[Assistant] What is the horizontal asymptote of y = 2 ^ x + 3?

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

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


[Assistant] Simplify the rational expression (x - 4)/(x - 2).

[User] I don't know how to simplify fractions with x.

[Assistant] {"error": 1, "info": "Rational expression simplification is new."}


[Assistant] What does the discriminant tell you?

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

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


[Assistant] Define the degree of a polynomial.

[User] What is a degree?

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


[Assistant] What is a^0 equal to?

[User] I'm not sure what zero exponent means.

[Assistant] {"error": 1, "info": "Zero-exponent rule is unknown to the student."}


[Assistant] Explain what an absolute-value inequality is.

[User] Never heard of that.

[Assistant] {"error": 1, "info": "Absolute - value inequalities are a new concept for the student."}


[Assistant] What makes two lines parallel?

[User] I'm not familiar with that idea.

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


[Assistant] Rewrite 'half of the sum of y and 10' as an algebraic expression.

[User] I'm not sure what 'sum' means in algebra.

[Assistant] {"error": 1, "info": "Student doesn't know terminology for algebraic translation."}


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

[Assistant] {"error": 1, "info": "User did not provide a median."}


[Assistant] Define inverse function.

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


[Assistant] Explain axis of symmetry.

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


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

[User] I don't know what vertex form means.

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


[Assistant] What is the vertex of a quadratic?

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


[Assistant] Explain trinomial.

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


[Assistant] Define zero exponent rule.

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


[Assistant] What is the substitution method?

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


[Assistant] What does it mean to isolate a variable?

[User] to get x alone

[Assistant] {"error": 1, "info": "The user appears new to solving equations."}


[Assistant] Define inequality.

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


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

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


[Assistant] Solve (x - 2) / (x + 1) = 0. Set numerator to zero.

[User] x - 2 = 0, x = 2

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


[Assistant] Rationalize the denominator of 1/3.

[User] Multiply by 3 / 3 = 3 / 3

[Assistant] {"error": 2, "info": "Correct process but numerator should be 1."}


[Assistant] Graph y = x^2 - 4. Where does it open?

[User] Downward

[Assistant] {"error": 2, "info": "Mis - applied; a = 1 means upward."}


[Assistant] Simplify: x^3 * x^4.

[User] x^12

[Assistant] {"error": 2, "info": "Mis-applied product rule: exponents should add ( 3 + 4 = 7 ), not multiply (3 * 4 = 12)."}


[Assistant] Parallel distinct lines give what type of system?

[User] Infinite solutions

[Assistant] {"error": 2, "info": "Parallel distinct lines have no solution."}


[Assistant] Write the solution to x > 4 in interval notation.

[User] (-, 4]

[Assistant] {"error": 2, "info": "Used a bracket instead of a parenthesis; 4 is not included."}


[Assistant] Find the slope of a line perpendicular to y = 1 / 2x + 9.

[User] Slope = - 1 / 2

[Assistant] {"error": 2, "info": "Only changed sign; should take negative reciprocal ( - 2 ) ."}


[Assistant] Write an expression for 'the product of 6 and the difference of y and 1'.

[User] 6y - 1

[Assistant] {"error": 2, "info": "Concept error: should be 6 ( y - 1 ) ; parentheses around the difference are needed."}


[Assistant] Domain of f*(x) = 1 / x.

[User] x! = 0

[Assistant] {"error": 2, "info": "User forgot to exclude zero."}


[Assistant] Rationalize: 1/2.

[User] 2/2

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


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

[User] 2/x^2

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


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

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

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


[Assistant] Determine solution of system with parallel lines.

[User] Infinite

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


[Assistant] Translate: 'twice a number plus seven'.

[User] x*2 + 7

[Assistant] {"error": 2, "info": "User used multiplication symbol incorrectly."}


[Assistant] Find intercepts of 2x + 3y = 12.

[User] x = 6,y = 4

[Assistant] {"error": 2, "info": "User swapped intercept values."}


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

[User] x = 4

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


[Assistant] Simplify 12.

[User] (43) = 43

[Assistant] {"error": 3, "info": "Misunderstood; 4 = 2, so 23."}


[Assistant] Convert y = x^2 - 2x - 3 to vertex form.

[User] y = (x - 1)

[Assistant] {"error": 3, "info": "Incorrect completion; missed constant adjustment."}


[Assistant] Expand (x + 1)^2.

[User] x^2 + 1

[Assistant] {"error": 3, "info": "Left out 2x term; misunderstanding of binomial square."}


[Assistant] To minimize C = 4x + y, what's the procedure after graphing constraints?

[User] Pick the smallest x value and the smallest y value separately

[Assistant] {"error": 3, "info": "Need to evaluate C at each vertex, not independent minima."}


[Assistant] Graph x > 2 on a number line. How many points should you draw?

[User] Just one point at 2.

[Assistant] {"error": 3, "info": "Thinks inequality solution is a single point instead of a half - line."}


[Assistant] Two lines are parallel if their slopes multiply to 1-true or false?

[User] True

[Assistant] {"error": 3, "info": "Fundamental misunderstanding: parallel lines have equal slopes, not product 1."}


[Assistant] Simplify: 4a + 2a.

[User] 6a^2

[Assistant] {"error": 3, "info": "Misunderstanding of combining like terms - introduced exponent."}


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

[User] 9

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


[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] Rationalize: 5/(x).

[User] 5x/x

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


[Assistant] Solve: 1 / (x - 3) = 0.

[User] x = 0

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


[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] Simplify: x^0.

[User] 0

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


[Assistant] Graph - 3 < = x < 2.

[User] x> -3 and x<2

[Assistant] {"error": 3, "info": "User misread inclusive bounds."}


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

[User] x = 1

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


[Assistant] Find slope of horizontal line.

[User] 0

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


[Assistant] Solve 3 / (x - 2) = 6. Multiply by (x - 2) .

[User] 3 = 6x - 12

[Assistant] {"error": 4, "info": "Arithmetic error; 6 ( x - 2 ) = 6x - 12."}


[Assistant] Solve x = 5. Compute x.

[User] x = 20

[Assistant] {"error": 4, "info": "Calculation error; 5 = 25."}


[Assistant] Find product (x - 3) * (x - 8) and give the x-term.

[User] 11x

[Assistant] {"error": 4, "info": "Coefficient error; middle term is - 11x."}


[Assistant] Compute 2^4 / 2^1.

[User] 2

[Assistant] {"error": 4, "info": "Calculation error: 2^4 / 2^1 = 2^3 = 8, not 2."}


[Assistant] Solve 3x = 15 during elimination.

[User] x = 6

[Assistant] {"error": 4, "info": "15 / 3 is not 6."}


[Assistant] Solve 9 < = 3x by dividing both sides by 3. What inequality results?

[User] x < = 3

[Assistant] {"error": 4, "info": "Direction kept but symbol wrong; should be x > = 3."}


[Assistant] Calculate the slope between (2, 7)*and (5, 1).

[User] Slope = (1 - 7) / (5 - 2) = - 5 / 3

[Assistant] {"error": 4, "info": "Arithmetic slip: numerator is - 6, slope should be - 6 / 3 = - 2."}


[Assistant] Find inverse of f*(x) = x - 5.

[User] f ^ { - 1} (x) = x + 5

[Assistant] {"error": 4, "info": "Calculation error in inverse."}


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

[User] g*(f*(x)) = x ^ 2 + 4

[Assistant] {"error": 4, "info": "Calculation error expanding."}


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

[User] x+1

[Assistant] {"error": 4, "info": "Calculation mistake in factoring."}


[Assistant] Multiply: (3/x)*(x/6).

[User] 1/2

[Assistant] {"error": 4, "info": "Calculation mistake multiplying fractions."}


[Assistant] Solve: x - 2y = 0 and 4x + y = 9.

[User] x = 1,y = 2

[Assistant] {"error": 4, "info": "Arithmetic mistake solving for y."}


[Assistant] Convert 1.2e3 to standard.

[User] 120

[Assistant] {"error": 4, "info": "Calculation mistake moving decimal."}


[Assistant] Solve: x+5>8.

[User] x>2

[Assistant] {"error": 4, "info": "Calculation error: 8 - 5 = 2 instead of 3."}


[Assistant] Write equation for slope 1/2 and intercept -2.

[User] y = 2x - 2

[Assistant] {"error": 4, "info": "Arithmetic error using fraction."}


[Assistant] Simplify: 6y - 4y.

[User] 3y

[Assistant] {"error": 4, "info": "Arithmetic mistake in coefficient subtraction."}


[Assistant] Solve x = 3.

[User] I love math!

[Assistant] {"error": 5, "info": "Off-topic response."}


[Assistant] Find the axis of symmetry for y = x^2 - 6x + 2.

[User] I like quadratic equations!

[Assistant] {"error": 5, "info": "Off-topic response."}


[Assistant] Give one root of x - 1 = 0.

[User] Red

[Assistant] {"error": 5, "info": "Non-numeric, nonsensical answer."}


[Assistant] What is x^2 called?

[User] I think math is pretty cool!

[Assistant] {"error": 5, "info": "Off-topsic response."}


[Assistant] Indicate which region to shade for y >= x.

[Assistant] {"error": 5, "info": "No answer was given."}


[Assistant] Identify the slope in y = - 4x + 2.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Solve: 2y + 6 = 14.

[User] y = apple

[Assistant] {"error": 5, "info": "Nonsensical variable value."}


[Assistant] Define outlier.

[Assistant] {"error": 5, "info": "User gave unrelated definition."}


[Assistant] Solve: (x + 3) / (x - 3) = 2.

[Assistant] {"error": 5, "info": "User gave invalid solution."}


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

[Assistant] {"error": 5, "info": "User combined inapplicable terms."}


[Assistant] Convert 0.03e2.

[Assistant] {"error": 5, "info": "User did not provide a solution."}


[Assistant] Solve: x + y = 5, 2x + 2y = 10.

[Assistant] {"error": 5, "info": "User wrote same equation twice."}


[Assistant] Explain half-life.

[Assistant] {"error": 5, "info": "User gave unrelated concept."}


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

[User] 3x + 2

[Assistant] {"error": 5, "info": "User omitted distribution step."}


[Assistant] Translate: 'x is at most 3'.

[User] x<3

[Assistant] {"error": 5, "info": "User wrote < instead of."}


[Assistant] Multiply (x/3) * (6/x).

[User] (6x) / (3x) = 2

[Assistant] {"error": 6, "info": "Correct multiplication and simplification."}


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

[User] (x - 2)/(x + 2)

[Assistant] {"error": 6, "info": "Correct simplification to (x - 2)/(x + 2)."}


[Assistant] Find the vertex x-coordinate of y = x^2 + 8x + 3.

[User] x = - 8 / (2*1) = - 4

[Assistant] {"error": 6, "info": "Correct use of vertex formula."}


[Assistant] Expand (x + 4)*(x + 1).

[User] x^2 + 5x + 4

[Assistant] {"error": 6, "info": "Correct binomial product."}


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

[User] x^3

[Assistant] {"error": 6, "info": "Correct application of quotient rule."}


[Assistant] For P = 5x + 2y, evaluate at corner (0,3) .

[User] P = 6

[Assistant] {"error": 6, "info": "Correct evaluation 5*0 + 2*3 = 6."}


[Assistant] Add 4 to both sides of the inequality y - 4 > -1. What is the new inequality?

[User] y > 3

[Assistant] {"error": 6, "info": "Correct first step after adding 4 to both sides."}


[Assistant] Solve: x / 4 = 3.

[User] Multiply both sides by 4

[Assistant] {"error": 6, "info": "Correct first move to isolate x."}


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

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

[Assistant] {"error": 6, "info": "No error: correct composition."}


[Assistant] Write explicit formula for geometric sequence 3,6,12.

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

[Assistant] {"error": 6, "info": "No error: correct formula."}


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

[User] x = 23

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Simplify: (16).

[User] 4

[Assistant] {"error": 6, "info": "No error: correct simplification."}


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

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

[Assistant] {"error": 6, "info": "No error: correct factoring."}


[Assistant] Graph: y = 2x and y = x + 1, find intersection.

[User] (1,3)

[Assistant] {"error": 6, "info": "No error: correct intersection."}


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

[User] Infinite solutions

[Assistant] {"error": 6, "info": "No error: dependent system."}


[Assistant] What is the slope of y = 2x + 3?

[User] 2

[Assistant] {"error": 6, "info": "No error: correct slope."}


[Assistant] Find slope from (0,5)*and (5,0).

[User] -1

[Assistant] {"error": 6, "info": "No error: correct slope."}