yashmahe2018/math-error-classification · Datasets at Hugging Face

conversations listlengths 3 3
[ { "from": "gpt", "value": "Compute mean of 2,4,6,8." }, { "from": "human", "value": "mean = 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct mean.\"}" } ]
[ { "from": "gpt", "value": "Given recursive an = an - 1 + 2,a1 = 5, find a2." }, { "from": "human", "value": "a2 = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct recursion.\"}" } ]
[ { "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.\"}" } ]
[ { "from": "gpt", "value": "Given f ( x ) = 2x + 3, find f ( 2 ) ." }, { "from": "human", "value": "f *( 2 ) = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct evaluation.\"}" } ]
[ { "from": "gpt", "value": "Domain of f *( x ) = 1 / x." }, { "from": "human", "value": "x! = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct domain.\"}" } ]
[ { "from": "gpt", "value": "Find 5th term of arithmetic sequence a1 = 2,d = 3." }, { "from": "human", "value": "a5 = 14" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct term.\"}" } ]
[ { "from": "gpt", "value": "Given recursive an = an - 1 + 2,a1 = 5, find a2." }, { "from": "human", "value": "a2 = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct recursion.\"}" } ]
[ { "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.\"}" } ]
[ { "from": "gpt", "value": "Find inverse of f *( x ) = x + 4." }, { "from": "human", "value": "f ^ { - 1} ( x ) = x - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct inverse.\"}" } ]
[ { "from": "gpt", "value": "Find 5th term of arithmetic sequence a1 = 2,d = 3." }, { "from": "human", "value": "a5 = 14" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct term.\"}" } ]
[ { "from": "gpt", "value": "Find inverse of f *( x ) = x + 4." }, { "from": "human", "value": "f ^ { - 1} ( x ) = x - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct inverse.\"}" } ]
[ { "from": "gpt", "value": "Solve: 5x + 3 = 18." }, { "from": "human", "value": "Subtract 3 from both sides" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first step.\"}" } ]
[ { "from": "gpt", "value": "Translate: 'the sum of n and 12'." }, { "from": "human", "value": "n + 12" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Accurate translation.\"}" } ]
[ { "from": "gpt", "value": "Combine like terms: 6a + 3a." }, { "from": "human", "value": "9a" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct coefficient addition.\"}" } ]
[ { "from": "gpt", "value": "Distribute: 2*(4 - k)." }, { "from": "human", "value": "8 - 2k" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Proper application of distributive property.\"}" } ]
[ { "from": "gpt", "value": "Simplify: -(2y - 5)." }, { "from": "human", "value": "-2y + 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Signs flipped correctly.\"}" } ]
[ { "from": "gpt", "value": "Translate: 'three times a number minus 4'." }, { "from": "human", "value": "3x - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct algebraic expression.\"}" } ]
[ { "from": "gpt", "value": "Combine constants: 10 - 3 + 2." }, { "from": "human", "value": "9" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification of constants.\"}" } ]
[ { "from": "gpt", "value": "Solve: 2 *( 7 - m ) = 0." }, { "from": "human", "value": "Set 7 - m = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Valid use of zero - product idea.\"}" } ]
[ { "from": "gpt", "value": "Find the slope between (0, 4) and (3, 10)." }, { "from": "human", "value": "Difference in y is 6 and difference in x is 3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct identification of rise and run.\"}" } ]
[ { "from": "gpt", "value": "In y = - 2x + 7, what is b?" }, { "from": "human", "value": "7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct y - intercept.\"}" } ]
[ { "from": "gpt", "value": "Given y - 5 = - 4 *( x - 2 ) , state the slope." }, { "from": "human", "value": "Slope is -4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct extraction of slope.\"}" } ]
[ { "from": "gpt", "value": "What is the slope of any line parallel to y = 1 / 4x - 3?" }, { "from": "human", "value": "1/4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - parallel lines have equal slopes.\"}" } ]
[ { "from": "gpt", "value": "First step to solve for y in 5x + y = 12?" }, { "from": "human", "value": "Subtract 5x from both sides" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Valid isolation step.\"}" } ]
[ { "from": "gpt", "value": "State the slope of x = 3." }, { "from": "human", "value": "Undefined" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - vertical line slope is undefined.\"}" } ]
[ { "from": "gpt", "value": "Slope of a line perpendicular to y = - 2x + 1?" }, { "from": "human", "value": "1/2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct negative reciprocal of - 2.\"}" } ]
[ { "from": "gpt", "value": "Write point-slope form through (-1, 0) with slope 3." }, { "from": "human", "value": "y - 0 = 3 *( x + 1 )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct point - slope equation.\"}" } ]
[ { "from": "gpt", "value": "Subtract 3 from both sides of x + 3 > 7." }, { "from": "human", "value": "x > 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first step in solving the inequality.\"}" } ]
[ { "from": "gpt", "value": "Divide both sides of -4x < 8 by -4. What is the new inequality?" }, { "from": "human", "value": "x > -2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correctly flipped the symbol after dividing by a negative.\"}" } ]
[ { "from": "gpt", "value": "Express x > 5 in interval notation." }, { "from": "human", "value": "(5, )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct interval notation.\"}" } ]
[ { "from": "gpt", "value": "On a number line for x < -1, should the dot at -1 be open or closed?" }, { "from": "human", "value": "Open dot" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct endpoint style for a strict inequality.\"}" } ]
[ { "from": "gpt", "value": "Split \|x - 3\| < = 4 into two inequalities." }, { "from": "human", "value": "x - 3 < = 4 and x - 3 > = - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct setup for absolute - value < = inequality.\"}" } ]
[ { "from": "gpt", "value": "For y > = 2x - 1, which side of the line should be shaded?" }, { "from": "human", "value": "Above (including the line)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct shading direction and inclusion.\"}" } ]
[ { "from": "gpt", "value": "Combine the solution sets x < -2 or x > 3. How many intervals are there?" }, { "from": "human", "value": "Two disjoint intervals" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct understanding of an OR compound inequality.\"}" } ]
[ { "from": "gpt", "value": "Write interval notation for 1 < = x < = 4." }, { "from": "human", "value": "[1, 4]" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct closed interval notation.\"}" } ]
[ { "from": "gpt", "value": "Convert x < = 0 to interval notation." }, { "from": "human", "value": "(-, 0]" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct interval for x < = 0.\"}" } ]
[ { "from": "gpt", "value": "Add the equations 2x - y = 1 and - 2x + y = 3. What do you notice?" }, { "from": "human", "value": "They cancel to 0 = 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct observation leading to no solution.\"}" } ]
[ { "from": "gpt", "value": "Subtract y = 3x - 2 from y = - x + 6 to set up elimination. What is the resulting equation?" }, { "from": "human", "value": "4x - 8 = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct subtraction: 3x - ( - x ) = 4x and - 2 - 6 = - 8.\"}" ...
[ { "from": "gpt", "value": "First step in solving by substitution: y = x + 1 and 2x + y = 7." }, { "from": "human", "value": "Replace y with x + 1 in 2x + y = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct substitution setup.\"}" } ]
[ { "from": "gpt", "value": "Identify the slopes of y = 2x + 5 and y = 2x - 3." }, { "from": "human", "value": "Both slopes are 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - parallel lines.\"}" } ]
[ { "from": "gpt", "value": "What region satisfies x + y < = 4 and x > = 0 and y > = 0?" }, { "from": "human", "value": "The triangle bounded by axes and the line x + y = 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct description of feasible region.\"}" } ]
[ { "from": "gpt", "value": "Solve 3x - y = 4 & 2x + y = 1 by adding the equations." }, { "from": "human", "value": "5x = 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct elimination step before dividing.\"}" } ]
[ { "from": "gpt", "value": "If a system gives back x = 2, how would you find y using y = x - 3?" }, { "from": "human", "value": "Plug to get y = - 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct substitution result.\"}" } ]
[ { "from": "gpt", "value": "What is the perpendicular slope to x = 4?" }, { "from": "human", "value": "0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - horizontal line slope is 0.\"}" } ]
[ { "from": "gpt", "value": "Simplify: x^3 x^2." }, { "from": "human", "value": "x^5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct application of product rule.\"}" } ]
[ { "from": "gpt", "value": "Simplify: (x^2)^3." }, { "from": "human", "value": "x^6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct use of power rule.\"}" } ]
[ { "from": "gpt", "value": "Express x^(-3) as a fraction." }, { "from": "human", "value": "1/x^3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct negative - exponent conversion.\"}" } ]
[ { "from": "gpt", "value": "What is 7^0?" }, { "from": "human", "value": "1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct zero - exponent result.\"}" } ]
[ { "from": "gpt", "value": "Convert 4.7*10^2 to standard form." }, { "from": "human", "value": "470" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct scientific - notation conversion.\"}" } ]
[ { "from": "gpt", "value": "Factor 6x^2 + 9x." }, { "from": "human", "value": "3x*(2x + 3)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct GCF factorization.\"}" } ]
[ { "from": "gpt", "value": "Factor x^2 - 36." }, { "from": "human", "value": "(x - 6)(x + 6)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct difference - of - squares factorization.\"}" } ]
[ { "from": "gpt", "value": "Expand (2x - 3)(x + 2)." }, { "from": "human", "value": "2x + x - 6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct FOIL and simplification.\"}" } ]
[ { "from": "gpt", "value": "Factor x^2 + 11x + 30." }, { "from": "human", "value": "(x + 5)(x + 6)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct trinomial factorization.\"}" } ]
[ { "from": "gpt", "value": "Expand (x - 2)(x + 7)." }, { "from": "human", "value": "x + 5x - 14" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct multiplication and combination.\"}" } ]
[ { "from": "gpt", "value": "Factor 8x - 18." }, { "from": "human", "value": "2 ( 4x - 9 ) = 2 ( 2x - 3 )*( 2x + 3 )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct multi - step GCF and difference - of - squares factoring.\"}" } ]
[ { "from": "gpt", "value": "Find the square of (3x + 1)." }, { "from": "human", "value": "9x + 6x + 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct binomial square expansion.\"}" } ]
[ { "from": "gpt", "value": "Factor 25 - y." }, { "from": "human", "value": "(5 - y)(5 + y)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct difference of squares.\"}" } ]
[ { "from": "gpt", "value": "Expand (x + 9)(x - 2)." }, { "from": "human", "value": "x + 7x - 18" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct product and simplification.\"}" } ]
[ { "from": "gpt", "value": "Solve x^2 - 4x + 4 = 0 by factoring." }, { "from": "human", "value": "( x - 2 )*( x - 2 ) = 0, x = 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct factoring and solution.\"}" } ]
[ { "from": "gpt", "value": "What is the discriminant of x^2 - 6x + 9." }, { "from": "human", "value": "6 - 419 = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct discriminant calculation.\"}" } ]
[ { "from": "gpt", "value": "Complete the square for x + 6x. Add what?" }, { "from": "human", "value": "( 6 / 2 ) = 9" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct number to complete the square.\"}" } ]
[ { "from": "gpt", "value": "Does y = - x + 2 open upward or downward?" }, { "from": "human", "value": "Downward" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct identification of parabola direction.\"}" } ]
[ { "from": "gpt", "value": "Solve x^2 + 2x - 3 = 0 by factoring." }, { "from": "human", "value": "( x + 3 )*( x - 1 ) = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct factors.\"}" } ]
[ { "from": "gpt", "value": "Find the axis of symmetry for y = 3x^2 - 6x + 1." }, { "from": "human", "value": "x = - ( - 6 ) / ( 23 ) = 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct axis of symmetry.\"}" } ]
[ { "from": "gpt", "value": "Simplify 32." }, { "from": "human", "value": "22222" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification.\"}" } ]
[ { "from": "gpt", "value": "Solve x = 6. Square both sides." }, { "from": "human", "value": "x = 36" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct squaring step.\"}" } ]
[ { "from": "gpt", "value": "Rationalize 3/3." }, { "from": "human", "value": "33 / 3 = 3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct rationalization.\"}" } ]
[ { "from": "gpt", "value": "Simplify: x^4 * x^2." }, { "from": "human", "value": "x^6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct exponent addition.\"}" } ]
[ { "from": "gpt", "value": "Simplify (25x)." }, { "from": "human", "value": "5\|x\|" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification with absolute value.\"}" } ]
[ { "from": "gpt", "value": "Solve x = 3. Cube both sides." }, { "from": "human", "value": "x = 27" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct cubing step.\"}" } ]
[ { "from": "gpt", "value": "Add 12 + 27. Simplify first." }, { "from": "human", "value": "23 + 33 = 53" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct addition of like radicals.\"}" } ]
[ { "from": "gpt", "value": "Solve ( x + 2 ) = 5. Square both sides." }, { "from": "human", "value": "x + 2 = 25" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct squaring step.\"}" } ]
[ { "from": "gpt", "value": "Simplify (x - 1)/(x + 1)." }, { "from": "human", "value": "x - 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification with cancellation.\"}" } ]
[ { "from": "gpt", "value": "Solve 1 / ( x - 2 ) = 3. Multiply by ( x - 2 ) ." }, { "from": "human", "value": "1 = 3 *( x - 2 )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct multiplication step.\"}" } ]
[ { "from": "gpt", "value": "Find the vertical asymptote of y = 1 / ( x + 4 ) ." }, { "from": "human", "value": "x = - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct asymptote identification.\"}" } ]
[ { "from": "gpt", "value": "Add (2/x) + (3/x). Combine terms." }, { "from": "human", "value": "5/x" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct addition with common denominator.\"}" } ]
[ { "from": "gpt", "value": "Simplify (x - 16)/(x - 4). Factor numerator." }, { "from": "human", "value": "(x - 4)(x + 4)/(x - 4)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct factoring step.\"}" } ]
[ { "from": "gpt", "value": "Divide (x/2) / (x/4). Rewrite as multiplication." }, { "from": "human", "value": "(x/2)*(4/x)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct reciprocal step.\"}" } ]
[ { "from": "gpt", "value": "Solve ( x - 1 ) / ( x + 2 ) = 0. Set numerator to zero." }, { "from": "human", "value": "x - 1 = 0, x = 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct numerator step.\"}" } ]
[ { "from": "gpt", "value": "Simplify 2^4 2^3." }, { "from": "human", "value": "2 ^ 7 = 128" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct exponent addition and evaluation.\"}" } ]
[ { "from": "gpt", "value": "Solve 3 ^ x = 9. Rewrite 9." }, { "from": "human", "value": "9 = 3 ^ 2, so x = 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct base matching.\"}" } ]
[ { "from": "gpt", "value": "Evaluate y = 2 ^ x for x = 0." }, { "from": "human", "value": "2 ^ 0 = 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct evaluation.\"}" } ]
[ { "from": "gpt", "value": "Simplify (5^2)^3." }, { "from": "human", "value": "5^6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct power rule application.\"}" } ]
[ { "from": "gpt", "value": "Find the horizontal asymptote of y = 3 ^ x + 5." }, { "from": "human", "value": "y = 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct asymptote identification.\"}" } ]
[ { "from": "gpt", "value": "Rewrite 2^-3." }, { "from": "human", "value": "1 / 2 ^ 3 = 1 / 8" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct negative exponent simplification.\"}" } ]
[ { "from": "gpt", "value": "Is y = 0.8 ^ x growth or decay?" }, { "from": "human", "value": "Decay" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct identification of decay.\"}" } ]
[ { "from": "gpt", "value": "Solve 4 ^ ( x + 1 ) = 16. Rewrite 16." }, { "from": "human", "value": "16 = 4 ^ 2, x + 1 = 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct base matching step.\"}" } ]
[ { "from": "gpt", "value": "Simplify 3^5 / 3^2." }, { "from": "human", "value": "3 ^ 3 = 27" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct exponent subtraction.\"}" } ]
[ { "from": "gpt", "value": "Find the y - intercept of y = 2 ^ x - 3." }, { "from": "human", "value": "y = 2 ^ 0 - 3 = - 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct y - intercept calculation.\"}" } ]
[ { "from": "gpt", "value": "Find the mean of 5, 10, 15." }, { "from": "human", "value": "( 5 + 10 + 15 ) / 3 = 10" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct mean calculation.\"}" } ]
[ { "from": "gpt", "value": "Calculate P(4) for a die roll." }, { "from": "human", "value": "1/6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct probability calculation.\"}" } ]
[ { "from": "gpt", "value": "Find the median of 2, 4, 6, 8, 10." }, { "from": "human", "value": "6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct median identification.\"}" } ]
[ { "from": "gpt", "value": "Compute 4C2." }, { "from": "human", "value": "( 4 * 3 ) / ( 2 * 1 ) = 6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct combination calculation.\"}" } ]
[ { "from": "gpt", "value": "Find the range of 1, 3, 5, 7." }, { "from": "human", "value": "7 - 1 = 6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct range calculation.\"}" } ]
[ { "from": "gpt", "value": "If P ( A ) = 0.5, P ( B ) = 0.4, independent, find P ( A and B ) ." }, { "from": "human", "value": "0.5 * 0.4 = 0.2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct independent event probability.\"}" } ]
[ { "from": "gpt", "value": "Find Q1 for 1, 3, 5, 7, 9." }, { "from": "human", "value": "3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first quartile identification.\"}" } ]
[ { "from": "gpt", "value": "Are events A and B mutually exclusive if P ( A and B ) = 0?" }, { "from": "human", "value": "Yes" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct mutually exclusive identification.\"}" } ]
[ { "from": "gpt", "value": "Find the IQR of 2, 4, 6, 8, 10." }, { "from": "human", "value": "Q3 - Q1 = 8 - 4 = 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct interquartile range calculation.\"}" } ]
[ { "from": "gpt", "value": "Calculate 5P3." }, { "from": "human", "value": "5 * 4 * 3 = 60" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct permutation calculation.\"}" } ]
[ { "from": "gpt", "value": "Find the median of 1, 2, 3, 4, 5." }, { "from": "human", "value": "3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct median identification.\"}" } ]

[ { "from": "gpt", "value": "Compute mean of 2,4,6,8." }, { "from": "human", "value": "mean = 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct mean.\"}" } ]

[ { "from": "gpt", "value": "Given recursive an = an - 1 + 2,a1 = 5, find a2." }, { "from": "human", "value": "a2 = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct recursion.\"}" } ]

[ { "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.\"}" } ]

[ { "from": "gpt", "value": "Given f *( x ) = 2x + 3, find f *( 2 ) ." }, { "from": "human", "value": "f *( 2 ) = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct evaluation.\"}" } ]

[ { "from": "gpt", "value": "Domain of f *( x ) = 1 / x." }, { "from": "human", "value": "x! = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct domain.\"}" } ]

[ { "from": "gpt", "value": "Find 5th term of arithmetic sequence a1 = 2,d = 3." }, { "from": "human", "value": "a5 = 14" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct term.\"}" } ]

[ { "from": "gpt", "value": "Given recursive an = an - 1 + 2,a1 = 5, find a2." }, { "from": "human", "value": "a2 = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct recursion.\"}" } ]

[ { "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.\"}" } ]

[ { "from": "gpt", "value": "Find inverse of f *( x ) = x + 4." }, { "from": "human", "value": "f ^ { - 1} ( x ) = x - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct inverse.\"}" } ]

[ { "from": "gpt", "value": "Find 5th term of arithmetic sequence a1 = 2,d = 3." }, { "from": "human", "value": "a5 = 14" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct term.\"}" } ]

[ { "from": "gpt", "value": "Find inverse of f *( x ) = x + 4." }, { "from": "human", "value": "f ^ { - 1} ( x ) = x - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"No error: correct inverse.\"}" } ]

[ { "from": "gpt", "value": "Solve: 5x + 3 = 18." }, { "from": "human", "value": "Subtract 3 from both sides" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first step.\"}" } ]

[ { "from": "gpt", "value": "Translate: 'the sum of n and 12'." }, { "from": "human", "value": "n + 12" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Accurate translation.\"}" } ]

[ { "from": "gpt", "value": "Combine like terms: 6a + 3a." }, { "from": "human", "value": "9a" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct coefficient addition.\"}" } ]

[ { "from": "gpt", "value": "Distribute: 2*(4 - k)." }, { "from": "human", "value": "8 - 2k" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Proper application of distributive property.\"}" } ]

[ { "from": "gpt", "value": "Simplify: -(2y - 5)." }, { "from": "human", "value": "-2y + 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Signs flipped correctly.\"}" } ]

[ { "from": "gpt", "value": "Translate: 'three times a number minus 4'." }, { "from": "human", "value": "3x - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct algebraic expression.\"}" } ]

[ { "from": "gpt", "value": "Combine constants: 10 - 3 + 2." }, { "from": "human", "value": "9" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification of constants.\"}" } ]

[ { "from": "gpt", "value": "Solve: 2 *( 7 - m ) = 0." }, { "from": "human", "value": "Set 7 - m = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Valid use of zero - product idea.\"}" } ]

[ { "from": "gpt", "value": "Find the slope between (0, 4) and (3, 10)." }, { "from": "human", "value": "Difference in y is 6 and difference in x is 3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct identification of rise and run.\"}" } ]

[ { "from": "gpt", "value": "In y = - 2x + 7, what is b?" }, { "from": "human", "value": "7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct y - intercept.\"}" } ]

[ { "from": "gpt", "value": "Given y - 5 = - 4 *( x - 2 ) , state the slope." }, { "from": "human", "value": "Slope is -4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct extraction of slope.\"}" } ]

[ { "from": "gpt", "value": "What is the slope of any line parallel to y = 1 / 4x - 3?" }, { "from": "human", "value": "1/4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - parallel lines have equal slopes.\"}" } ]

[ { "from": "gpt", "value": "First step to solve for y in 5x + y = 12?" }, { "from": "human", "value": "Subtract 5x from both sides" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Valid isolation step.\"}" } ]

[ { "from": "gpt", "value": "State the slope of x = 3." }, { "from": "human", "value": "Undefined" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - vertical line slope is undefined.\"}" } ]

[ { "from": "gpt", "value": "Slope of a line perpendicular to y = - 2x + 1?" }, { "from": "human", "value": "1/2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct negative reciprocal of - 2.\"}" } ]

[ { "from": "gpt", "value": "Write point-slope form through (-1, 0) with slope 3." }, { "from": "human", "value": "y - 0 = 3 *( x + 1 )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct point - slope equation.\"}" } ]

[ { "from": "gpt", "value": "Subtract 3 from both sides of x + 3 > 7." }, { "from": "human", "value": "x > 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first step in solving the inequality.\"}" } ]

[ { "from": "gpt", "value": "Divide both sides of -4x < 8 by -4. What is the new inequality?" }, { "from": "human", "value": "x > -2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correctly flipped the symbol after dividing by a negative.\"}" } ]

[ { "from": "gpt", "value": "Express x > 5 in interval notation." }, { "from": "human", "value": "(5, )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct interval notation.\"}" } ]

[ { "from": "gpt", "value": "On a number line for x < -1, should the dot at -1 be open or closed?" }, { "from": "human", "value": "Open dot" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct endpoint style for a strict inequality.\"}" } ]

[ { "from": "gpt", "value": "Split |x - 3| < = 4 into two inequalities." }, { "from": "human", "value": "x - 3 < = 4 and x - 3 > = - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct setup for absolute - value < = inequality.\"}" } ]

[ { "from": "gpt", "value": "For y > = 2x - 1, which side of the line should be shaded?" }, { "from": "human", "value": "Above (including the line)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct shading direction and inclusion.\"}" } ]

[ { "from": "gpt", "value": "Combine the solution sets x < -2 or x > 3. How many intervals are there?" }, { "from": "human", "value": "Two disjoint intervals" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct understanding of an OR compound inequality.\"}" } ]

[ { "from": "gpt", "value": "Write interval notation for 1 < = x < = 4." }, { "from": "human", "value": "[1, 4]" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct closed interval notation.\"}" } ]

[ { "from": "gpt", "value": "Convert x < = 0 to interval notation." }, { "from": "human", "value": "(-, 0]" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct interval for x < = 0.\"}" } ]

[ { "from": "gpt", "value": "Add the equations 2x - y = 1 and - 2x + y = 3. What do you notice?" }, { "from": "human", "value": "They cancel to 0 = 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct observation leading to no solution.\"}" } ]

[ { "from": "gpt", "value": "Subtract y = 3x - 2 from y = - x + 6 to set up elimination. What is the resulting equation?" }, { "from": "human", "value": "4x - 8 = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct subtraction: 3x - ( - x ) = 4x and - 2 - 6 = - 8.\"}" ...

[ { "from": "gpt", "value": "First step in solving by substitution: y = x + 1 and 2x + y = 7." }, { "from": "human", "value": "Replace y with x + 1 in 2x + y = 7" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct substitution setup.\"}" } ]

[ { "from": "gpt", "value": "Identify the slopes of y = 2x + 5 and y = 2x - 3." }, { "from": "human", "value": "Both slopes are 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - parallel lines.\"}" } ]

[ { "from": "gpt", "value": "What region satisfies x + y < = 4 and x > = 0 and y > = 0?" }, { "from": "human", "value": "The triangle bounded by axes and the line x + y = 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct description of feasible region.\"}" } ]

[ { "from": "gpt", "value": "Solve 3x - y = 4 & 2x + y = 1 by adding the equations." }, { "from": "human", "value": "5x = 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct elimination step before dividing.\"}" } ]

[ { "from": "gpt", "value": "If a system gives back x = 2, how would you find y using y = x - 3?" }, { "from": "human", "value": "Plug to get y = - 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct substitution result.\"}" } ]

[ { "from": "gpt", "value": "What is the perpendicular slope to x = 4?" }, { "from": "human", "value": "0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct - horizontal line slope is 0.\"}" } ]

[ { "from": "gpt", "value": "Simplify: x^3 x^2." }, { "from": "human", "value": "x^5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct application of product rule.\"}" } ]

[ { "from": "gpt", "value": "Simplify: (x^2)^3." }, { "from": "human", "value": "x^6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct use of power rule.\"}" } ]

[ { "from": "gpt", "value": "Express x^(-3) as a fraction." }, { "from": "human", "value": "1/x^3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct negative - exponent conversion.\"}" } ]

[ { "from": "gpt", "value": "What is 7^0?" }, { "from": "human", "value": "1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct zero - exponent result.\"}" } ]

[ { "from": "gpt", "value": "Convert 4.7*10^2 to standard form." }, { "from": "human", "value": "470" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct scientific - notation conversion.\"}" } ]

[ { "from": "gpt", "value": "Factor 6x^2 + 9x." }, { "from": "human", "value": "3x*(2x + 3)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct GCF factorization.\"}" } ]

[ { "from": "gpt", "value": "Factor x^2 - 36." }, { "from": "human", "value": "(x - 6)(x + 6)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct difference - of - squares factorization.\"}" } ]

[ { "from": "gpt", "value": "Expand (2x - 3)(x + 2)." }, { "from": "human", "value": "2x + x - 6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct FOIL and simplification.\"}" } ]

[ { "from": "gpt", "value": "Factor x^2 + 11x + 30." }, { "from": "human", "value": "(x + 5)(x + 6)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct trinomial factorization.\"}" } ]

[ { "from": "gpt", "value": "Expand (x - 2)(x + 7)." }, { "from": "human", "value": "x + 5x - 14" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct multiplication and combination.\"}" } ]

[ { "from": "gpt", "value": "Factor 8x - 18." }, { "from": "human", "value": "2 *( 4x - 9 ) = 2 *( 2x - 3 )*( 2x + 3 )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct multi - step GCF and difference - of - squares factoring.\"}" } ]

[ { "from": "gpt", "value": "Find the square of (3x + 1)." }, { "from": "human", "value": "9x + 6x + 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct binomial square expansion.\"}" } ]

[ { "from": "gpt", "value": "Factor 25 - y." }, { "from": "human", "value": "(5 - y)(5 + y)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct difference of squares.\"}" } ]

[ { "from": "gpt", "value": "Expand (x + 9)(x - 2)." }, { "from": "human", "value": "x + 7x - 18" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct product and simplification.\"}" } ]

[ { "from": "gpt", "value": "Solve x^2 - 4x + 4 = 0 by factoring." }, { "from": "human", "value": "( x - 2 )*( x - 2 ) = 0, x = 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct factoring and solution.\"}" } ]

[ { "from": "gpt", "value": "What is the discriminant of x^2 - 6x + 9." }, { "from": "human", "value": "6 - 419 = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct discriminant calculation.\"}" } ]

[ { "from": "gpt", "value": "Complete the square for x + 6x. Add what?" }, { "from": "human", "value": "( 6 / 2 ) = 9" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct number to complete the square.\"}" } ]

[ { "from": "gpt", "value": "Does y = - x + 2 open upward or downward?" }, { "from": "human", "value": "Downward" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct identification of parabola direction.\"}" } ]

[ { "from": "gpt", "value": "Solve x^2 + 2x - 3 = 0 by factoring." }, { "from": "human", "value": "( x + 3 )*( x - 1 ) = 0" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct factors.\"}" } ]

[ { "from": "gpt", "value": "Find the axis of symmetry for y = 3x^2 - 6x + 1." }, { "from": "human", "value": "x = - ( - 6 ) / ( 23 ) = 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct axis of symmetry.\"}" } ]

[ { "from": "gpt", "value": "Simplify 32." }, { "from": "human", "value": "2*2*2*2*2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification.\"}" } ]

[ { "from": "gpt", "value": "Solve x = 6. Square both sides." }, { "from": "human", "value": "x = 36" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct squaring step.\"}" } ]

[ { "from": "gpt", "value": "Rationalize 3/3." }, { "from": "human", "value": "33 / 3 = 3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct rationalization.\"}" } ]

[ { "from": "gpt", "value": "Simplify: x^4 * x^2." }, { "from": "human", "value": "x^6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct exponent addition.\"}" } ]

[ { "from": "gpt", "value": "Simplify (25x)." }, { "from": "human", "value": "5|x|" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification with absolute value.\"}" } ]

[ { "from": "gpt", "value": "Solve x = 3. Cube both sides." }, { "from": "human", "value": "x = 27" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct cubing step.\"}" } ]

[ { "from": "gpt", "value": "Add 12 + 27. Simplify first." }, { "from": "human", "value": "23 + 33 = 53" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct addition of like radicals.\"}" } ]

[ { "from": "gpt", "value": "Solve ( x + 2 ) = 5. Square both sides." }, { "from": "human", "value": "x + 2 = 25" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct squaring step.\"}" } ]

[ { "from": "gpt", "value": "Simplify (x - 1)/(x + 1)." }, { "from": "human", "value": "x - 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct simplification with cancellation.\"}" } ]

[ { "from": "gpt", "value": "Solve 1 / ( x - 2 ) = 3. Multiply by ( x - 2 ) ." }, { "from": "human", "value": "1 = 3 *( x - 2 )" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct multiplication step.\"}" } ]

[ { "from": "gpt", "value": "Find the vertical asymptote of y = 1 / ( x + 4 ) ." }, { "from": "human", "value": "x = - 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct asymptote identification.\"}" } ]

[ { "from": "gpt", "value": "Add (2/x) + (3/x). Combine terms." }, { "from": "human", "value": "5/x" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct addition with common denominator.\"}" } ]

[ { "from": "gpt", "value": "Simplify (x - 16)/(x - 4). Factor numerator." }, { "from": "human", "value": "(x - 4)(x + 4)/(x - 4)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct factoring step.\"}" } ]

[ { "from": "gpt", "value": "Divide (x/2) / (x/4). Rewrite as multiplication." }, { "from": "human", "value": "(x/2)*(4/x)" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct reciprocal step.\"}" } ]

[ { "from": "gpt", "value": "Solve ( x - 1 ) / ( x + 2 ) = 0. Set numerator to zero." }, { "from": "human", "value": "x - 1 = 0, x = 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct numerator step.\"}" } ]

[ { "from": "gpt", "value": "Simplify 2^4 2^3." }, { "from": "human", "value": "2 ^ 7 = 128" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct exponent addition and evaluation.\"}" } ]

[ { "from": "gpt", "value": "Solve 3 ^ x = 9. Rewrite 9." }, { "from": "human", "value": "9 = 3 ^ 2, so x = 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct base matching.\"}" } ]

[ { "from": "gpt", "value": "Evaluate y = 2 ^ x for x = 0." }, { "from": "human", "value": "2 ^ 0 = 1" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct evaluation.\"}" } ]

[ { "from": "gpt", "value": "Simplify (5^2)^3." }, { "from": "human", "value": "5^6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct power rule application.\"}" } ]

[ { "from": "gpt", "value": "Find the horizontal asymptote of y = 3 ^ x + 5." }, { "from": "human", "value": "y = 5" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct asymptote identification.\"}" } ]

[ { "from": "gpt", "value": "Rewrite 2^-3." }, { "from": "human", "value": "1 / 2 ^ 3 = 1 / 8" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct negative exponent simplification.\"}" } ]

[ { "from": "gpt", "value": "Is y = 0.8 ^ x growth or decay?" }, { "from": "human", "value": "Decay" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct identification of decay.\"}" } ]

[ { "from": "gpt", "value": "Solve 4 ^ ( x + 1 ) = 16. Rewrite 16." }, { "from": "human", "value": "16 = 4 ^ 2, x + 1 = 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct base matching step.\"}" } ]

[ { "from": "gpt", "value": "Simplify 3^5 / 3^2." }, { "from": "human", "value": "3 ^ 3 = 27" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct exponent subtraction.\"}" } ]

[ { "from": "gpt", "value": "Find the y - intercept of y = 2 ^ x - 3." }, { "from": "human", "value": "y = 2 ^ 0 - 3 = - 2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct y - intercept calculation.\"}" } ]

[ { "from": "gpt", "value": "Find the mean of 5, 10, 15." }, { "from": "human", "value": "( 5 + 10 + 15 ) / 3 = 10" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct mean calculation.\"}" } ]

[ { "from": "gpt", "value": "Calculate P(4) for a die roll." }, { "from": "human", "value": "1/6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct probability calculation.\"}" } ]

[ { "from": "gpt", "value": "Find the median of 2, 4, 6, 8, 10." }, { "from": "human", "value": "6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct median identification.\"}" } ]

[ { "from": "gpt", "value": "Compute 4C2." }, { "from": "human", "value": "( 4 * 3 ) / ( 2 * 1 ) = 6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct combination calculation.\"}" } ]

[ { "from": "gpt", "value": "Find the range of 1, 3, 5, 7." }, { "from": "human", "value": "7 - 1 = 6" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct range calculation.\"}" } ]

[ { "from": "gpt", "value": "If P ( A ) = 0.5, P ( B ) = 0.4, independent, find P ( A and B ) ." }, { "from": "human", "value": "0.5 * 0.4 = 0.2" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct independent event probability.\"}" } ]

[ { "from": "gpt", "value": "Find Q1 for 1, 3, 5, 7, 9." }, { "from": "human", "value": "3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct first quartile identification.\"}" } ]

[ { "from": "gpt", "value": "Are events A and B mutually exclusive if P ( A and B ) = 0?" }, { "from": "human", "value": "Yes" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct mutually exclusive identification.\"}" } ]

[ { "from": "gpt", "value": "Find the IQR of 2, 4, 6, 8, 10." }, { "from": "human", "value": "Q3 - Q1 = 8 - 4 = 4" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct interquartile range calculation.\"}" } ]

[ { "from": "gpt", "value": "Calculate 5P3." }, { "from": "human", "value": "5 * 4 * 3 = 60" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct permutation calculation.\"}" } ]

[ { "from": "gpt", "value": "Find the median of 1, 2, 3, 4, 5." }, { "from": "human", "value": "3" }, { "from": "gpt", "value": "{\"error\": 6, \"info\": \"Correct median identification.\"}" } ]