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

[User] x + 7x + 7

[Assistant] {"error": 2, "info": "Concept error: constant term should be 10, not 7."}


[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 + 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 + 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 - 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] 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] 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] Factor 5x + 10 completely.

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


[Assistant] Expand (x - 1).

[User] I love pizza.

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


[Assistant] Find factors of x + 4x + 3.

[User] (x+)( )

[Assistant] {"error": 5, "info": "Incomplete factoring response."}


[Assistant] State the constant in 7x - 2x + 5.

[User] x

[Assistant] {"error": 5, "info": "Incorrect type; constant is 5."}


[Assistant] Factor 4 - x.

[User] I'm not sure maybe shrug

[Assistant] {"error": 5, "info": "Uncertain / invalid response."}


[Assistant] Expand (x + 6)(x - 6).

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] What is the degree of 2?

[User] Probably x

[Assistant] {"error": 5, "info": "Response unrelated; degree of constant 2 is 0."}


[Assistant] Factor 6x + 9x.

[User] 3x(2x + 3)

[Assistant] {"error": 6, "info": "Correct GCF factorization."}


[Assistant] Factor x - 36.

[User] (x - 6)(x + 6)

[Assistant] {"error": 6, "info": "Correct difference - of - squares factorization."}


[Assistant] Expand (2x - 3)(x + 2).

[User] 2x + x - 6

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


[Assistant] Factor x + 11x + 30.

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

[Assistant] {"error": 6, "info": "Correct trinomial factorization."}


[Assistant] Expand (x - 2)(x + 7).

[User] x + 5x - 14

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


[Assistant] Factor 8x - 18.

[User] 2 ( 4x - 9 ) = 2 ( 2x - 3 ) ( 2x + 3 )

[Assistant] {"error": 6, "info": "Correct multi - step GCF and difference - of - squares factoring."}


[Assistant] Find the square of (3x + 1).

[User] 9x + 6x + 1

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


[Assistant] Factor 25 - y.

[User] (5 - y)(5 + y)

[Assistant] {"error": 6, "info": "Correct difference of squares."}


[Assistant] Expand (x + 9)(x - 2).

[User] x + 7x - 18

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


[Assistant] Identify the vertex of y = x + 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] Find the vertex of y = x + 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 - 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 - 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 - 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 + 6x + 9.

[User] 6 - 419 = 0

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


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

[User] x = 9 = 3

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


[Assistant] Solve x + 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 + 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 - 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 + 1 = 0 using square roots.

[User] x = 1

[Assistant] {"error": 3, "info": "Misunderstood; x = - 1 has no real roots."}


[Assistant] Find the discriminant of x - 4x + 4.

[User] 4 - 414 = 0

[Assistant] {"error": 4, "info": "Correct formula but 16 - 16 = 0, not evaluated."}


[Assistant] Solve x - 4 = 0. Compute x.

[User] x = 4

[Assistant] {"error": 4, "info": "Square root error; 4 = 2."}


[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 - 8x + 3.

[User] x = - 8 / ( 22 ) = - 2

[Assistant] {"error": 4, "info": "Sign error; b = 8, so x = 2."}


[Assistant] Solve x - 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 + 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 - 4x + 1.

[User] y = 1 - 41 + 1 = - 2

[Assistant] {"error": 4, "info": "Arithmetic error; 1 - 4 + 1 = - 2 incorrect."}


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

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


[Assistant] Complete the square: x + 4x + 7. First step?

[User] x + 4x + = 7 +

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] State one root of x - 16 = 0.

[User] Blue

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] What is the vertex of y = x?

[User] v

[Assistant] {"error": 5, "info": "Variable placeholder instead of value."}


[Assistant] Does x + 4 = 0 have real roots?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Write vertex form for y = x + 2x + 1.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Find discriminant of x - 2x + 1.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Solve x - 4x + 4 = 0 by factoring.

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

[Assistant] {"error": 6, "info": "Correct factoring and solution."}


[Assistant] Solve x - 25 = 0 using square roots.

[User] x = 25, x = 5

[Assistant] {"error": 6, "info": "Correct square root method."}


[Assistant] What is the discriminant of x - 6x + 9?

[User] 6 - 419 = 0

[Assistant] {"error": 6, "info": "Correct discriminant calculation."}


[Assistant] Complete the square for x + 6x. Add what?

[User] ( 6 / 2 ) = 9

[Assistant] {"error": 6, "info": "Correct number to complete the square."}


[Assistant] Does y = - x + 2 open upward or downward?

[User] Downward

[Assistant] {"error": 6, "info": "Correct identification of parabola direction."}


[Assistant] Solve x + 2x - 3 = 0 by factoring.

[User] ( x + 3 ) ( x - 1 ) = 0

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


[Assistant] Find the axis of symmetry for y = 3x - 6x + 1.

[User] x = - ( - 6 ) / ( 23 ) = 1

[Assistant] {"error": 6, "info": "Correct axis of symmetry."}


[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] 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] Rewrite x^(1/3) as a radical.

[User] x

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


[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] Solve x - 2 = 0. Isolate the radical.

[User] x = 0

[Assistant] {"error": 3, "info": "Incorrect isolation; should be x = 2."}


[Assistant] Rationalize 5/5.

[User] 5 / 5 = 1

[Assistant] {"error": 3, "info": "Misunderstood rationalizing; should multiply by 5."}


[Assistant] Rewrite x^(2/3) as a radical.

[User] x/

[Assistant] {"error": 3, "info": "Misconception; should be ( x ) ."}


[Assistant] Simplify (16x).

[User] 16x

[Assistant] {"error": 3, "info": "Missed radical rules; should be 4|x|."}


[Assistant] Solve x = - 2. Cube both sides.

[User] x = - 2 = - 6

[Assistant] {"error": 3, "info": "Misunderstood; ( - 2 ) = - 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] 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 = 7."}


[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 correct, but 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] Simplify 36.

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


[Assistant] Rationalize 2/5. First step?

[User] 2/5

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] Simplify 25. State the value.

[User] Green

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Rewrite x^(1/4) as a radical.

[User] x

[Assistant] {"error": 5, "info": "Incorrect; should be fourth root."}


[Assistant] Does x = x always?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Simplify (9x).

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Solve ( x - 1 ) = 4.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Simplify 32.

[User] 42

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


[Assistant] Solve x = 6. Square both sides.

[User] x = 36

[Assistant] {"error": 6, "info": "Correct squaring step."}


[Assistant] Rationalize 3/3.

[User] 33 / 3 = 3

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


[Assistant] Rewrite x^(1/3) as a radical.

[User] x

[Assistant] {"error": 6, "info": "Correct radical form."}


[Assistant] Simplify (25x).

[User] 5|x|

[Assistant] {"error": 6, "info": "Correct simplification with absolute value."}


[Assistant] Solve x = 3. Cube both sides.

[User] x = 27

[Assistant] {"error": 6, "info": "Correct cubing step."}


[Assistant] Add 12 + 27. Simplify first.

[User] 23 + 33 = 53

[Assistant] {"error": 6, "info": "Correct addition of like radicals."}


[Assistant] Solve ( x + 2 ) = 5. Square both sides.

[User] x + 2 = 25

[Assistant] {"error": 6, "info": "Correct squaring step."}


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

[User] x + 1 = 2x - 1

[Assistant] {"error": 3, "info": "Correct step but didn't check x! = 1."}


[Assistant] Simplify (x - 16)/(x - 4).

[User] x - 4

[Assistant] {"error": 3, "info": "Incorrect cancellation; should be x + 4."}


[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] Simplify (x - 9)/(x - 3x).

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


[Assistant] Solve 2 / x = 1.

[User] I like fractions!

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


[Assistant] Add (1/(x - 2)) + (1/(x + 2)). State denominator.

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

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] State the excluded value of (x - 1)/(x + 3).

[User] Yellow

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Simplify (x/5)/(x/5).

[User] x

[Assistant] {"error": 5, "info": "Incorrect; should be 1."}


[Assistant] Does ( x - 2 ) / ( x - 2 ) = 1 for all x?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Find the vertical asymptote of y = 1 / x.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


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

[Assistant] {"error": 5, "info": "Blank response."}


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

[User] x - 1

[Assistant] {"error": 6, "info": "Correct simplification with cancellation."}


[Assistant] Solve 1 / ( x - 2 ) = 3. Multiply by ( x - 2 ) .

[User] 1 = 3 ( x - 2 )

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


[Assistant] Find the vertical asymptote of y = 1 / ( x + 4 ) .

[User] x = - 4

[Assistant] {"error": 6, "info": "Correct asymptote identification."}


[Assistant] Add (2/x) + (3/x). Combine terms.

[User] 5/x

[Assistant] {"error": 6, "info": "Correct addition with common denominator."}


[Assistant] Simplify (x - 16)/(x - 4). Factor numerator.

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

[Assistant] {"error": 6, "info": "Correct factoring step."}


[Assistant] Divide (x/2) / (x/4). Rewrite as multiplication.

[User] (x/2) (4/x)

[Assistant] {"error": 6, "info": "Correct reciprocal step."}


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

[User] x - 1 = 0, x = 1

[Assistant] {"error": 6, "info": "Correct numerator step."}


[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] 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] 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] 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] Simplify 2^3 / 2^5.

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


[Assistant] Solve 3 ^ x = 27.

[User] I like exponents!

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


[Assistant] What is the asymptote of y = 2 ^ x + 4?

[User] y = 4

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] Evaluate 5^2.

[User] Red

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


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

[User] x

[Assistant] {"error": 5, "info": "Incorrect; should be x ^ 6."}


[Assistant] Is 2^x always positive?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Rewrite 4^-1.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Solve 2 ^ ( x + 2 ) = 4.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Simplify 2^4 2^3.

[User] 2 ^ 7 = 128

[Assistant] {"error": 6, "info": "Correct exponent addition and evaluation."}


[Assistant] Solve 3 ^ x = 9. Rewrite 9.

[User] 9 = 3 ^ 2, so x = 2

[Assistant] {"error": 6, "info": "Correct base matching."}


[Assistant] Evaluate y = 2 ^ x for x = 0.

[User] 2 ^ 0 = 1

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


[Assistant] Simplify (5^2)^3.

[User] 5^6

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


[Assistant] Find the horizontal asymptote of y = 3 ^ x + 5.

[User] y = 5

[Assistant] {"error": 6, "info": "Correct asymptote identification."}


[Assistant] Rewrite 2^-3.

[User] 1 / 2 ^ 3 = 1 / 8

[Assistant] {"error": 6, "info": "Correct negative exponent simplification."}


[Assistant] Is y = 0.8 ^ x growth or decay?

[User] Decay

[Assistant] {"error": 6, "info": "Correct identification of decay."}


[Assistant] Solve 4 ^ ( x + 1 ) = 16. Rewrite 16.

[User] 16 = 4 ^ 2, x + 1 = 2

[Assistant] {"error": 6, "info": "Correct base matching step."}


[Assistant] Simplify 3^5 / 3^2.

[User] 3 ^ 3 = 27

[Assistant] {"error": 6, "info": "Correct exponent subtraction."}


[Assistant] Find the y - intercept of y = 2 ^ x - 3.

[User] y = 2 ^ 0 - 3 = - 2

[Assistant] {"error": 6, "info": "Correct y - intercept calculation."}


[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] 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 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 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] Find the mean of 1, 2, 3.

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


[Assistant] What is P(A or B) for mutually exclusive events?

[User] I love stats!

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


[Assistant] Find the median of 1, 3, 5. First step?

[User] 3

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] What is the probability of drawing a red card?

[User] Blue

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Calculate 4P3.

[User] 4

[Assistant] {"error": 5, "info": "Incorrect; should be 24."}


[Assistant] Are all probabilities equal to 1?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


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

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Calculate P(A and B) for independent events.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Find the mean of 5, 10, 15.

[User] ( 5 + 10 + 15 ) / 3 = 10

[Assistant] {"error": 6, "info": "Correct mean calculation."}


[Assistant] Calculate P(4) for a die roll.

[User] 1/6

[Assistant] {"error": 6, "info": "Correct probability calculation."}


[Assistant] Find the median of 2, 4, 6, 8, 10.

[User] 6

[Assistant] {"error": 6, "info": "Correct median identification."}


[Assistant] Compute 4C2.

[User] ( 4 * 3 ) / ( 2 * 1 ) = 6

[Assistant] {"error": 6, "info": "Correct combination calculation."}


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

[User] 7 - 1 = 6

[Assistant] {"error": 6, "info": "Correct range calculation."}


[Assistant] If P ( A ) = 0.5, P ( B ) = 0.4, independent, find P ( A and B ) .

[User] 0.5 * 0.4 = 0.2

[Assistant] {"error": 6, "info": "Correct independent event probability."}


[Assistant] Find Q1 for 1, 3, 5, 7, 9.

[User] 3

[Assistant] {"error": 6, "info": "Correct first quartile identification."}


[Assistant] Are events A and B mutually exclusive if P ( A and B ) = 0?

[User] Yes

[Assistant] {"error": 6, "info": "Correct mutually exclusive identification."}


[Assistant] Find the IQR of 2, 4, 6, 8, 10.

[User] Q3 - Q1 = 8 - 4 = 4

[Assistant] {"error": 6, "info": "Correct interquartile range calculation."}


[Assistant] Calculate 5P3.

[User] 5 * 4 * 3 = 60

[Assistant] {"error": 6, "info": "Correct permutation calculation."}


[Assistant] What is a histogram in statistics?

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

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


[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] 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] Calculate 6P2.

[User] 6 * 5 = 10

[Assistant] {"error": 4, "info": "Calculation error; 6P2 = 6 * 5 = 30."}


[Assistant] What is the probability of rolling a 6 on a die?

[User] I like dice!

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


[Assistant] Find the median of 1, 2, 3, 4, 5.

[User] 3

[Assistant] {"error": 6, "info": "Correct median identification."}