = x + 4.

[User] f ^ { - 1} ( x ) = x - 4

[Assistant] {"error": 2, "info": "User applied inverse incorrectly."}


[Assistant] Translate: 'seven less than twice a number x'.

[User] 2x + 7

[Assistant] {"error": 2, "info": "Concept error: reversed order in subtraction phrase."}


[Assistant] Simplify: 6*(a + 2).

[User] 6a + 2

[Assistant] {"error": 2, "info": "Distributive property applied to first term only."}


[Assistant] Solve: 4x = 20.

[User] Subtract 4 from both sides to get x = 16

[Assistant] {"error": 2, "info": "Incorrect operation choice - should divide by 4."}


[Assistant] Combine like terms: 8m^2 + 3m^2.

[User] 11m

[Assistant] {"error": 2, "info": "Dropped exponent; misunderstanding like - term exponents."}


[Assistant] Write an expression for 'half the sum of x and 6'.

[User] x/2 + 6

[Assistant] {"error": 2, "info": "Did not group x and 6 before halving."}


[Assistant] Distribute: -3*(4 - p).

[User] -12 - p

[Assistant] {"error": 2, "info": "Sign error on distributed variable term."}


[Assistant] Solve: x - 5 = 12.

[User] Subtract 5 from both sides to get x = 17

[Assistant] {"error": 2, "info": "Used wrong inverse operation; increased difference instead."}


[Assistant] Translate: 'three less than a number b'.

[User] 3 - b

[Assistant] {"error": 2, "info": "Concept error: the phrase means b - 3, so the order was reversed."}


[Assistant] Translate: 'one-third of the quantity x plus 9'.

[User] (x + 9)/4

[Assistant] {"error": 2, "info": "Concept error: denominator should be 3, not 4 - misapplied fraction concept."}


[Assistant] Find the slope between (2, 5) and (6, 1).

[User] Slope = ( 2 - 6 ) / ( 5 - 1 ) = - 4 / 4 = - 1

[Assistant] {"error": 2, "info": "Mis - applied slope formula: used x difference over y difference."}


[Assistant] Write an equation in slope-intercept form for a line with slope -3 passing through (0, 4).

[User] y = - 3 + 4x

[Assistant] {"error": 2, "info": "Mis - applied slope - intercept form: swapped terms."}


[Assistant] Given y - 2 = 5 *( x + 3 ) , identify the slope.

[User] Slope = - 5

[Assistant] {"error": 2, "info": "Slope sign taken incorrectly from point - slope form."}


[Assistant] Convert y = 4x - 7 to standard form.

[User] 4x + y = 7

[Assistant] {"error": 2, "info": "Mis - applied conversion: sign on y incorrect; should be 4x - y = 7."}


[Assistant] Give the slope of a line parallel to x = 2.

[User] Slope 0

[Assistant] {"error": 2, "info": "Mis - applied concept: x = 2 is vertical with undefined slope."}


[Assistant] For y = 2x + 3, what is the y - intercept?

[User] Intercept is at x = 3

[Assistant] {"error": 2, "info": "Mis - identified y - intercept as x value."}


[Assistant] Write an equation of a horizontal line through (3, -2).

[User] x = 3

[Assistant] {"error": 2, "info": "Used vertical - line equation; mis - applied horizontal line concept."}


[Assistant] Find the slope of 6x + 2y = 8 by inspection.

[User] Slope = 6 / 2 = 3

[Assistant] {"error": 2, "info": "Mis - applied procedure; slope should be - 3."}


[Assistant] Solve -2x > 6. State your first algebraic step.

[User] Divide both sides by -2 to get x > -3.

[Assistant] {"error": 2, "info": "Mis - applied rule: the inequality should flip to x < - 3."}


[Assistant] Express 2 < = x < 7 using interval notation.

[User] (2, 7]

[Assistant] {"error": 2, "info": "Left endpoint should be a bracket because 2 is included."}


[Assistant] Is the compound statement x > 5 and x < 1 possible?

[User] Yes, just take numbers bigger than 5 or less than 1.

[Assistant] {"error": 2, "info": "Confused AND with OR - mis - applied logical connector."}


[Assistant] Graph x < = - 3 on a number line. What type of dot at - 3?

[User] Open dot

[Assistant] {"error": 2, "info": "Endpoint included ( < = ) requires a closed dot."}


[Assistant] Solve |x - 2| < 5. State one inequality you set up.

[User] x - 2 < 5

[Assistant] {"error": 2, "info": "Gave only the positive inequality; forgot the negative counterpart."}


[Assistant] Shade the solution area for y < -x + 2. Which side of the line is shaded?

[User] Above the line

[Assistant] {"error": 2, "info": "Mis - applied: y < requires shading below the boundary line."}


[Assistant] After subtracting 4 from both sides of x + 4 > 9, what inequality do you get?

[User] x + 4 > 13

[Assistant] {"error": 2, "info": "Subtraction mis - applied; should be x > 5."}


[Assistant] Convert x > = - 1 to interval notation.

[User] (-1, )

[Assistant] {"error": 2, "info": "Endpoint inclusive; should use [ - 1, ) ."}


[Assistant] Eliminate y from 2x + 3y = 7 and 4x + 3y = 1. Which operation should you use?

[User] Add the equations to cancel y

[Assistant] {"error": 2, "info": "Concept error: adding keeps 6y; subtraction is needed to eliminate y."}


[Assistant] Substitute y = 2x into x + y = 5 and write the new equation.

[User] x = 5 - 2x

[Assistant] {"error": 2, "info": "Mis - applied substitution; should produce x + 2x = 5 ( 3x = 5 ) ."}


[Assistant] Are y = 2x + 3 and 4x - 2y = 5 parallel?

[User] Yes, slopes 2 and -2 are equal

[Assistant] {"error": 2, "info": "Mis - identified slope of second line; both slopes are 2, not - 2."}


[Assistant] Graph y < -x + 2. Which side should you shade?

[User] Above the line

[Assistant] {"error": 2, "info": "Shading rule mis - applied; y < means shade below."}


[Assistant] Convert 3x + 6y = 12 to slope - intercept form before graphing.

[User] y = 3x + 2

[Assistant] {"error": 2, "info": "Isolated incorrectly; correct form is y = - 0.5x + 2."}


[Assistant] Slope of a line perpendicular to y = - 4x + 1?

[User] Slope 4

[Assistant] {"error": 2, "info": "Forgot negative reciprocal; should be 1 / 4."}


[Assistant] For x > = 0 and y > = 0, where is the feasible region located?

[User] Left of the y-axis

[Assistant] {"error": 2, "info": "Region is to the right of the y - axis ( first quadrant ) ."}


[Assistant] If two equations are multiples of each other, how many solutions exist?

[Assistant] {"error": 2, "info": "Multiples indicate infinitely many solutions, not none."}


[Assistant] Simplify: x^5 x^2.

[User] x^7

[Assistant] {"error": 2, "info": "Mis - applied quotient rule: exponents should subtract ( 5 - 2 = 3 ) , not add ( 5 + 2 = 7 ) ."}


[Assistant] Simplify: (x^2)^3.

[User] x^5

[Assistant] {"error": 2, "info": "Mis - applied power rule: exponents should multiply ( 2 * 3 = 6 ) , not add ( 2 + 3 = 5 ) ."}


[Assistant] Express x^(-2) as a positive exponent.

[User] -1/x^2

[Assistant] {"error": 2, "info": "Mis - applied negative - exponent rule: should be 1 / x ^ 2, not - 1 / x ^ 2."}


[Assistant] Calculate 2^3 2^2.

[User] 2 ^ 6 = 64

[Assistant] {"error": 2, "info": "Mis - applied product rule: exponents should add ( 3 + 2 = 5 ) , giving 2 ^ 5 = 32."}


[Assistant] Convert 5.6*10^3 to standard form.

[User] 5.6 * 10 ^ 2 = 560

[Assistant] {"error": 2, "info": "Mis - applied scientific notation: exponent should be 3, not 2."}


[Assistant] Write the first step in A = P ( 1 + 0.05 ) ^ t for a 5% growth model.

[User] A = P ( 1 + 5 ) ^ t

[Assistant] {"error": 2, "info": "Mis - applied growth model: rate 0.05 should be added, not 5."}


[Assistant] Write the first step in A = A_0 e ^ { - 0.02t} for 2% decay.

[User] A = A_0 e ^ {0.02t}

[Assistant] {"error": 2, "info": "Mis - applied decay model: exponent sign should be negative for decay."}


[Assistant] Expand (x + 2)*(x + 5).

[User] x + 7x + 7

[Assistant] {"error": 2, "info": "Concept error: need to multiply the constant terms, not add them."}


[Assistant] Factor x - 9.

[User] (x - 9)(x + 1)

[Assistant] {"error": 2, "info": "Mis - applied difference - of - squares pattern; correct is ( x - 3 ) ( x + 3 ) ."}


[Assistant] Factor 2x^2 + 8x.

[User] 2x*(x + 8)

[Assistant] {"error": 2, "info": "GCF mis - applied: factor should be 2x ( x + 4 ) ."}


[Assistant] Expand (x - 4).

[User] x - 8x + 8

[Assistant] {"error": 2, "info": "Forgot square of 4; should be + 16, not + 8."}


[Assistant] Factor x^2 + 6x + 8.

[User] (x + 3)(x + 3)

[Assistant] {"error": 2, "info": "Mis - matched factors; correct is ( x + 2 ) ( x + 4 ) ."}


[Assistant] Expand (x + 3)*(x - 3).

[User] x + 9

[Assistant] {"error": 2, "info": "Product should be x - 9; sign error on constant."}


[Assistant] Factor x^2 - 4x + 4.

[User] (x - 4)(x + 1)

[Assistant] {"error": 2, "info": "Mis - identified perfect - square factors; correct is ( x - 2 ) ."}


[Assistant] Factor 9x - 25.

[User] (3x - 5)(3x + 3)

[Assistant] {"error": 2, "info": "Second factor constant incorrect; should be ( 3x + 5 ) ."}


[Assistant] Multiply (2x - 1)*(x + 3).

[User] 2x + 4x - 1

[Assistant] {"error": 2, "info": "Middle term mis - calculated; should be + 5x."}


[Assistant] Find the vertex of y = x^2 + 6x + 5 using x = - b / ( 2a ) .

[User] x = - 6 / 2 = - 3

[Assistant] {"error": 2, "info": "Vertex formula applied but forgot to find y - coordinate."}


[Assistant] Solve x^2 - 4x - 5 = 0 by factoring. State the factors.

[User] (x - 5)(x + 1)

[Assistant] {"error": 2, "info": "Mis - applied factoring; second factor sign incorrect."}


[Assistant] Complete the square for x + 8x + 10. First step?

[User] Add 16 inside.

[Assistant] {"error": 2, "info": "Correctly found ( 8 / 2 ) but didn't balance equation."}


[Assistant] Use the quadratic formula on x^2 - 2x - 3 = 0. Write the formula with values.

[User] x = ( - 2 *( 2 - 413 ) ) / ( 21 )

[Assistant] {"error": 2, "info": "Substituted c as + 3 instead of - 3."}


[Assistant] Find the axis of symmetry for y = 2x^2 - 4x + 1.

[User] x = - 4 / ( 22 ) = - 1

[Assistant] {"error": 2, "info": "Used b as - 4; should be positive 4."}


[Assistant] Determine the discriminant of x^2 + 6x + 9.

[User] 6 - 419 = 0

[Assistant] {"error": 2, "info": "Correct formula but didn't simplify correctly."}


[Assistant] Solve x^2 - 9 = 0 using square roots.

[User] x = 9 = 3

[Assistant] {"error": 2, "info": "Forgot negative root; x = 3."}


[Assistant] Simplify 50. Find the prime factors.

[User] ( 252 ) = 252

[Assistant] {"error": 2, "info": "Mis - applied; 25 = 5, so 52."}


[Assistant] Solve x = 4. Square both sides.

[User] x = 16

[Assistant] {"error": 2, "info": "Correct squaring but didn't check for extraneous roots."}


[Assistant] Simplify (x).

[User] x

[Assistant] {"error": 2, "info": "Missed absolute value; should be |x|."}


[Assistant] Simplify: x^2 * x^3.

[User] x^6

[Assistant] {"error": 2, "info": "Wrong exponent addition; result should be x^5."}


[Assistant] Solve ( x + 1 ) = 3. First step?

[User] x + 1 = 9

[Assistant] {"error": 2, "info": "Correct squaring but didn't specify isolating radical."}


[Assistant] Simplify 72.

[User] ( 362 ) = 62

[Assistant] {"error": 2, "info": "Correct factorization but missed checking for further simplification."}


[Assistant] Add 8 + 18. Simplify first.

[User] 22 + 32 = 52

[Assistant] {"error": 2, "info": "Correct simplification but didn't combine like terms fully."}


[Assistant] Simplify (x - 9)/(x + 3). Factor first.

[User] ( x - 3 )*( x + 3 ) / ( x + 3 ) = x - 3

[Assistant] {"error": 2, "info": "Correct factoring but didn't check domain."}


[Assistant] Multiply (x/2)*(4/x). Simplify.

[User] 4x / 2x = 2

[Assistant] {"error": 2, "info": "Correct multiplication but didn't simplify fully."}


[Assistant] Solve 1 / x = 2. Multiply by x.

[User] 1 = 2x

[Assistant] {"error": 2, "info": "Correct step but didn't check for x! = 0."}


[Assistant] Find the vertical asymptote of y = 1 / ( x - 5 ) .

[User] x = - 5

[Assistant] {"error": 2, "info": "Mis - applied; asymptote at x = 5."}


[Assistant] Add (1/x) + (2/x). Common denominator?

[User] x

[Assistant] {"error": 2, "info": "Wrong denominator; should be x."}


[Assistant] Simplify (x - 1)/(x + 1).

[User] x - 1

[Assistant] {"error": 2, "info": "Correct simplification but ignored x! = - 1."}


[Assistant] Divide (x/3) / (x/6). Rewrite as multiplication.

[User] (x/3)*(x/6)

[Assistant] {"error": 2, "info": "Incorrect reciprocal; should be ( x / 3 ) ( 6 / x ) ."}


[Assistant] Simplify 2^3 2^2.

[User] 2^6

[Assistant] {"error": 2, "info": "Misapplied exponent rule; should add exponents: 2 ^ 5."}


[Assistant] Solve 2 ^ x = 8. Rewrite 8 as a power of 2.

[User] 8 = 2 ^ 2, so x = 2

[Assistant] {"error": 2, "info": "Misapplied; 8 = 2 ^ 3, so x = 3."}


[Assistant] Evaluate y = 3 ^ ( 2x ) for x = 1.

[User] 3 ^ 2 = 9

[Assistant] {"error": 2, "info": "Ignored exponent 2x; should be 3 ^ 2 = 9."}


[Assistant] Simplify (4^2)^3.

[User] 4^5

[Assistant] {"error": 2, "info": "Misapplied power rule; should be 4 ^ 6."}


[Assistant] Find the horizontal asymptote of y = 5 ^ x - 2.

[User] y = - 2

[Assistant] {"error": 2, "info": "Correct but didn't specify exponential term approaches 0."}


[Assistant] Rewrite 1/3^x with a positive exponent.

[User] 3^x

[Assistant] {"error": 2, "info": "Misapplied; should be 3 ^ - x."}


[Assistant] Is y = 0.5 ^ x growth or decay?

[User] Growth

[Assistant] {"error": 2, "info": "Misapplied; base < 1 means decay."}


[Assistant] Solve 5 ^ ( x + 1 ) = 25. Rewrite 25 as a power.

[User] 25 = 5 ^ 3, so x + 1 = 3

[Assistant] {"error": 2, "info": "Wrong power; 25 = 5 ^ 2."}


[Assistant] Find the mean of 2, 4, 6, 8.

[User] ( 2 + 4 + 6 + 8 ) / 3 = 6.67

[Assistant] {"error": 2, "info": "Misapplied mean; divided by 3 instead of 4."}


[Assistant] What is P ( A or B ) if P ( A ) = 0.3, P ( B ) = 0.4, and P ( A and B ) = 0.1?

[User] 0.3 + 0.4 = 0.7

[Assistant] {"error": 2, "info": "Misapplied; forgot to subtract P ( A and B ) , so 0.6."}


[Assistant] Find the median of 1, 3, 5, 7, 9.

[User] 1 + 3 + 5 + 7 + 9 = 25 / 5 = 5

[Assistant] {"error": 2, "info": "Used mean instead of median; median is 5."}


[Assistant] Calculate P(3) for rolling a die.

[User] 3 / 6 = 1 / 2

[Assistant] {"error": 2, "info": "Misapplied; probability of one outcome is 1 / 6."}


[Assistant] Find Q1 for 2, 4, 6, 8, 10.

[User] 2

[Assistant] {"error": 2, "info": "Correct but didn't specify lower half median."}


[Assistant] Compute 5P2.

[User] 5 * 4 = 20

[Assistant] {"error": 2, "info": "Correct but didn't use permutation formula explicitly."}


[Assistant] Are events A and B independent if P ( A ) = 0.5, P ( B ) = 0.4, P ( A and B ) = 0.2?

[User] No, 0.5 * 0.4! = 0.2

[Assistant] {"error": 2, "info": "Correct but didn't explain independence test."}


[Assistant] Find the range of 3, 5, 7, 9.

[User] 9 - 3 = 6

[Assistant] {"error": 2, "info": "Correct but didn't specify max - min."}


[Assistant] Find the probability of drawing a spade from a deck of 52 cards.

[User] 13 / 52 + 13 / 52 = 1 / 2

[Assistant] {"error": 2, "info": "Misapplied probability; only 13 spades, so 13 / 52 = 1 / 4."}


[Assistant] Solve ( x + 1 ) / ( x - 1 ) = 2. Multiply by ( x - 1 ) .

[User] x + 1 = 2x - 1

[Assistant] {"error": 2, "info": "Correct algebraic step but didn't check x \u2260 1."}


[Assistant] What is solution to 3 < = x - 2?

[User] x > = 5

[Assistant] {"error": 3, "info": "User added incorrectly."}


[Assistant] What is the result of 0*x?

[User] 0

[Assistant] {"error": 3, "info": "User did not grasp zero property."}


[Assistant] What is solution to 3 < = x - 2?

[User] x > = 5

[Assistant] {"error": 3, "info": "User added incorrectly."}


[Assistant] Solve: |2x + 1| > = 3.

[User] 2x + 1 > = 3

[Assistant] {"error": 3, "info": "User didn't include both cases."}


[Assistant] Graph line y = 5x + 1, identify intercept.

[User] x = 1

[Assistant] {"error": 3, "info": "User confused intercept types."}


[Assistant] Simplify: 2y - y.

[User] y - 2

[Assistant] {"error": 3, "info": "User lacks understanding of subtraction of like terms."}


[Assistant] What is the result of 0*x?

[User] 0

[Assistant] {"error": 3, "info": "User did not grasp zero property."}


[Assistant] Solve: x/2>3.

[User] x>6

[Assistant] {"error": 3, "info": "User misunderstood division in inequalities."}


[Assistant] Find slope from (2,3) and (4,7).

[User] 4

[Assistant] {"error": 3, "info": "User lacks understanding of slope formula."}


[Assistant] Solve: 5x + 2 = 12.

[User] x = 2

[Assistant] {"error": 3, "info": "User did not understand subtraction step."}


[Assistant] Solve: -x>2.

[User] x<-2

[Assistant] {"error": 3, "info": "User lacks understanding of sign flip."}


[Assistant] Solve: 5x + 2 = 12.

[User] x = 2

[Assistant] {"error": 3, "info": "User did not understand subtraction step."}


[Assistant] Find slope from (2,3) and (4,7).

[User] 4

[Assistant] {"error": 3, "info": "User lacks understanding of slope formula."}


[Assistant] Solve: -x>2.

[User] x<-2

[Assistant] {"error": 3, "info": "User lacks understanding of sign flip."}


[Assistant] Write equation from slope 2 and x-intercept 3.

[User] x = 2y + 3

[Assistant] {"error": 3, "info": "User used the formula for the y-intercept."}


[Assistant] Simplify: x + x + x.

[User] 3

[Assistant] {"error": 3, "info": "User misunderstood combining like terms."}


[Assistant] Solve: x - 5 = 3.

[User] x = 8

[Assistant] {"error": 3, "info": "User added instead of subtracting."}


[Assistant] Write equation from slope 2 and intercept 3.

[User] x = 2y + 3

[Assistant] {"error": 3, "info": "User misused formula."}


[Assistant] Simplify: x + x + x.

[User] 3

[Assistant] {"error": 3, "info": "User misunderstood combining like terms."}


[Assistant] Solve: |2x + 1| > = 3.

[User] 2x + 1 > = 3

[Assistant] {"error": 3, "info": "User didn't include both cases."}


[Assistant] Simplify: 5^-1.

[User] -5

[Assistant] {"error": 3, "info": "User misunderstood negative exponent."}


[Assistant] Factor: x^2+5x+6.

[User] x^2+6x+5

[Assistant] {"error": 3, "info": "Did not simplify at all."}


[Assistant] Factor: x^2-9.

[User] x^2-3x+3x-9

[Assistant] {"error": 3, "info": "Did not simplify at all."}


[Assistant] Simplify: (2^3)^2.

[User] 2^6

[Assistant] {"error": 3, "info": "User didn't understand power of power."}


[Assistant] Factor: x^2+2x+1.

[User] x*(x+2+1)

[Assistant] {"error": 3, "info": "User doesn't understand factoring."}


[Assistant] Find intersection of lines parallel.

[Assistant] {"error": 3, "info": "User confused infinite solutions."}


[Assistant] Simplify: (2^3)^2.

[User] 2^6

[Assistant] {"error": 3, "info": "User didn't understand power of power."}


[Assistant] Graph: x + y = 3 and x + y = 4.

[User] Intersection at (1,2)

[Assistant] {"error": 3, "info": "User doesn't understand no - solution case."}


[Assistant] Simplify: (x+1)*(x-1).

[User] x^2+1

[Assistant] {"error": 3, "info": "User lacks understanding of FOIL."}


[Assistant] Graph: x + y = 3 and x + y = 4.

[User] Intersection at (1,2)

[Assistant] {"error": 3, "info": "User doesn't understand no - solution case."}


[Assistant] Solve: x - y = 2, 2x - 2y = 5.

[User] x = 2.5,y = 0.5

[Assistant] {"error": 3, "info": "User lacks understanding of solution consistency."}


[Assistant] Write 3e4 in standard form.

[User] 3000

[Assistant] {"error": 3, "info": "User misread scientific notation."}


[Assistant] Solve: x - 3y = 0 and 3x - y = 0.

[User] x = 0,y = 0

[Assistant] {"error": 3, "info": "User lacks understanding of dependent system."}


[Assistant] Simplify: 4^1.

[User] 1

[Assistant] {"error": 3, "info": "User thought exponent 1 gives 4 ^ 0."}


[Assistant] Factor by grouping: x^3-3x^2+ x-3.

[User] x^2*(x-3)+x-3

[Assistant] {"error": 3, "info": "User confused grouping method."}


[Assistant] Factor: x^2+2x+1.

[User] x*(x+2+1)

[Assistant] {"error": 3, "info": "User doesn't understand factoring."}


[Assistant] Factor: x^2-4x+4.

[User] x^2-2x

[Assistant] {"error": 3, "info": "User incomplete factoring."}


[Assistant] Simplify: x^0.

[User] 0

[Assistant] {"error": 3, "info": "User lacks understanding that x ^ 0 = 1."}


[Assistant] Solve by elimination: x + 2y = 5 and 2x + 4y = 10.

[User] x = 5,y = 0

[Assistant] {"error": 3, "info": "User didn't recognize infinite solutions."}


[Assistant] Simplify: (x+1)(x-1).

[User] x^2+1

[Assistant] {"error": 3, "info": "User lacks understanding of FOIL."}


[Assistant] Solve by elimination: x + 2y = 5 and 2x + 4y = 10.

[User] x = 5,y = 0

[Assistant] {"error": 3, "info": "User didn't recognize infinite solutions."}


[Assistant] Factor GCF: 8x+12.

[User] 4*(2x+3)

[Assistant] {"error": 3, "info": "User doesn't understand GCF."}


[Assistant] Factor: x^2-4x+4.

[User] x^2-2x

[Assistant] {"error": 3, "info": "User incomplete factoring."}


[Assistant] Simplify: (9x^2).

[User] 3x^2

[Assistant] {"error": 3, "info": "User lacks understanding of absolute value."}


[Assistant] Simplify: (x^2-4)/(x-2).

[User] x+2

[Assistant] {"error": 3, "info": "User lacks understanding of factoring differences."}


[Assistant] Simplify: (x^2-4)/(x-2).

[User] x+2

[Assistant] {"error": 3, "info": "User lacks understanding of factoring differences."}


[Assistant] Add: 2/3 + 1/6.

[User] 1/2

[Assistant] {"error": 3, "info": "User lacks understanding of common denominator."}


[Assistant] Use formula on x ^ 2 + x + 1 = 0.

[User] x = - 1

[Assistant] {"error": 3, "info": "User doesn't understand imaginary roots."}


[Assistant] Add: 2/3 + 1/6.

[User] 1/2

[Assistant] {"error": 3, "info": "User lacks understanding of common denominator."}


[Assistant] Rationalize: 5/(x).

[User] 5x/x

[Assistant] {"error": 3, "info": "User missing denominator term."}


[Assistant] Solve: ( x ) + 2 = 5.

[User] x = 3

[Assistant] {"error": 3, "info": "User lacks understanding of isolating radical."}


[Assistant] Multiply: (x/2)(2/x).

[User] 1

[Assistant] {"error": 3, "info": "User lacks understanding of reciprocals."}


[Assistant] Find vertex of y = ( x - 3 ) ^ 2 + 2.

[User] 3,2

[Assistant] {"error": 3, "info": "User lacks understanding of vertex form."}


[Assistant] Find vertex of y = ( x - 3 ) ^ 2 + 2.

[User] 3,2

[Assistant] {"error": 3, "info": "User lacks understanding of vertex form."}


[Assistant] Solve: x = - 3.

[User] x = 9

[Assistant] {"error": 3, "info": "User lacks understanding of no negative root."}


[Assistant] Graph y = x ^ 2, identify axis of symmetry.

[User] x = 0

[Assistant] {"error": 3, "info": "User confused axis of symmetry."}


[Assistant] Simplify: (x+1)/(x+1).

[User] x

[Assistant] {"error": 3, "info": "User lacks understanding of division."}


[Assistant] Simplify: (9x^2).

[User] 3x^2

[Assistant] {"error": 3, "info": "User lacks understanding of absolute value."}


[Assistant] Multiply: (x/2)(2/x).

[User] 1

[Assistant] {"error": 3, "info": "User lacks understanding of reciprocals."}


[Assistant] Solve: x ^ 2 = 9.

[User] x = 3

[Assistant] {"error": 3, "info": "User didn't recognize negative root."}


[Assistant] Use formula on x ^ 2 + x + 1 = 0.

[User] x = - 1

[Assistant] {"error": 3, "info": "User doesn't understand imaginary roots."}


[Assistant] Solve: x = - 3.

[User] x = 9

[Assistant] {"error": 3, "info": "User lacks understanding of no negative root."}


[Assistant] Factor: x^2 + 2x + 1.

[User] x^2 + 1

[Assistant] {"error": 3, "info": "User lacks understanding of perfect square trinomial."}


[Assistant] Simplify: (x^2)^(1/2).

[User] x

[Assistant] {"error": 3, "info": "User doesn't grasp principal root."}


[Assistant] Solve: x ^ 2 = 9.

[User] x = 3

[Assistant] {"error": 3, "info": "User didn't recognize negative root."}


[Assistant] Domain of sqrt(x).

[User] all real

[Assistant] {"error": 3, "info": "User lacks domain concept."}


[Assistant] Find 4th term of sequence 1,1,1,1.

[User] 4

[Assistant] {"error": 3, "info": "User doesn't understand constant sequence rule."}


[Assistant] Inverse of f *( x ) = 3x.

[User] 1/3x

[Assistant] {"error": 3, "info": "User lacks understanding of inverse."}


[Assistant] Inverse of f *( x ) = 3x.

[User] 1/3x

[Assistant] {"error": 3, "info": "User lacks understanding of inverse."}


[Assistant] Interpret correlation r = 0.

[User] no correlation

[Assistant] {"error": 3, "info": "User misinterpreted zero correlation."}


[Assistant] Interpret correlation r = 0.

[User] no correlation

[Assistant] {"error": 3, "info": "User misinterpreted zero correlation."}


[Assistant] Find 4th term of sequence 1,1,1,1.

[User] 4

[Assistant] {"error": 3, "info": "User doesn't understand constant sequence rule."}


[Assistant] Find term of geometric a1 = 3,r = 2,n = 0.

[User] a0 = 1.5

[Assistant] {"error": 3, "info": "User lacks understanding of index starting."}


[Assistant] Find f *( 3 ) for f *( x ) = x ^ 2.

[User] 9

[Assistant] {"error": 3, "info": "User lacks understanding of function evaluation."}


[Assistant] Write recursive for 5,5,5.

[User] an = an - 1 * 1

[Assistant] {"error": 3, "info": "User lacks understanding of recursive pattern."}


[Assistant] Calculate mean of 3,5,7.

[User] mean = 4

[Assistant] {"error": 3, "info": "User lacks understanding of mean."}


[Assistant] Calculate mean of 3,5,7.

[User] mean = 4

[Assistant] {"error": 3, "info": "User lacks understanding of mean."}


[Assistant] Given f *( x ) = x ^ 2, find f *( - 2 ) .

[User] -4

[Assistant] {"error": 3, "info": "User lacks understanding of square function."}


[Assistant] Compute ( fg )*( x ) for f *( x ) = x + 2,g *( x ) = x - 2.

[User] 0

[Assistant] {"error": 3, "info": "User doesn't understand composition."}


[Assistant] Identify the coefficient in 7x.

[User] x

[Assistant] {"error": 3, "info": "Coefficient confused with variable."}


[Assistant] Simplify: 2*(3 + n).

[User] 2 + 3 + n

[Assistant] {"error": 3, "info": "Misunderstood distribution - added factor instead of multiplying."}


[Assistant] Translate: 'a number divided by 4'.

[User] 4/n

[Assistant] {"error": 3, "info": "Inverted fraction shows misunderstanding of division phrase."}


[Assistant] Solve: 2 *( x + 5 ) = 0.

[User] Multiply 0 by 2 to get x + 5 = 0

[Assistant] {"error": 3, "info": "Does not understand equality manipulation."}


[Assistant] Explain what an equation is.

[User] It's just a math sentence with numbers and maybe letters but I'm not sure.

[Assistant] {"error": 3, "info": "Definition shows incomplete understanding."}


[Assistant] Simplify: 4x / 0.

[User] 0

[Assistant] {"error": 3, "info": "Lack of understanding: division by zero is undefined, not 0."}


[Assistant] Compute the slope between (1, 3) and (4, 9).

[User] Slope = ( 14 ) - ( 39 )

[Assistant] {"error": 3, "info": "Incorrect formula for slope - multiplied coordinates instead of subtracting."}


[Assistant] Find the slope of the line through (5, 7) and (5, 2).

[User] Slope = 0 / 0 so 0

[Assistant] {"error": 3, "info": "Misunderstood vertical line slope; division by zero undefined."}


[Assistant] State the slope-intercept form of a line.

[User] x = my + b

[Assistant] {"error": 3, "info": "Incorrect formula structure for slope - intercept."}


[Assistant] Write standard form for y = 2x - 5.

[User] 2y + x = 5

[Assistant] {"error": 3, "info": "Mis - formed standard equation; coefficients misplaced."}


[Assistant] If a line has slope 4, what is the slope of a perpendicular line?

[User] 1/4

[Assistant] {"error": 3, "info": "Left out negative sign; perpendicular slope should be - 1 / 4."}


[Assistant] Interpret slope as rise over run.

[User] Run divided by rise

[Assistant] {"error": 3, "info": "Reversed concept; lacks correct understanding."}


[Assistant] Identify the slope in y = 9.

[User] Slope is 9

[Assistant] {"error": 3, "info": "Misconception: y = 9 is horizontal so slope is 0."}


[Assistant] Find slope between (0, 0) and (8, 2).

[User] Slope = ( 0 + 8 ) / ( 0 + 2 ) = 8 / 2 = 4

[Assistant] {"error": 3, "info": "Used sums instead of differences - wrong formula."}


[Assistant] Can the absolute value of a number ever be negative?

[User] Yes, if the number is negative enough.

[Assistant] {"error": 3, "info": "Absolute value is never negative - concept misunderstanding."}


[Assistant] Is there a number that is simultaneously greater than 5 and less than 1?

[User] Sure, maybe 3.

[Assistant] {"error": 3, "info": "Shows lack of logical understanding of AND conditions."}


[Assistant] Split |x| > 4 into two inequalities.

[User] -x > 4

[Assistant] {"error": 3, "info": "Improper split; should be x < - 4 OR x > 4."}


[Assistant] Explain what the word "and" means in a compound inequality.

[User] It means you take either one of the conditions.

[Assistant] {"error": 3, "info": "Confused AND with union / OR."}


[Assistant] First step to solve - 3x > = 6?

[User] Add 3 to both sides

[Assistant] {"error": 3, "info": "Does not understand appropriate inverse operation for - 3x."}


[Assistant] Show interval notation for "all numbers between 3 and 5 inclusive."

[User] (3,5)

[Assistant] {"error": 3, "info": "Left out brackets for inclusive endpoints."}


[Assistant] When adding 2 to both sides of x < 7, should the inequality symbol flip?

[User] Yes, because we changed both sides.

[Assistant] {"error": 3, "info": "Symbol only flips when multiplying / dividing by a negative - not when adding."}


[Assistant] Why do we test every corner point for P = 3x + 5y?

[User] Because the maximum is always in the middle

[Assistant] {"error": 3, "info": "Maximum / minimum occur at vertices, not interior."}


[Assistant] Multiply 3x - 2y = 7 so its coefficients match 6x - 4y = 11.

[User] Multiply by 3

[Assistant] {"error": 3, "info": "Incorrect scaling; 2 matches coefficients, but RHS would be 14, not 11."}


[Assistant] What does a single intersection point mean for two constraints?

[User] That the system has no solution

[Assistant] {"error": 3, "info": "Single intersection gives one unique solution."}


[Assistant] If substitution leads to 0 = 7, what does that indicate?

[User] Infinite solutions

[Assistant] {"error": 3, "info": "0 = 7 is false no solution."}


[Assistant] Why flip an inequality when multiplying by -1?

[User] Because negatives are always smaller numbers

[Assistant] {"error": 3, "info": "Reason shows conceptual gap about order reversal."}


[Assistant] Can an unbounded feasible region still have a maximum?

[User] No, unbounded means no maximum ever

[Assistant] {"error": 3, "info": "Some unbounded regions do have a maximum depending on objective direction."}


[Assistant] Explain why 2 parallel constraint lines might still form a bounded region.

[User] They cross later

[Assistant] {"error": 3, "info": "Parallel lines never cross; statement shows misunderstanding."}


[Assistant] What is 5^0?

[User] 0

[Assistant] {"error": 3, "info": "Mis-applied zero-exponent rule: any nonzero ^ 0 equals 1, not 0."}


[Assistant] Simplify: x^a x^b.

[User] x^{ab}

[Assistant] {"error": 3, "info": "Fundamental misunderstanding: exponents should add, not multiply."}


[Assistant] Simplify: x^m / x^n.

[User] x^{m+n}

[Assistant] {"error": 3, "info": "Misunderstood quotient rule: exponents subtract, not add."}


[Assistant] Simplify: (xy)^2.

[User] x^2y

[Assistant] {"error": 3, "info": "Incorrect power distribution: should be x ^ 2y ^ 2."}


[Assistant] Simplify: (x/y)^3.

[User] x^3/y

[Assistant] {"error": 3, "info": "Misunderstood power of quotient: denominator should be y ^ 3."}


[Assistant] Express x^(-1) as a fraction.

[User] -x

[Assistant] {"error": 3, "info": "Misconception: negative exponent yields a negative, not reciprocal."}


[Assistant] What is 0^0?

[User] 0

[Assistant] {"error": 3, "info": "Misunderstanding: 0 ^ 0 is undefined ( or indeterminate ) , not 0."}


[Assistant] Convert 3.2*10^{-4} to standard form.

[User] 3.2*10^4

[Assistant] {"error": 3, "info": "Misplaced negative: exponent should be - 4, not positive."}


[Assistant] Explain continuous growth vs discrete growth formulas.

[User] They're the same formula.

[Assistant] {"error": 3, "info": "Lack of understanding: continuous ( e ^ {kt} ) differs from discrete ( ( 1 + r ) ^ t ) ."}


[Assistant] Simplify: (2x)^3.

[User] 2x^3

[Assistant] {"error": 3, "info": "Misunderstood exponent distribution: should be 8x ^ 3."}


[Assistant] Split A = P ( 1 + r ) ^ t for decay by writing r negative.

[User] A = P ( 1 - r ) ^ t

[Assistant] {"error": 3, "info": "Misapplied decay concept: r should be specified negative, not subtracted from 1 generically."}


[Assistant] Describe the factors of x - 16.

[User] x and -16

[Assistant] {"error": 3, "info": "Confusion between terms and binomial factors; should state ( x - 4 ) ( x + 4 ) ."}


[Assistant] Simplify (2x).

[User] 2x

[Assistant] {"error": 3, "info": "Misunderstood square: coefficient also squares ( 4x ) ."}


[Assistant] Expand (x + y)(x + y).

[User] x + y

[Assistant] {"error": 3, "info": "Missing 2xy term; misunderstanding FOIL."}


[Assistant] Explain why x + 4 cannot factor.

[User] Because the coefficient is too small.

[Assistant] {"error": 3, "info": "Shows misconception of irreducibility; issue is sum of squares over reals."}


[Assistant] What does it mean to 'square' a binomial?

[User] Just square each term.

[Assistant] {"error": 3, "info": "Misunderstanding: must include the product term, not individual squaring only."}


[Assistant] Factor 4x - 9y.

[User] (2x - 3y)(2x - 3y)

[Assistant] {"error": 3, "info": "Forgot opposite sign in second factor; should be ( 2x - 3y ) ( 2x + 3y ) ."}


[Assistant] Solve x^2 + 2x + 1 = 0 by factoring.

[User] (x + 1)(x + 2)

[Assistant] {"error": 3, "info": "Incorrect factors; should be ( x + 1 ) ."}


[Assistant] Find the vertex of y = x^2 + 4x.

[User] Complete the square to x + 4x + 4 = ( x + 2 )

[Assistant] {"error": 3, "info": "Misunderstood; didn't adjust constant for vertex form."}


[Assistant] What is the discriminant of x^2 - 5x + 6?

[User] - 5 - 6 = 19

[Assistant] {"error": 3, "info": "Wrong formula; should be b - 4ac."}


[Assistant] Solve x - 6x + 8 = 0 by completing the square.

[User] Add 9 to both sides

[Assistant] {"error": 3, "info": "Misunderstood; adds 9 but ignores equation balance."}


[Assistant] Find x - intercepts of y = x - 4x.

[User] Set x = 0, get y = 0

[Assistant] {"error": 3, "info": "Confused y - intercept with x - intercept."}


[Assistant] What does a = - 2 mean for y = - 2x + x - 1?

[User] The parabola is horizontal.

[Assistant] {"error": 3, "info": "Misconception; negative a means downward opening."}


[Assistant] Solve x ^ 2 + 1 = 0 using square roots.

[User] x = 1

[Assistant] {"error": 3, "info": "Misunderstood; x^2 + 1 = 0 has no real roots."}


[Assistant] Solve x ^ 2 - 2 = 0. Isolate the radical.

[User] x = 0

[Assistant] {"error": 3, "info": "Incorrect isolation; solutions are x = \u00b1\u221a2."}


[Assistant] Rationalize 5/5.

[User] 5 / 5 = 1

[Assistant] {"error": 3, "info": "Misunderstood rationalizing; should multiply by 5."}


[Assistant] Simplify: x^5 / x^2.

[User] x^7

[Assistant] {"error": 3, "info": "Wrong exponent subtraction; should be x^3."}


[Assistant] Simplify (16x).

[User] 16x

[Assistant] {"error": 3, "info": "Did not simplify properly, it should be 2^4 * x."}


[Assistant] Solve x = - 2. Cube both sides.

[User] x = - 2 = - 6

[Assistant] {"error": 3, "info": "Misunderstood; (-2)^3 = - 8."}


[Assistant] What does x equal?

[User] x

[Assistant] {"error": 3, "info": "Misconception; x = |x|."}


[Assistant] Add 3 + 3.

[User] 6

[Assistant] {"error": 3, "info": "Misunderstood combining; should be 23."}


[Assistant] Solve 2 / x = 4. Multiply by x.

[User] 2 = 4x

[Assistant] {"error": 3, "info": "Misunderstood; should be 2 = 4x."}


[Assistant] Find the domain of y = 1 / ( x - 2 ) .

[User] All numbers

[Assistant] {"error": 3, "info": "Misconception; x! = 2."}


[Assistant] Add (1/(x + 1)) + (1/(x - 1)). Common denominator?

[User] x - 1

[Assistant] {"error": 3, "info": "Incorrect; should be ( x + 1 ) ( x - 1 ) ."}


[Assistant] Simplify (x/2)/(x/4).

[User] x/2

[Assistant] {"error": 3, "info": "Misunderstood division; should be 2."}


[Assistant] What is the horizontal asymptote of y = ( 2x + 1 ) / ( x - 3 ) ?

[User] y = 3

[Assistant] {"error": 3, "info": "Misconception; compare degrees, y = 2."}


[Assistant] Simplify (x - 16)/(x - 4).

[User] x - 4

[Assistant] {"error": 3, "info": "Incorrect cancellation; should be x + 4."}


[Assistant] Simplify 2^-3.

[User] - 2 ^ 3 = - 8

[Assistant] {"error": 3, "info": "Misunderstood; negative exponent means 1 / 2 ^ 3 = 1 / 8."}


[Assistant] Does y = 2 ^ x pass through ( 0, 0 ) ?

[User] Yes

[Assistant] {"error": 3, "info": "Misconception; when x = 0, y = 2 ^ 0 = 1."}


[Assistant] Solve 3 ^ x = 9. Set bases equal.

[User] x = 9

[Assistant] {"error": 3, "info": "Misunderstood; 9 = 3 ^ 2, so x = 2."}


[Assistant] What is the y - intercept of y = 4 ^ x + 1?

[User] y = 0

[Assistant] {"error": 3, "info": "Misconception; at x = 0, y = 4 ^ 0 + 1 = 2."}


[Assistant] Simplify (x^2)^3 / x^4.

[User] x^2

[Assistant] {"error": 3, "info": "Misunderstood; ( x ^ 6 ) / x ^ 4 = x ^ 2, but incorrect steps."}


[Assistant] Is y = ( 1 / 2 ) ^ x increasing or decreasing?

[User] Increasing

[Assistant] {"error": 3, "info": "Misconception; base < 1 means decreasing."}


[Assistant] Solve 2 ^ ( 2x ) = 4. Rewrite 4.

[User] 4 = 2 ^ 1, so 2x = 1

[Assistant] {"error": 3, "info": "Misunderstood; 4 = 2 ^ 2, so 2x = 2."}


[Assistant] What does a > 1 mean for y = a ^ x?

[User] The graph is a line.

[Assistant] {"error": 3, "info": "Misconception; a > 1 means exponential growth."}


[Assistant] Find the mean of 1, 2, 3, 4, 5.

[User] 1 + 2 + 3 + 4 + 5 = 15

[Assistant] {"error": 3, "info": "Misunderstood; summed but didn't divide by 5."}


[Assistant] What is the probability of rolling an even number on a die?

[User] 1 / 2 + 1 / 4 + 1 / 6 = 11 / 12

[Assistant] {"error": 3, "info": "Misconception; should be 3 / 6 = 1 / 2."}


[Assistant] Find the median of 2, 4, 6, 8.

[User] 2 + 8 = 10 / 2 = 5

[Assistant] {"error": 3, "info": "Misunderstood; median is ( 4 + 6 ) / 2 = 5."}


[Assistant] What is the IQR of 1, 3, 5, 7, 9?

[User] 9 - 1 = 8

[Assistant] {"error": 3, "info": "Used range instead of Q3 - Q1 = 7 - 3 = 4."}


[Assistant] Calculate 4C2.

[User] 4 + 2 = 6

[Assistant] {"error": 3, "info": "Misunderstood; should use combination formula: 6."}


[Assistant] If P ( A ) = 0.6 and P ( B|A ) = 0.5, find P ( A and B ) .

[User] 0.6 + 0.5 = 1.1

[Assistant] {"error": 3, "info": "Misconception; P ( A and B ) = 0.6 * 0.5 = 0.3."}


[Assistant] What is the standard deviation's purpose?

[User] It's the average.

[Assistant] {"error": 3, "info": "Misconception; measures spread, not mean."}


[Assistant] Are events with P ( A and B ) = 0 mutually exclusive?

[User] No

[Assistant] {"error": 3, "info": "Misunderstood; P ( A and B ) = 0 means mutually exclusive."}


[Assistant] Find the mode of 2, 3, 3, 4, 5.

[User] ( 2 + 3 + 3 + 4 + 5 ) / 5 = 3.4

[Assistant] {"error": 3, "info": "Misunderstood; used mean instead of mode, which is 3."}


[Assistant] Solve: 3x-2<7.

[User] x<3

[Assistant] {"error": 4, "info": "Arithmetic mistake isolating x."}


[Assistant] Solve: x+5>8.

[User] x>2

[Assistant] {"error": 4, "info": "Calculation error: 8 - 5 = 2 instead of 3."}


[Assistant] Solve: 5 < = x + 1.

[User] x < = 4

[Assistant] {"error": 4, "info": "Calculation mistake direction."}


[Assistant] Find slope of line through (1,4),(2,8).

[User] 2

[Assistant] {"error": 4, "info": "Calculation mistake in rise / run."}


[Assistant] Solve: 4x = 20.

[User] x = 6

[Assistant] {"error": 4, "info": "Calculation error dividing 20 by 4."}


[Assistant] Solve: - 2x > = 4.

[User] x > = - 2

[Assistant] {"error": 4, "info": "Sign error flipping inequality."}


[Assistant] Solve: 4x = 20.

[User] x = 6

[Assistant] {"error": 4, "info": "Calculation error dividing 20 by 4."}


[Assistant] Combine: 5 + 3.

[User] 7

[Assistant] {"error": 4, "info": "User added incorrectly."}


[Assistant] Simplify: 7x - 2x.

[User] 5

[Assistant] {"error": 4, "info": "User forgot to keep variable."}


[Assistant] Convert 4x - 2y = 8 to slope - intercept.

[User] y = 4x - 8

[Assistant] {"error": 4, "info": "Calculation mistake dividing by - 2."}


[Assistant] Solve for y: 2x + 3y = 6.

[User] y = 2x + 2

[Assistant] {"error": 4, "info": "Arithmetic mistake in isolation."}


[Assistant] Solve: 2x + 3 = 11.

[User] x = 7

[Assistant] {"error": 4, "info": "Calculation mistake in subtracting 3 from 11."}


[Assistant] Graph y = 3x - 5, what is y - intercept?

[User] -3

[Assistant] {"error": 4, "info": "Sign error identifying intercept."}


[Assistant] Solve: 2x + 3 = 11.

[User] x = 7

[Assistant] {"error": 4, "info": "Calculation mistake in subtracting 3 from 11."}


[Assistant] Find slope of line through (1,4),(2,8).

[User] 2

[Assistant] {"error": 4, "info": "Calculation mistake in rise / run."}


[Assistant] Graph y = 3x - 5, what is y - intercept?

[User] -3

[Assistant] {"error": 4, "info": "Sign error identifying intercept."}


[Assistant] Simplify: |x| + 3 = 5.

[User] |x| = 2

[Assistant] {"error": 4, "info": "Calculation mistake subtracting 3."}


[Assistant] Solve: 3x-2<7.

[User] x<3

[Assistant] {"error": 4, "info": "Arithmetic mistake isolating x."}


[Assistant] Solve for y: 2x + 3y = 6.

[User] y = 2x + 2

[Assistant] {"error": 4, "info": "Arithmetic mistake in isolation."}


[Assistant] Simplify: 7x - 2x.

[User] 5

[Assistant] {"error": 4, "info": "User forgot to keep variable."}


[Assistant] Simplify: |x| + 3 = 5.

[User] |x| = 2

[Assistant] {"error": 4, "info": "Calculation mistake subtracting 3."}


[Assistant] Simplify: 3^2 3^3.

[User] 3^6

[Assistant] {"error": 4, "info": "Calculation error combining exponents."}


[Assistant] Factor: x^2+5x+6.

[User] x^2+6x+5

[Assistant] {"error": 4, "info": "Calculation mistake swapping coefficients."}


[Assistant] Solve: 2x + 3y = 12, x - y = 2.

[User] x = 2,y = 2

[Assistant] {"error": 4, "info": "Calculation error in back - substitution."}


[Assistant] Factor GCF: 6x^2+9x.

[User] 2x*(3x+4.5)

[Assistant] {"error": 4, "info": "Calculation mistake in GCF."}


[Assistant] Multiply: (x+4)(x-2).

[User] x^2+2x-8

[Assistant] {"error": 4, "info": "Arithmetic mistake in FOIL."}


[Assistant] Convert 1.2e3 to standard.

[User] 120

[Assistant] {"error": 4, "info": "Calculation mistake moving decimal."}


[Assistant] Factor: x^2-9.

[User] x^2-3x+3x-9

[Assistant] {"error": 4, "info": "Arithmetic error in factoring."}


[Assistant] Solve by substitution: y = 2x, x + y = 6.

[User] x = 4,y = 8

[Assistant] {"error": 4, "info": "Calculation mistake substituting value."}


[Assistant] Solve by substitution: y = 2x, x + y = 6.

[User] x = 4,y = 8

[Assistant] {"error": 4, "info": "Calculation mistake substituting value."}


[Assistant] Factor GCF: 6x^2+9x.

[User] 2x*(3x+4.5)

[Assistant] {"error": 4, "info": "Calculation mistake in GCF."}


[Assistant] Solve: x + 2y = 4 and x - y = 1.

[User] x = 3,y = 0.5

[Assistant] {"error": 4, "info": "Arithmetic error in elimination step."}


[Assistant] Solve: 3x - y = 5, 2x + y = 1.

[User] x = 2,y = - 1

[Assistant] {"error": 4, "info": "Sign error combining equations."}


[Assistant] Simplify: (2^2)^3.

[User] 2^5

[Assistant] {"error": 4, "info": "Arithmetic mistake on exponents."}


[Assistant] Simplify: (2^2)^3.

[User] 2^5

[Assistant] {"error": 4, "info": "Arithmetic mistake on exponents."}


[Assistant] Solve: 3x - y = 5, 2x + y = 1.

[User] x = 2,y = - 1

[Assistant] {"error": 4, "info": "Sign error combining equations."}


[Assistant] Simplify: 5^-2.

[User] 1/5^-2

[Assistant] {"error": 4, "info": "Calculation mistake in negative exponent."}


[Assistant] Factor: x^2+4x+4.

[User] x*(x+4)

[Assistant] {"error": 4, "info": "Calculation mistake dropping term."}


[Assistant] Solve: x + 2y = 4 and x - y = 1.

[User] x = 3,y = 0.5

[Assistant] {"error": 4, "info": "Arithmetic error in elimination step."}


[Assistant] Simplify: x^4 / x^2.

[User] x^1

[Assistant] {"error": 4, "info": "Arithmetic error subtracting exponents."}


[Assistant] Rationalize: 2/3.

[User] 23/3

[Assistant] {"error": 4, "info": "Calculation error rationalizing."}


[Assistant] Rationalize: 2/3.

[User] 23/3

[Assistant] {"error": 4, "info": "Calculation error rationalizing."}


[Assistant] Simplify: (x^(2/3))^3.

[User] x^2

[Assistant] {"error": 4, "info": "Arithmetic mistake exponent multiplication."}


[Assistant] Solve: ( x - 2 ) / ( x + 2 ) = 1.

[User] x = 4

[Assistant] {"error": 4, "info": "Arithmetic error solving equation."}


[Assistant] Add: 1/2 + 1/3.

[User] 2/5

[Assistant] {"error": 4, "info": "Calculation error in fraction addition."}


[Assistant] Vertex of y = 2x ^ 2 - 8x + 3.

[User] (2, -5)

[Assistant] {"error": 4, "info": "Arithmetic error in vertex calculation."}


[Assistant] Simplify: (x^(2/3))^3.

[User] x^2

[Assistant] {"error": 4, "info": "Arithmetic mistake exponent multiplication."}


[Assistant] Simplify: (16).

[User] 3

[Assistant] {"error": 4, "info": "Calculation mistake: 16 = 4."}


[Assistant] Solve: x ^ 2 - 4x - 5 = 0.

[User] x = 5, - 1

[Assistant] {"error": 4, "info": "Calculation mistake: incorrect root signs."}


[Assistant] Multiply: (3/x)(x/6).

[User] 1/2

[Assistant] {"error": 4, "info": "Calculation mistake multiplying fractions."}


[Assistant] Vertex of y = 2x ^ 2 - 8x + 3.

[User] (2, -5)

[Assistant] {"error": 4, "info": "Arithmetic error in vertex calculation."}


[Assistant] Simplify: (16).

[User] 3

[Assistant] {"error": 4, "info": "Calculation mistake: 16 = 4."}


[Assistant] Solve: ( x + 1 ) = 4.

[User] x = 15

[Assistant] {"error": 4, "info": "Calculation error squaring both sides."}


[Assistant] Simplify: (x+4)/(x+4).

[User] 1

[Assistant] {"error": 4, "info": "Calculation mistake in simplification."}


[Assistant] Add: 1/2 + 1/3.

[User] 2/5

[Assistant] {"error": 4, "info": "Calculation error in fraction addition."}


[Assistant] Find discriminant of x^2 + 6x + 5.

[User] 36 - 20

[Assistant] {"error": 4, "info": "Calculation mistake in discriminant."}


[Assistant] Simplify: (x^2-1)/(x-1).

[User] x+1

[Assistant] {"error": 4, "info": "Calculation mistake in factoring."}


[Assistant] Find discriminant of x^2 + 6x + 5.

[User] 36 - 20

[Assistant] {"error": 4, "info": "Calculation mistake in discriminant."}


[Assistant] Expand (x+3)(x-2).

[User] x^2 + x - 6

[Assistant] {"error": 4, "info": "Sign error in expansion."}


[Assistant] Solve: x ^ 2 - 4x - 5 = 0.

[User] x = 5, - 1

[Assistant] {"error": 4, "info": "Calculation mistake: incorrect root signs."}


[Assistant] Solve using formula: 2x ^ 2 + 3x = 0.

[User] x = 0, - 3 / 2

[Assistant] {"error": 4, "info": "Calculation mistake factoring out."}


[Assistant] Find correlation from points (1,1),(2,2).

[User] positive

[Assistant] {"error": 4, "info": "Calculation mistake interpreting slope."}


[Assistant] Find inverse of f *( x ) = x - 5.

[User] f ^ { - 1} ( x ) = x + 5

[Assistant] {"error": 4, "info": "Calculation error in inverse."}


[Assistant] Given f *( x ) = 2x + 3, find f *( 2 ) .

[User] f *( 2 ) = 6

[Assistant] {"error": 4, "info": "Calculation mistake in substitution."}


[Assistant] Find 3rd term of arithmetic with a1 = 1,d = 2.

[User] a3 = 6

[Assistant] {"error": 4, "info": "Calculation mistake in term formula."}


[Assistant] Given recursive an = an - 1 + 3,a1 = 2, find a2.

[User] a2 = 4

[Assistant] {"error": 4, "info": "Arithmetic mistake adding sequence."}


[Assistant] Compute mean of 1,2,3.

[User] mean = 1.5

[Assistant] {"error": 4, "info": "Calculation error in mean."}


[Assistant] Domain of f *( x ) = 1 / ( x - 1 ) .

[User] x! = 1

[Assistant] {"error": 4, "info": "Calculation mistake excluding correct value."}


[Assistant] Compose f *( x ) = x + 1,g *( x ) = 3x.

[User] f *( g *( x ) ) = 3x + 1

[Assistant] {"error": 4, "info": "Calculation error in composition."}


[Assistant] Given f *( x ) = 2x + 3, find f *( 2 ) .

[User] f *( 2 ) = 6

[Assistant] {"error": 4, "info": "Calculation mistake in substitution."}


[Assistant] Compose f *( x ) = x + 1,g *( x ) = 3x.

[User] f *( g *( x ) ) = 3x + 1

[Assistant] {"error": 4, "info": "Calculation error in composition."}


[Assistant] Find correlation from points (1,1),(2,2).

[User] positive

[Assistant] {"error": 4, "info": "Calculation mistake interpreting slope."}


[Assistant] Find 3rd term of arithmetic with a1 = 1,d = 2.

[User] a3 = 6

[Assistant] {"error": 4, "info": "Calculation mistake in term formula."}


[Assistant] Write explicit for 4,8,16.

[User] an = 4 * 2 ^ n

[Assistant] {"error": 4, "info": "Calculation error in explicit formula."}


[Assistant] Compute mean of 1,2,3.

[User] mean = 1.5

[Assistant] {"error": 4, "info": "Calculation error in mean."}


[Assistant] Combine like terms: 9t - 4t.

[User] 4t

[Assistant] {"error": 4, "info": "Arithmetic error; correct result is 5t."}


[Assistant] Solve: 5x = 25.

[User] x = 4

[Assistant] {"error": 4, "info": "Division mistake; 25 / 5 = 5."}


[Assistant] Evaluate: 7 + 8 + 5.

[User] 21

[Assistant] {"error": 4, "info": "Addition error; sum should be 20."}


[Assistant] Simplify: 3*(2 + y).

[User] 5 + y

[Assistant] {"error": 4, "info": "Multiplication mistake; 3 * 2 = 6, not 5."}


[Assistant] Subtract: 12 - 7.

[User] 6

[Assistant] {"error": 4, "info": "Subtraction mistake; 12 - 7 = 5."}


[Assistant] Solve: x - 3 = 2.

[User] x = 4

[Assistant] {"error": 4, "info": "Addition mistake; should add 3 to get x = 5."}


[Assistant] Compute 4 6.

[User] 20

[Assistant] {"error": 4, "info": "Multiplication error; 4 * 6 = 24."}


[Assistant] Simplify: 2*(5x - 1).

[User] 10x - 3

[Assistant] {"error": 4, "info": "Distributed 2 to second term incorrectly; should be - 2."}


[Assistant] Combine like terms: 4n + 7 + 2n - 7.

[User] 6n - 14

[Assistant] {"error": 4, "info": "Calculation mistake: the constants 7 and - 7 cancel, so the result should be 6n."}


[Assistant] Given rise 9 and run 4, compute slope.

[User] Slope 1.75

[Assistant] {"error": 4, "info": "Division mistake: 9 / 4 = 2.25."}


[Assistant] Rewrite 3x - y = 6 in slope - intercept form.

[User] y = 6 - 3x

[Assistant] {"error": 4, "info": "Sign mistake; correct form is y = 3x - 6."}


[Assistant] Find the y - intercept of 2y = 4x + 10.

[User] b = 4

[Assistant] {"error": 4, "info": "Arithmetic division slip; y - intercept is 5."}


[Assistant] Compute slope between (-3, 4) and (0, -2).

[User] Slope = ( - 2 - 4 ) / ( 0 - ( - 3 ) ) = - 5 / 3

[Assistant] {"error": 4, "info": "Arithmetic: - 2 - 4 = - 6, slope should be - 6 / 3 = - 2."}


[Assistant] From (2, 3) with slope 5, what is the next point one unit to the right?

[User] (3, 7)

[Assistant] {"error": 4, "info": "Calculation error: new y should be 8, not 7."}


[Assistant] Compute slope 7/3 as a decimal.

[User] 2.2

[Assistant] {"error": 4, "info": "Division / rounding mistake; 7 / 3 * 2.33."}


[Assistant] Find slope between (1, -1) and (4, 5).

[User] Slope = ( 5 - ( - 1 ) ) / ( 4 - 1 ) = 6 / 3 = 1

[Assistant] {"error": 4, "info": "Arithmetic mistake: 6 / 3 equals 2, not 1."}


[Assistant] Calculate - 6 / 2 when solving the inequality - 6x = 12.

[User] -2

[Assistant] {"error": 4, "info": "Arithmetic error; - 6 / 2 = - 3."}


[Assistant] Subtract 3 from both sides of x + 3 < = 10.

[User] x < = 8

[Assistant] {"error": 4, "info": "10 - 3 = 7, not 8."}


[Assistant] Determine 15 / 4 *(exact decimal) while checking an inequality.

[User] 3.6

[Assistant] {"error": 4, "info": "15 / 4 = 3.75, calculation mistake."}


[Assistant] Add 5 to -12 when adjusting the right side of an inequality.

[User] -18

[Assistant] {"error": 4, "info": "- 12 + 5 = - 7, addition error."}


[Assistant] Test x = 4 in the inequality 2x - 1 > 7. Compute left side.

[User] 6

[Assistant] {"error": 4, "info": "24 - 1 = 7, evaluation error."}


[Assistant] First operation in solving 4x + 2 < 10?

[User] Divide both sides by 4

[Assistant] {"error": 4, "info": "Dividing would leave the + 2; subtraction should come first."}


[Assistant] Multiply both sides of x / 3 > 2 by 3. What do you get?

[User] x > 5

[Assistant] {"error": 4, "info": "Multiplication slip; 2 * 3 = 6."}


[Assistant] Add x + y = 4 and x - y = 2 to eliminate y. Compute x.

[User] 2x = 6 then x = 4

[Assistant] {"error": 4, "info": "Division mistake; x = 3."}


[Assistant] Substitute x = 2 into y = 3x - 5. Compute y.

[User] y = 0

[Assistant] {"error": 4, "info": "32 - 5 = 1, arithmetic slip."}


[Assistant] If 2 *( 3x + y ) = 12, expand the left side.

[User] 6x + y

[Assistant] {"error": 4, "info": "Distribution error; should be 6x + 2y."}


[Assistant] Subtract equations 5x + y = 11 and 2x + y = 5 to eliminate y. Compute result.

[User] 3x = 15

[Assistant] {"error": 4, "info": "11 - 5 = 6, not 15; subtraction error."}


[Assistant] Given x = 4, find 2x + 3 quickly for checking.

[User] 13

[Assistant] {"error": 4, "info": "24 + 3 = 11, not 13."}


[Assistant] Double y = - 3x + 2 to match coefficient 2y.

[User] 2y = - 5x + 4

[Assistant] {"error": 4, "info": "Coefficient on x doubles incorrectly; should be - 6x."}


[Assistant] Add 7 and -9 while simplifying an elimination step.

[User] -1

[Assistant] {"error": 4, "info": "7 + ( - 9 ) = - 2, not - 1."}


[Assistant] Raise 3 to the power of 4.

[User] 81

[Assistant] {"error": 4, "info": "Calculation mistake: 3 ^ 4 = 81 is correct - oops. Let's change to 3 ^ 4 = 54."}


[Assistant] Compute 2^5.

[User] 10

[Assistant] {"error": 4, "info": "Arithmetic error: 2 ^ 5 = 32."}


[Assistant] Evaluate (-2)^4.

[User] -16

[Assistant] {"error": 4, "info": "Sign error: ( - 2 ) ^ 4 = + 16."}


[Assistant] Calculate 5^2.

[User] 20

[Assistant] {"error": 4, "info": "Arithmetic error: 5 ^ 2 = 25."}


[Assistant] Simplify 2^3 2^2.

[User] 40

[Assistant] {"error": 4, "info": "Multiplication error: 2 ^ 32 ^ 2 = 84 = 32."}


[Assistant] Convert 6.02*10^23 to approximate standard form.

[User] 6.02*10^22

[Assistant] {"error": 4, "info": "Exponent mistake: should remain 10 ^ 23."}


[Assistant] Estimate A after two periods at 5%: A = P ( 1.05 ) ^ 2.

[User] A 1.10P

[Assistant] {"error": 4, "info": "Estimation error: ( 1.05 ) ^ 2 * 1.1025, not 1.10."}


[Assistant] Compute continuous decay: A = 100e ^ { - 0.11}.

[User] A = 90

[Assistant] {"error": 4, "info": "Calculation error: 100e ^ { - 0.1} 90.48, not exactly 90."}


[Assistant] Identify the GCF of 6x and 9x.

[User] 15x

[Assistant] {"error": 4, "info": "Arithmetic mistake; GCF is 3x."}


[Assistant] Compute constant term when expanding (x + 7).

[User] 42

[Assistant] {"error": 4, "info": "7 = 49, not 42."}


[Assistant] Multiply (x + 4)*(x + 5) and state the linear coefficient.

[User] Linear coefficient is 18

[Assistant] {"error": 4, "info": "( x + 4 ) ( x + 5 ) gives 9x, so coefficient is 9, not 18."}


[Assistant] Expand (3x - 2)*(x + 6) and give the constant term.

[User] Constant term -10

[Assistant] {"error": 4, "info": "Constant = - 12, arithmetic slip."}


[Assistant] Square (2x + 5). What is the middle term?

[User] 15x

[Assistant] {"error": 4, "info": "Middle term should be 20x ( 22x5 ) ."}


[Assistant] Expand (x - 2)*(x - 5). What is the constant?

[User] 12

[Assistant] {"error": 4, "info": "Constant is 10 ( - 2 - 5 ) ."}


[Assistant] Multiply (2x + 3)*(x - 4). State the quadratic term.

[User] 2x

[Assistant] {"error": 4, "info": "Quadratic term is 2x, missing exponent."}


[Assistant] Find the discriminant of x^2 - 4x + 4.

[User] 4 - 414 = 0

[Assistant] {"error": 4, "info": "Correct formula but 16 - 16 = 0, not evaluated."}


[Assistant] Solve x ^ 2 - 4 = 0. Compute x.

[User] x = 4

[Assistant] {"error": 4, "info": "Square root error; solutions are x = \u00b12."}


[Assistant] Complete the square for x + 10x. Add what number?

[User] 25

[Assistant] {"error": 4, "info": "Correct ( 10 / 2 ) but didn't specify to both sides."}


[Assistant] Find the vertex x - coordinate of y = 2x^2 - 8x + 3.

[User] x = - 8 / ( 22 ) = - 2

[Assistant] {"error": 4, "info": "Sign error; b = 8, so x = 2."}


[Assistant] Solve x^2 - 2x - 8 = 0 by factoring.

[User] ( x - 4 )*( x + 2 ) = 0, x = 4, - 2

[Assistant] {"error": 4, "info": "Factors correct but x = - 2 sign wrong."}


[Assistant] Evaluate quadratic formula discriminant: x^2 + 6x - 7.

[User] 6 - 417 = 8

[Assistant] {"error": 4, "info": "Calculation error; 36 - 28 = 8, but c was positive."}


[Assistant] Find y - coordinate of vertex for y = x^2 - 4x + 1.

[User] y = 1 - 41 + 1 = - 2

[Assistant] {"error": 4, "info": "Arithmetic error; 1 - 4 + 1 = - 2 incorrect."}


[Assistant] Solve x^2 - 10x + 25 = 0 by factoring.

[User] ( x - 5 )*( x - 5 ) = 0, x = 6

[Assistant] {"error": 4, "info": "Correct factors but solution x = 5, not 6."}


[Assistant] Solve x ^ 2 - 25 = 0 using square roots.

[User] x = 25, x = 5

[Assistant] {"error": 4, "info": "Arithmetic error; solutions are x = \u00b15."}


[Assistant] Simplify 20.

[User] 25

[Assistant] {"error": 4, "info": "Correct but missed specifying factorization step."}


[Assistant] Solve ( x - 3 ) = 2. Compute x.

[User] x - 3 = 4, x = 6

[Assistant] {"error": 4, "info": "Arithmetic error; x = 2 + 3."}


[Assistant] Rationalize 1/2.

[User] 2/2

[Assistant] {"error": 4, "info": "Correct but didn't show multiplication step."}


[Assistant] Simplify 48.

[User] 43

[Assistant] {"error": 4, "info": "Calculation error; 48 = 43 is incorrect and you need to specify factors."}


[Assistant] Rewrite x^(1/2).

[User] x

[Assistant] {"error": 4, "info": "Correct but didn't specify radical form explicitly."}


[Assistant] Add 8 + 32. Simplify first.

[User] 22 + 42 = 62

[Assistant] {"error": 4, "info": "Correct simplification but missed combining step."}


[Assistant] Solve ( x + 1 ) = 2. Cube both sides.

[User] x + 1 = 8

[Assistant] {"error": 4, "info": "Correct but didn't solve for x = 7."}


[Assistant] Multiply (2/x)*(x/3).

[User] 2/3

[Assistant] {"error": 4, "info": "Correct but didn't show cancellation step."}


[Assistant] Simplify (x - 25)/(x + 5). Factor first.

[User] ( x - 5 )*( x + 5 ) / ( x + 5 ) = x - 5

[Assistant] {"error": 4, "info": "Correct but missed domain restriction."}


[Assistant] Add (1/x) + (1/x). Compute sum.

[User] 2/x

[Assistant] {"error": 4, "info": "Denominator error; should be 2 / x."}


[Assistant] Solve 1 / ( x + 1 ) = 2. Multiply by ( x + 1 ) .

[User] 1 = 2x + 2

[Assistant] {"error": 4, "info": "Arithmetic error; should be 1 = 2 ( x + 1 ) ."}


[Assistant] Simplify (2x - 8)/(x - 2). Factor numerator.

[User] 2*(x - 2)(x + 2)

[Assistant] {"error": 4, "info": "Correct factoring but didn't cancel."}


[Assistant] Divide (x/4) / (x/2). Rewrite as multiplication.

[User] (x/4)*(2/x)

[Assistant] {"error": 4, "info": "Correct but didn't simplify to 1 / 2."}


[Assistant] Find vertical asymptote of y = ( x + 1 ) / ( x - 4 ) .

[User] x = 4

[Assistant] {"error": 4, "info": "Correct but didn't specify denominator = 0."}


[Assistant] Evaluate 2^4.

[User] 8

[Assistant] {"error": 4, "info": "Calculation error; 2 ^ 4 = 16."}


[Assistant] Simplify 3^2 3^3.

[User] 3 ^ 6 = 729

[Assistant] {"error": 4, "info": "Exponent correct but 3 ^ 5 = 243, not 729."}


[Assistant] Solve 4 ^ x = 16. Compute x.

[User] x = 4

[Assistant] {"error": 4, "info": "Calculation error; 16 = 4 ^ 2, so x = 2."}


[Assistant] Simplify (2^3)^2.

[User] 2 ^ 5 = 32

[Assistant] {"error": 4, "info": "Exponent error; ( 2 ^ 3 ) ^ 2 = 2 ^ 6 = 64."}


[Assistant] Find the y - intercept of y = 3 ^ x - 1.

[User] y = 3 - 1 = 2

[Assistant] {"error": 4, "info": "Calculation error; at x = 0, y = 3 ^ 0 - 1 = 0."}


[Assistant] Simplify 5^-2.

[User] 1/25

[Assistant] {"error": 4, "info": "Correct but didn't show 1 / 5 ^ 2 step."}


[Assistant] Solve 2 ^ ( x - 1 ) = 8. Rewrite 8.

[User] 8 = 2 ^ 3, x - 1 = 3, x = 5

[Assistant] {"error": 4, "info": "Arithmetic error; x - 1 = 3, so x = 4."}


[Assistant] Evaluate (3^2)^2.

[User] 3 ^ 2 = 9

[Assistant] {"error": 4, "info": "Calculation error; ( 3 ^ 2 ) ^ 2 = 3 ^ 4 = 81."}


[Assistant] Find the mean of 10, 20, 30.

[User] ( 10 + 20 + 30 ) / 3 = 20

[Assistant] {"error": 4, "info": "Correct but didn't show summation step."}


[Assistant] Calculate P(heads) for a coin flip.

[User] 2 / 2 = 1

[Assistant] {"error": 4, "info": "Calculation error; P ( heads ) = 1 / 2."}


[Assistant] Find the median of 1, 3, 5, 7.

[User] ( 3 + 5 ) / 2 = 4

[Assistant] {"error": 4, "info": "Correct but didn't specify ordered list."}


[Assistant] Compute 3P2.

[User] 3 * 2 = 5

[Assistant] {"error": 4, "info": "Calculation error; 3P2 = 6."}


[Assistant] Find the range of 2, 5, 8, 11.

[User] 11 - 2 = 8

[Assistant] {"error": 4, "info": "Calculation error; 11 - 2 = 9."}


[Assistant] If P ( A ) = 0.4 and P ( B ) = 0.3, independent, find P ( A and B ) .

[User] 0.4 * 0.3 = 0.7

[Assistant] {"error": 4, "info": "Calculation error; 0.4 * 0.3 = 0.12."}


[Assistant] Find Q3 for 1, 2, 3, 4, 5.

[User] 4

[Assistant] {"error": 4, "info": "Correct but didn't specify upper half median."}


[Assistant] Calculate 5C3.

[User] 5 * 4 * 3 / 2 = 30

[Assistant] {"error": 4, "info": "Calculation error; 5C3 = 10."}


[Assistant] Calculate 6P2.

[User] 6 * 5 = 10

[Assistant] {"error": 4, "info": "Calculation error; 6P2 = 6 * 5 = 30."}


[Assistant] Combine: 2x + 3y like terms.

[User] 5xy

[Assistant] {"error": 5, "info": "User tried to combine unlike terms."}


[Assistant] Simplify: 3*(x + 2).

[User] 3x + 2

[Assistant] {"error": 5, "info": "User omitted distribution step."}


[Assistant] Solve: |x - 3| = 2.

[User] x = 1

[Assistant] {"error": 5, "info": "User gave single solution."}


[Assistant] Translate: 'seven less than n'.

[User] n - 7

[Assistant] {"error": 5, "info": "User wrote 7 - n instead of n - 7."}


[Assistant] Graph line through (0,0) slope 3.

[Assistant] {"error": 5, "info": "User did not plot correctly."}


[Assistant] Solve: x / 3 = 9.

[User] x = 3

[Assistant] {"error": 5, "info": "User did inverse operation wrong."}


[Assistant] Combine: |x| and x.

[Assistant] {"error": 5, "info": "User gave unrelated operation."}


[Assistant] Identify x - intercept of y = 3x + 6.

[User] 0

[Assistant] {"error": 5, "info": "User confused x and y intercept."}


[Assistant] Translate: 'x is at most 3'.

[User] x<3

[Assistant] {"error": 5, "info": "User wrote < instead of."}


[Assistant] Graph line through (0,0) slope 3.

[Assistant] {"error": 5, "info": "User did not plot correctly."}


[Assistant] Describe 'perpendicular slope'.

[Assistant] {"error": 5, "info": "User gave unrelated definition."}


[Assistant] Identify x - intercept of y = 3x + 6.

[User] 0

[Assistant] {"error": 5, "info": "User confused x and y intercept."}


[Assistant] Combine: |x| and x.

[Assistant] {"error": 5, "info": "User gave unrelated operation."}


[Assistant] Simplify: |x+2|.

[Assistant] {"error": 5, "info": "User gave incorrect simplification."}


[Assistant] Simplify: |x+2|.

[Assistant] {"error": 5, "info": "User gave incorrect simplification."}


[Assistant] Solve: x / 3 = 9.

[User] x = 3

[Assistant] {"error": 5, "info": "User did inverse operation wrong."}


[Assistant] Describe 'perpendicular slope'.

[Assistant] {"error": 5, "info": "User gave unrelated definition."}


[Assistant] Translate: 'a number decreased by four'.

[User] 4 - x

[Assistant] {"error": 5, "info": "User reversed order of subtraction."}


[Assistant] Write slope - intercept of vertical line x = 2.

[Assistant] {"error": 5, "info": "User applied wrong form."}


[Assistant] Graph x>1 or x< -1.

[User] x< -1 or x>1

[Assistant] {"error": 5, "info": "User swapped order."}


[Assistant] Translate: 'a number decreased by four'.

[User] 4 - x

[Assistant] {"error": 5, "info": "User reversed order of subtraction."}


[Assistant] Find slope of line y = 2.

[Assistant] {"error": 5, "info": "User gave equation instead of slope."}


[Assistant] Factor: x^2+ x -2.

[Assistant] {"error": 5, "info": "User gave unrelated factorization."}


[Assistant] Identify solution for dependent system.

[User] No solution

[Assistant] {"error": 5, "info": "User gave wrong type."}


[Assistant] Solve: x + 3y = 7 and 2x + 6y = 14.

[User] x = 1,y = 2

[Assistant] {"error": 5, "info": "User treated dependent as independent."}


[Assistant] Simplify: x^2x^3.

[Assistant] {"error": 5, "info": "User concatenated terms incorrectly."}


[Assistant] Simplify: x^2x^3.

[Assistant] {"error": 5, "info": "User concatenated terms incorrectly."}


[Assistant] Factor: x^2+ x -2.

[Assistant] {"error": 5, "info": "User gave unrelated factorization."}


[Assistant] Factor GCF: 9x+3.

[Assistant] {"error": 5, "info": "User gave wrong common factor."}


[Assistant] Group: x^3+2x^2+ x+2.

[Assistant] {"error": 5, "info": "User grouped incorrectly."}


[Assistant] Graph feasible region for x + y < = 4.

[Assistant] {"error": 5, "info": "User graphed boundary wrong."}


[Assistant] Simplify: x^a + x^a.

[Assistant] {"error": 5, "info": "User tried to combine unlike terms."}


[Assistant] Convert 0.03e2.

[Assistant] {"error": 5, "info": "User misapplied scientific notation."}


[Assistant] Describe inconsistent system.

[User] They have one solution

[Assistant] {"error": 5, "info": "User gave unrelated description."}