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test.jsonl

@@ -1,100 +1,100 @@
-{"conversations": [{"from": "assistant", "value": "What is the horizontal asymptote of y = 2 ^ x + 3?"}, {"from": "human", "value": "I don't know what an asymptote is."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Horizontal asymptote concept is new.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Multiply (x/3) (6/x)."}, {"from": "human", "value": "( x6 ) / ( 3x ) = 2"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"Correct multiplication and simplification.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve 3 / ( x - 2 ) = 6. Multiply by ( x - 2 ) ."}, {"from": "human", "value": "3 = 6x - 12"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Arithmetic error; 6 ( x - 2 ) = 6x - 12.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify (x - 4)/(x + 4x + 4)."}, {"from": "human", "value": "(x - 2)/(x + 2)"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Mis - factored denominator; should be ( x + 2 ) .\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve ( x - 2 ) / ( x + 1 ) = 0. Set numerator to zero."}, {"from": "human", "value": "x - 2 = 0, x = 2"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Correct numerator but didn't check denominator! = 0.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify the rational expression (x - 4)/(x - 2)."}, {"from": "human", "value": "I don't know how to simplify fractions with x."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Rational expression simplification is new.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve x = 3."}, {"from": "human", "value": "I love math!"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"Off - topic response.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve x = 5. Compute x."}, {"from": "human", "value": "x = 20"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation error; 5 = 25.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify 12."}, {"from": "human", "value": "( 43 ) = 43"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Misunderstood; 4 = 2, so 23.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Rationalize the denominator of 1/3."}, {"from": "human", "value": "Multiply by 3 / 3 = 3 / 3"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Correct process but numerator should be 1.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find the vertex x - coordinate of y = x + 8x + 3."}, {"from": "human", "value": "x = - 8 / ( 21 ) = - 4"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"Correct use of vertex formula.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find the axis of symmetry for y = x - 6x + 2."}, {"from": "human", "value": "I like quadratic equations!"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"Off - topic response.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Convert y = x - 2x - 3 to vertex form."}, {"from": "human", "value": "y = ( x - 1 )"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Incorrect completion; missed constant adjustment.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Graph y = x - 4. Where does it open?"}, {"from": "human", "value": "Downward"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Mis - applied; a = 1 means upward.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What does the discriminant tell you?"}, {"from": "human", "value": "I don't know what discriminant means."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Discriminant concept is new.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Expand (x + 4)(x + 1)."}, {"from": "human", "value": "x + 5x + 4"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"Correct binomial product.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Give one root of x - 1 = 0."}, {"from": "human", "value": "Red"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"Non - numeric, nonsensical answer.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find product (x - 3)(x - 8) and give the x-term."}, {"from": "human", "value": "11x"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Coefficient error; middle term is - 11x.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Expand (x + 1)."}, {"from": "human", "value": "x + 1"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Left out 2x term; misunderstanding of binomial square.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Define the degree of a polynomial."}, {"from": "human", "value": "Never heard of degree in this context."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Degree of a polynomial is unfamiliar.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: x^5 x^2."}, {"from": "human", "value": "x^3"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"Correct application of quotient rule.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What is x^2 called?"}, {"from": "human", "value": "I like cookies."}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"Off - topic response.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Compute 2^4 2^1."}, {"from": "human", "value": "4 / 2 = 2"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Incorrect: 2 ^ 4 / 2 ^ 1 = 2 ^ 3 = 8.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: x^3 x^4."}, {"from": "human", "value": "x^12"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Mis - applied product rule: exponents should add ( 3 + 4 = 7 ) , not multiply ( 3 * 4 = 12 ) .\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What is a^0 equal to?"}, {"from": "human", "value": "I'm not sure what zero exponent means."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Zero - exponent rule is unknown to the student.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "For P = 5x + 2y, evaluate at corner ( 0,3 ) ."}, {"from": "human", "value": "P = 6"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"Correct evaluation 50 + 23 = 6.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Indicate which region to shade for y > = x."}, {"from": "human", "value": ""}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"Non - mathematical symbols.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve 3x = 15 during elimination."}, {"from": "human", "value": "x = 6"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"15 / 3 = 5, not 6.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "To minimize C = 4x + y, what's the procedure after graphing constraints?"}, {"from": "human", "value": "Pick the smallest x value and the smallest y value separately"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Need to evaluate C at each vertex, not independent minima.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Parallel distinct lines give what type of system?"}, {"from": "human", "value": "Infinite solutions"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Parallel distinct lines have no solution.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Add 4 to both sides of the inequality y - 4 > -1. What is the new inequality?"}, {"from": "human", "value": "y > 3"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"Correct first step after adding 4 to both sides.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve 9 < = 3x by dividing both sides by 3. What inequality results?"}, {"from": "human", "value": "x < = 3"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Direction kept but symbol wrong; should be x > = 3.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Graph x > 2 on a number line. How many points should you draw?"}, {"from": "human", "value": "Just one point at 2."}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Thinks inequality solution is a single point instead of a half - line.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Write the solution to x > 4 in interval notation."}, {"from": "human", "value": "(-, 4]"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Used a bracket instead of a parenthesis; 4 is not included.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Explain what an absolute-value inequality is."}, {"from": "human", "value": "Never heard of that."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Absolute - value inequalities are a new concept for the student.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Identify the slope in y = - 4x + 2."}, {"from": "human", "value": ""}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"No response provided.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Calculate the slope between (2, 7) and (5, 1)."}, {"from": "human", "value": "Slope = ( 1 - 7 ) / ( 5 - 2 ) = - 5 / 3"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Arithmetic slip: numerator is - 6, slope should be - 6 / 3 = - 2.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Two lines are parallel if their slopes multiply to 1-true or false?"}, {"from": "human", "value": "True"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Fundamental misunderstanding: parallel lines have equal slopes, not product 1.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find the slope of a line perpendicular to y = 1 / 2x + 9."}, {"from": "human", "value": "Slope = - 1 / 2"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Only changed sign; should take negative reciprocal ( - 2 ) .\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What makes two lines parallel?"}, {"from": "human", "value": "I'm not familiar with that idea."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Parallel - line criterion is new to the student.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Write an expression for 'the product of 6 and the difference of y and 1'."}, {"from": "human", "value": "6y - 1"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"Concept error: should be 6 ( y - 1 ) ; parentheses around the difference are needed.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: x / 4 = 3."}, {"from": "human", "value": "Multiply both sides by 4"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"Correct first move to isolate x.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: 2y + 6 = 14."}, {"from": "human", "value": "y = apple"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"Nonsensical variable value.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: 4a + 2a."}, {"from": "human", "value": "6a^2"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"Misunderstanding of combining like terms - introduced exponent.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Rewrite 'half of the sum of y and 10' as an algebraic expression."}, {"from": "human", "value": "I'm not sure what 'sum' means in algebra."}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"Student doesn't know terminology for algebraic translation.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find f ( 3 ) for f ( x ) = x ^ 2."}, {"from": "human", "value": "9"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User lacks understanding of function evaluation.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Compose f ( x ) = x + 1,g ( x ) = 2x."}, {"from": "human", "value": "f ( g ( x ) ) = 2x + 1"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct composition.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Domain of f ( x ) = 1 / x."}, {"from": "human", "value": "x! = 0"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User forgot to exclude zero.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find inverse of f ( x ) = x - 5."}, {"from": "human", "value": "f ^ { - 1} ( x ) = x + 5"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation error in inverse.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Calculate median of 1,3,5,7,9."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User gave wrong median.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Define inverse function."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User new to inverse concept.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Compute ( fg ) ( x ) for f ( x ) = x + 2,g ( x ) = x - 2."}, {"from": "human", "value": "0"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User doesn't understand composition.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Write explicit formula for geometric sequence 3,6,12."}, {"from": "human", "value": "an = 3 * 2 ^ ( n - 1 )"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct formula.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Evaluate g ( f ( x ) ) for f = x + 2,g = x ^ 2."}, {"from": "human", "value": "g ( f ( x ) ) = x ^ 2 + 4"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation error expanding.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Define outlier."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User gave unrelated definition.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: (x^2-1)/(x-1)."}, {"from": "human", "value": "x+1"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation mistake in factoring.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: ( x + 2 ) = 5."}, {"from": "human", "value": "x = 23"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct solution.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Rationalize: 1/2."}, {"from": "human", "value": "2/2"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User did denominator rationalization wrong.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Explain axis of symmetry."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User unaware of axis of symmetry.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: ( x + 3 ) / ( x - 3 ) = 2."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User gave invalid solution.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Rationalize: 5/(x)."}, {"from": "human", "value": "5x/x"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User missing denominator term.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Explain axis of symmetry."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User unaware of axis of symmetry.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Multiply: (3/x)(x/6)."}, {"from": "human", "value": "1/2"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation mistake multiplying fractions.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve using quadratic formula: x ^ 2 + 2x - 3 = 0."}, {"from": "human", "value": "x = 1"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User used formula but dropped one solution.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: 1/(x+1) + x."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User combined inapplicable terms.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Rationalize: 1/(x +1)."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation mistake in conjugate.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What is the vertex of a quadratic?"}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User does not know vertex definition.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Add: 1/x + 1/x."}, {"from": "human", "value": "2/x^2"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User added denominators instead of creating common denominator.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: (16)."}, {"from": "human", "value": "4"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct simplification.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: 1 / ( x - 3 ) = 0."}, {"from": "human", "value": "x = 0"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User misinterpreted equation.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: x - 2y = 0 and 4x + y = 9."}, {"from": "human", "value": "x = 1,y = 2"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Arithmetic mistake solving for y.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Convert 0.03e2."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User misapplied scientific notation.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Factor: x^2+5x+6."}, {"from": "human", "value": "(x+2)(x+3)"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct factoring.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Factor: x^2+5x+6."}, {"from": "human", "value": "x(x+5)+6"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User applied grouping incorrectly.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Explain trinomial."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User unaware of trinomial concept.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: x - y = 2, 2x - 2y = 5."}, {"from": "human", "value": "x = 2.5,y = 0.5"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User lacks understanding of solution consistency.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: x + y = 5, 2x + 2y = 10."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User wrote same equation twice.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Graph: y = 2x and y = x + 1, find intersection."}, {"from": "human", "value": "(1,3)"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct intersection.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Determine solution of system with parallel lines."}, {"from": "human", "value": "Infinite"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User confused parallel with infinite solutions.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Define zero exponent rule."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User unfamiliar with exponent laws.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What is the substitution method?"}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User does not know substitution method.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Explain half-life."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User gave unrelated concept.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: x^0."}, {"from": "human", "value": "0"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User lacks understanding that x ^ 0 = 1.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Convert 1.2e3 to standard."}, {"from": "human", "value": "120"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation mistake moving decimal.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: 2x + y = 5 and 4x + 2y = 10."}, {"from": "human", "value": "Infinite solutions"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: dependent system.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Solve: x+5>8."}, {"from": "human", "value": "x>2"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Calculation error: 8 - 5 = 2 instead of 3.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Translate: 'twice a number plus seven'."}, {"from": "human", "value": "x*2 + 7"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User used multiplication symbol incorrectly.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What is the slope of y = 2x + 3?"}, {"from": "human", "value": "2"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct slope.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: 3(x + 2)."}, {"from": "human", "value": "3x + 2"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User omitted distribution step.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Graph - 3 < = x < 2."}, {"from": "human", "value": "x> -3 and x<2"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User misread inclusive bounds.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Write equation for slope 1/2 and intercept -2."}, {"from": "human", "value": "y = 2x - 2"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Arithmetic error using fraction.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find intercepts of 2x + 3y = 12."}, {"from": "human", "value": "x = 6,y = 4"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User swapped intercept values.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Graph line y = 5x + 1, identify intercept."}, {"from": "human", "value": "x = 1"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User confused intercept types.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Translate: 'x is at most 3'."}, {"from": "human", "value": "x<3"}, {"from": "assistant", "value": "{\"error\": 5, \"info\": \"User wrote < instead of.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "What does it mean to isolate a variable?"}, {"from": "human", "value": "to get x alone"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"The user appears new to solving equations.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find slope of horizontal line."}, {"from": "human", "value": "0"}, {"from": "assistant", "value": "{\"error\": 3, \"info\": \"User doesn't understand horizontal line slope.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Define inequality."}, {"from": "human", "value": "N/A"}, {"from": "assistant", "value": "{\"error\": 1, \"info\": \"User doesn't know inequality meaning.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find slope of y = 4x - 1."}, {"from": "human", "value": "x = 4"}, {"from": "assistant", "value": "{\"error\": 2, \"info\": \"User mixed variable and coefficient.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Find slope from (0,5) and (5,0)."}, {"from": "human", "value": "-1"}, {"from": "assistant", "value": "{\"error\": 6, \"info\": \"No error: correct slope.\"}"}]}
-{"conversations": [{"from": "assistant", "value": "Simplify: 6y - 4y."}, {"from": "human", "value": "3y"}, {"from": "assistant", "value": "{\"error\": 4, \"info\": \"Arithmetic mistake in coefficient subtraction.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What is the horizontal asymptote of y = 2 ^ x + 3?"}, {"from": "human", "value": "I don't know what an asymptote is."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Horizontal asymptote concept is new.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Multiply (x/3) (6/x)."}, {"from": "human", "value": "( x6 ) / ( 3x ) = 2"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct multiplication and simplification.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve 3 / ( x - 2 ) = 6. Multiply by ( x - 2 ) ."}, {"from": "human", "value": "3 = 6x - 12"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Arithmetic error; 6 ( x - 2 ) = 6x - 12.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify (x - 4)/(x + 4x + 4)."}, {"from": "human", "value": "(x - 2)/(x + 2)"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Mis - factored denominator; should be ( x + 2 ) .\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve ( x - 2 ) / ( x + 1 ) = 0. Set numerator to zero."}, {"from": "human", "value": "x - 2 = 0, x = 2"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Correct numerator but didn't check denominator! = 0.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify the rational expression (x - 4)/(x - 2)."}, {"from": "human", "value": "I don't know how to simplify fractions with x."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Rational expression simplification is new.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve x = 3."}, {"from": "human", "value": "I love math!"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"Off - topic response.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve x = 5. Compute x."}, {"from": "human", "value": "x = 20"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation error; 5 = 25.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify 12."}, {"from": "human", "value": "( 43 ) = 43"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Misunderstood; 4 = 2, so 23.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Rationalize the denominator of 1/3."}, {"from": "human", "value": "Multiply by 3 / 3 = 3 / 3"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Correct process but numerator should be 1.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find the vertex x - coordinate of y = x + 8x + 3."}, {"from": "human", "value": "x = - 8 / ( 21 ) = - 4"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct use of vertex formula.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find the axis of symmetry for y = x - 6x + 2."}, {"from": "human", "value": "I like quadratic equations!"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"Off - topic response.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Convert y = x - 2x - 3 to vertex form."}, {"from": "human", "value": "y = ( x - 1 )"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Incorrect completion; missed constant adjustment.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Graph y = x - 4. Where does it open?"}, {"from": "human", "value": "Downward"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Mis - applied; a = 1 means upward.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What does the discriminant tell you?"}, {"from": "human", "value": "I don't know what discriminant means."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Discriminant concept is new.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Expand (x + 4)(x + 1)."}, {"from": "human", "value": "x + 5x + 4"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct binomial product.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Give one root of x - 1 = 0."}, {"from": "human", "value": "Red"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"Non - numeric, nonsensical answer.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find product (x - 3)(x - 8) and give the x-term."}, {"from": "human", "value": "11x"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Coefficient error; middle term is - 11x.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Expand (x + 1)."}, {"from": "human", "value": "x + 1"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Left out 2x term; misunderstanding of binomial square.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Define the degree of a polynomial."}, {"from": "human", "value": "Never heard of degree in this context."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Degree of a polynomial is unfamiliar.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: x^5 x^2."}, {"from": "human", "value": "x^3"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct application of quotient rule.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What is x^2 called?"}, {"from": "human", "value": "I like cookies."}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"Off - topic response.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Compute 2^4 2^1."}, {"from": "human", "value": "4 / 2 = 2"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Incorrect: 2 ^ 4 / 2 ^ 1 = 2 ^ 3 = 8.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: x^3 x^4."}, {"from": "human", "value": "x^12"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Mis - applied product rule: exponents should add ( 3 + 4 = 7 ) , not multiply ( 3 * 4 = 12 ) .\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What is a^0 equal to?"}, {"from": "human", "value": "I'm not sure what zero exponent means."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Zero - exponent rule is unknown to the student.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "For P = 5x + 2y, evaluate at corner ( 0,3 ) ."}, {"from": "human", "value": "P = 6"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct evaluation 50 + 23 = 6.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Indicate which region to shade for y > = x."}, {"from": "human", "value": ""}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"Non - mathematical symbols.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve 3x = 15 during elimination."}, {"from": "human", "value": "x = 6"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"15 / 3 = 5, not 6.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "To minimize C = 4x + y, what's the procedure after graphing constraints?"}, {"from": "human", "value": "Pick the smallest x value and the smallest y value separately"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Need to evaluate C at each vertex, not independent minima.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Parallel distinct lines give what type of system?"}, {"from": "human", "value": "Infinite solutions"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Parallel distinct lines have no solution.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Add 4 to both sides of the inequality y - 4 > -1. What is the new inequality?"}, {"from": "human", "value": "y > 3"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first step after adding 4 to both sides.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve 9 < = 3x by dividing both sides by 3. What inequality results?"}, {"from": "human", "value": "x < = 3"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Direction kept but symbol wrong; should be x > = 3.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Graph x > 2 on a number line. How many points should you draw?"}, {"from": "human", "value": "Just one point at 2."}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Thinks inequality solution is a single point instead of a half - line.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Write the solution to x > 4 in interval notation."}, {"from": "human", "value": "(-, 4]"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Used a bracket instead of a parenthesis; 4 is not included.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Explain what an absolute-value inequality is."}, {"from": "human", "value": "Never heard of that."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Absolute - value inequalities are a new concept for the student.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Identify the slope in y = - 4x + 2."}, {"from": "human", "value": ""}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"No response provided.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Calculate the slope between (2, 7) and (5, 1)."}, {"from": "human", "value": "Slope = ( 1 - 7 ) / ( 5 - 2 ) = - 5 / 3"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Arithmetic slip: numerator is - 6, slope should be - 6 / 3 = - 2.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Two lines are parallel if their slopes multiply to 1-true or false?"}, {"from": "human", "value": "True"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Fundamental misunderstanding: parallel lines have equal slopes, not product 1.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find the slope of a line perpendicular to y = 1 / 2x + 9."}, {"from": "human", "value": "Slope = - 1 / 2"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Only changed sign; should take negative reciprocal ( - 2 ) .\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What makes two lines parallel?"}, {"from": "human", "value": "I'm not familiar with that idea."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Parallel - line criterion is new to the student.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Write an expression for 'the product of 6 and the difference of y and 1'."}, {"from": "human", "value": "6y - 1"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"Concept error: should be 6 ( y - 1 ) ; parentheses around the difference are needed.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: x / 4 = 3."}, {"from": "human", "value": "Multiply both sides by 4"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first move to isolate x.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: 2y + 6 = 14."}, {"from": "human", "value": "y = apple"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"Nonsensical variable value.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: 4a + 2a."}, {"from": "human", "value": "6a^2"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"Misunderstanding of combining like terms - introduced exponent.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Rewrite 'half of the sum of y and 10' as an algebraic expression."}, {"from": "human", "value": "I'm not sure what 'sum' means in algebra."}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"Student doesn't know terminology for algebraic translation.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find f ( 3 ) for f ( x ) = x ^ 2."}, {"from": "human", "value": "9"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User lacks understanding of function evaluation.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Compose f ( x ) = x + 1,g ( x ) = 2x."}, {"from": "human", "value": "f ( g ( x ) ) = 2x + 1"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct composition.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Domain of f ( x ) = 1 / x."}, {"from": "human", "value": "x! = 0"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User forgot to exclude zero.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find inverse of f ( x ) = x - 5."}, {"from": "human", "value": "f ^ { - 1} ( x ) = x + 5"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation error in inverse.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Calculate median of 1,3,5,7,9."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User gave wrong median.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Define inverse function."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User new to inverse concept.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Compute ( fg ) ( x ) for f ( x ) = x + 2,g ( x ) = x - 2."}, {"from": "human", "value": "0"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User doesn't understand composition.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Write explicit formula for geometric sequence 3,6,12."}, {"from": "human", "value": "an = 3 * 2 ^ ( n - 1 )"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct formula.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Evaluate g ( f ( x ) ) for f = x + 2,g = x ^ 2."}, {"from": "human", "value": "g ( f ( x ) ) = x ^ 2 + 4"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation error expanding.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Define outlier."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User gave unrelated definition.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: (x^2-1)/(x-1)."}, {"from": "human", "value": "x+1"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation mistake in factoring.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: ( x + 2 ) = 5."}, {"from": "human", "value": "x = 23"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct solution.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Rationalize: 1/2."}, {"from": "human", "value": "2/2"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User did denominator rationalization wrong.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Explain axis of symmetry."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User unaware of axis of symmetry.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: ( x + 3 ) / ( x - 3 ) = 2."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User gave invalid solution.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Rationalize: 5/(x)."}, {"from": "human", "value": "5x/x"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User missing denominator term.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Explain axis of symmetry."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User unaware of axis of symmetry.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Multiply: (3/x)(x/6)."}, {"from": "human", "value": "1/2"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation mistake multiplying fractions.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve using quadratic formula: x ^ 2 + 2x - 3 = 0."}, {"from": "human", "value": "x = 1"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User used formula but dropped one solution.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: 1/(x+1) + x."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User combined inapplicable terms.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Rationalize: 1/(x +1)."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation mistake in conjugate.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What is the vertex of a quadratic?"}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User does not know vertex definition.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Add: 1/x + 1/x."}, {"from": "human", "value": "2/x^2"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User added denominators instead of creating common denominator.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: (16)."}, {"from": "human", "value": "4"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct simplification.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: 1 / ( x - 3 ) = 0."}, {"from": "human", "value": "x = 0"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User misinterpreted equation.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: x - 2y = 0 and 4x + y = 9."}, {"from": "human", "value": "x = 1,y = 2"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Arithmetic mistake solving for y.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Convert 0.03e2."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User misapplied scientific notation.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Factor: x^2+5x+6."}, {"from": "human", "value": "(x+2)(x+3)"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct factoring.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Factor: x^2+5x+6."}, {"from": "human", "value": "x(x+5)+6"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User applied grouping incorrectly.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Explain trinomial."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User unaware of trinomial concept.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: x - y = 2, 2x - 2y = 5."}, {"from": "human", "value": "x = 2.5,y = 0.5"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User lacks understanding of solution consistency.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: x + y = 5, 2x + 2y = 10."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User wrote same equation twice.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Graph: y = 2x and y = x + 1, find intersection."}, {"from": "human", "value": "(1,3)"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct intersection.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Determine solution of system with parallel lines."}, {"from": "human", "value": "Infinite"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User confused parallel with infinite solutions.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Define zero exponent rule."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User unfamiliar with exponent laws.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What is the substitution method?"}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User does not know substitution method.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Explain half-life."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User gave unrelated concept.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: x^0."}, {"from": "human", "value": "0"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User lacks understanding that x ^ 0 = 1.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Convert 1.2e3 to standard."}, {"from": "human", "value": "120"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation mistake moving decimal.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: 2x + y = 5 and 4x + 2y = 10."}, {"from": "human", "value": "Infinite solutions"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: dependent system.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Solve: x+5>8."}, {"from": "human", "value": "x>2"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Calculation error: 8 - 5 = 2 instead of 3.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Translate: 'twice a number plus seven'."}, {"from": "human", "value": "x*2 + 7"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User used multiplication symbol incorrectly.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What is the slope of y = 2x + 3?"}, {"from": "human", "value": "2"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct slope.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: 3(x + 2)."}, {"from": "human", "value": "3x + 2"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User omitted distribution step.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Graph - 3 < = x < 2."}, {"from": "human", "value": "x> -3 and x<2"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User misread inclusive bounds.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Write equation for slope 1/2 and intercept -2."}, {"from": "human", "value": "y = 2x - 2"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Arithmetic error using fraction.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find intercepts of 2x + 3y = 12."}, {"from": "human", "value": "x = 6,y = 4"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User swapped intercept values.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Graph line y = 5x + 1, identify intercept."}, {"from": "human", "value": "x = 1"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User confused intercept types.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Translate: 'x is at most 3'."}, {"from": "human", "value": "x<3"}, {"from": "gpt", "value": "{\"error\": 5, \"info\": \"User wrote < instead of.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "What does it mean to isolate a variable?"}, {"from": "human", "value": "to get x alone"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"The user appears new to solving equations.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find slope of horizontal line."}, {"from": "human", "value": "0"}, {"from": "gpt", "value": "{\"error\": 3, \"info\": \"User doesn't understand horizontal line slope.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Define inequality."}, {"from": "human", "value": "N/A"}, {"from": "gpt", "value": "{\"error\": 1, \"info\": \"User doesn't know inequality meaning.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find slope of y = 4x - 1."}, {"from": "human", "value": "x = 4"}, {"from": "gpt", "value": "{\"error\": 2, \"info\": \"User mixed variable and coefficient.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Find slope from (0,5) and (5,0)."}, {"from": "human", "value": "-1"}, {"from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct slope.\"}"}]}
+{"conversations": [{"from": "gpt", "value": "Simplify: 6y - 4y."}, {"from": "human", "value": "3y"}, {"from": "gpt", "value": "{\"error\": 4, \"info\": \"Arithmetic mistake in coefficient subtraction.\"}"}]}