bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Recognise and name an identity Which of the following is the most appropriate name for this:\n\\(p-3 \\equiv-(3-p)\\) Equation" }, { "from": "gpt", "value": "Confuses an equation with an identity" } ]
[ { "from": "human", "value": "Recognise and name an identity Which of the following is the most appropriate name for this:\n\\(p-3 \\equiv-(3-p)\\) Expression" }, { "from": "gpt", "value": "\nHas incorrect belief about the meaning of \"expression\"" } ]
[ { "from": "human", "value": "Recognise and name an identity Which of the following is the most appropriate name for this:\n\\(p-3 \\equiv-(3-p)\\) Formula" }, { "from": "gpt", "value": "\nHas incorrect belief about the meaning of \"formula\"" } ]
[ { "from": "human", "value": "Identify the outcomes of a single event This is a fair spinner.\n\nHow many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]() \\( 3 \\)" }, { "from": "gpt", "value": "Confuses all possible outcomes with options available" } ]
[ { "from": "human", "value": "Identify the outcomes of a single event This is a fair spinner.\n\nHow many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]() \\( 1 \\)" }, { "from": "gpt", "value": "Fails to consider all possible outcomes" } ]
[ { "from": "human", "value": "Identify the outcomes of a single event This is a fair spinner.\n\nHow many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]() \\( 1,3 \\) or \\( 5 \\)" }, { "from": "gpt", "value": "Lists outcomes rather than counts how many outcomes" } ]
[ { "from": "human", "value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) Which of the following answers shows a correct expansion of the expression below? \\( (x-2)^{3} \\) \\( x^{3}-8 \\)" }, { "from": "gpt", "value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets" } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Tom and Katie are discussing the output of this 2-step function machine ![A two step function machine with x as the input. The first functions is x5 and the second function says 'subtracted from 8'. The output is blank.]() Tom says the output is \\( \\mathbf{5} \\boldsymbol{x}-\\mathbf{8} \\)\n\nKatie says the output is \\( \\mathbf{8}-\\mathbf{5} \\boldsymbol{x} \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Has not noticed the difference between 'subtract' and 'subtract from'" } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Tom and Katie are discussing the output of this 2-step function machine ![A two step function machine with x as the input. The first functions is x5 and the second function says 'subtracted from 8'. The output is blank.]() Tom says the output is \\( \\mathbf{5} \\boldsymbol{x}-\\mathbf{8} \\)\n\nKatie says the output is \\( \\mathbf{8}-\\mathbf{5} \\boldsymbol{x} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Has not noticed the difference between 'subtract' and 'subtract from'" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer Jamie is counting up in threes. He starts at \\( -14 \\).\n\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -26 \\)" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer Jamie is counting up in threes. He starts at \\( -14 \\).\n\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -29 \\)" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 100 What is \\( \\mathbf{1 6 5 1 . 4 3} \\) rounded to the nearest hundred? \\( 2000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 100 What is \\( \\mathbf{1 6 5 1 . 4 3} \\) rounded to the nearest hundred? \\( 1600 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 100 What is \\( \\mathbf{1 6 5 1 . 4 3} \\) rounded to the nearest hundred? \\( 1650 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Use a protractor to measure angles between 90° and 180° What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]() \\( 15^{\\circ} \\)" }, { "from": "gpt", "value": "Reads the wrong scale on the protractor when measuring obtuse angles" } ]
[ { "from": "human", "value": "Use a protractor to measure angles between 90° and 180° What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]() \\( 0^{\\circ} \\)" }, { "from": "gpt", "value": "Reads 0 on protractor as size of angle when angle is not in usual orientation" } ]
[ { "from": "human", "value": "Use a protractor to measure angles between 90° and 180° What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]() This is not an angle" }, { "from": "gpt", "value": "Thinks angles can only be measured when one line is horizontal" } ]
[ { "from": "human", "value": "Convert fractions to two digit integer percentages Convert this fraction to a percentage\n\\( \\frac{4}{5} \\) \\( 45 \\% \\)" }, { "from": "gpt", "value": "Converts a fraction to a percentage by writing the numerator followed by the denominator" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 n^{2}-9 \\) \\( 6 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 n^{2}-9 \\) \\( 9 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks a term will be a factor" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 n^{2}-9 \\) \\( n \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]
[ { "from": "human", "value": "Mark a point in the second quadrant of a 2D grid having been given its coordinates, where both values are integers Which region describes where \\( \\boldsymbol{x}>\\mathbf{0} \\) and \\( \\boldsymbol{y}<\\mathbf{0} \\) ? ![A set of axis showing all four quadrants. y axis from -3 to 3 and x axis from -3 to 3]() D" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Identify and represent sets using set notation Tom and Katie are discussing the probability spinner\n\nTom says the sample space can be written as: \\( S=\\{5,6\\} \\)\n\nKatie says the sample space can be written as: \\( S=\\{5,5,6,6,6\\} \\)\nWho do you agree with? ![A circle divided into 5 equal sections. 3 of the sections are labelled with a purple number 6. 2 of the sections are labelled with a blue number 5.]() Only Katie" }, { "from": "gpt", "value": "Believes a sample space should show repeated outcomes, not just unique possible outcomes." } ]
[ { "from": "human", "value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation In which region would \\( x=-5.3 \\) belong? ![A Venn diagram made up of two overlapping circles. One circle is labelled x+5.3 is less than or equal to 0 and the other circle is labelled -(5.3+x)/2 is greater than 0.\nA is in the x+5.3 is less than or equal to 0 circle only.\nB is in the overlap of the two circles.\nC is in the -(5.3+x)/2 is great than 0 circle only.\nD is outside both circles.]() B" }, { "from": "gpt", "value": "Believes greater than/less than symbols include end values" } ]
[ { "from": "human", "value": "Convert between kg and tonne \\( 3000 \\mathrm{~kg} \\) is the same as \\( ___ \\) tonnes \\( 30 \\)" }, { "from": "gpt", "value": "Thinks there are 100kg in a tonne" } ]
[ { "from": "human", "value": "Convert between kg and tonne \\( 3000 \\mathrm{~kg} \\) is the same as \\( ___ \\) tonnes \\( 300 \\)" }, { "from": "gpt", "value": "Thinks there are 10kg in a tonne" } ]
[ { "from": "human", "value": "Convert between kg and tonne \\( 3000 \\mathrm{~kg} \\) is the same as \\( ___ \\) tonnes \\( 3000000 \\)" }, { "from": "gpt", "value": "Multiplies rather than divides" } ]
[ { "from": "human", "value": "Calculate the square root of a number What is the square root of sixteen? \\( 8 \\)" }, { "from": "gpt", "value": "Halves when asked to find the square root" } ]
[ { "from": "human", "value": "Calculate the square root of a number What is the square root of sixteen? \\( 32 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and multiplying by 2 or doubling" } ]
[ { "from": "human", "value": "Calculate the square root of a number What is the square root of sixteen? \\( 256 \\)" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\[\n73975\n\\] \\( 80000 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\[\n73975\n\\] \\( 7 \\)" }, { "from": "gpt", "value": "Forgotten placeholders when rounding to significant figures" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\[\n73975\n\\] \\( 74000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Given a situation sketch an appropriate real life graph A taxi company has a \\( £ 1.50 \\) fixed charge and then charges \\( 60 p \\) per mile. Sam correctly sketches a graph to show the cost of different length journeys with the company. Which of the following graphs would best match Sam's sketch? ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive vertical axis and travels horizontally right.]()" }, { "from": "gpt", "value": "Believes a horizontal line can show a constant rate of change" } ]
[ { "from": "human", "value": "Given a situation sketch an appropriate real life graph A taxi company has a \\( £ 1.50 \\) fixed charge and then charges \\( 60 p \\) per mile. Sam correctly sketches a graph to show the cost of different length journeys with the company. Which of the following graphs would best match Sam's sketch? ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at the origin and travels in a straight line right and upwards.]()" }, { "from": "gpt", "value": "Assumes that a graph always starts at the origin" } ]
[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for the curve y = x3 + c Tom and Katie are discussing the table of values for \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 27 \\) \\\\\n\\hline\n\\end{tabular} Tom says the star could be \\( 3 \\).\n\nKatie says the star could be \\( -3 \\).\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Thinks multiplying two or more negative numbers together always gives a positive answer, regardless of how many negative numbers there are in the sum" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p+5)(p-4) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=+1 \\)" }, { "from": "gpt", "value": "Adds instead of multiplying when expanding bracket" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p+5)(p-4) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=+20 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Find 100 less than a given number What number is \\( 100 \\) less than \\( 876,099 ? \\) \\( 876.099 \\)" }, { "from": "gpt", "value": "Divides rather than subtracts when given the command 'less than'" } ]
[ { "from": "human", "value": "Find 100 less than a given number What number is \\( 100 \\) less than \\( 876,099 ? \\) \\( 875,099 \\)" }, { "from": "gpt", "value": "When subtracting a power of 10, subtracts from the wrong column" } ]
[ { "from": "human", "value": "Divide two decimals with a different number of decimal places \\( 50.09 \\div 0.1= \\) \\( 50.009 \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]
[ { "from": "human", "value": "Divide two decimals with a different number of decimal places \\( 50.09 \\div 0.1= \\) \\( 500.09 \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]
[ { "from": "human", "value": "Divide two decimals with a different number of decimal places \\( 50.09 \\div 0.1= \\) \\( 5.009 \\)" }, { "from": "gpt", "value": "Believes dividing by 0.1 is the same as dividing by 10" } ]
[ { "from": "human", "value": "Change decimals of hours into minutes \\( 0.6 \\) hours \\( = _____\\) minutes \\( 6 \\)" }, { "from": "gpt", "value": "Thinks there are 10 minutes in an hour" } ]
[ { "from": "human", "value": "Change decimals of hours into minutes \\( 0.6 \\) hours \\( = _____\\) minutes \\( 60 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]
[ { "from": "human", "value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]() \\( 290^{\\circ} \\)" }, { "from": "gpt", "value": "Incorrectly identifies angles as vertically opposite" } ]
[ { "from": "human", "value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]() \\( 50^{\\circ} \\)" }, { "from": "gpt", "value": "Does not know that angles around a point sum to 360" } ]
[ { "from": "human", "value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]() \\( 45^{\\circ} \\)" }, { "from": "gpt", "value": "Does not know that angles around a point sum to 360" } ]
[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\[\nx+y=8\n\\]\nWhich pair of numbers fits the equation? \\( \\begin{array}{l}x=10 \\\\ y=2\\end{array} \\)" }, { "from": "gpt", "value": "Changes the given operation when substituting" } ]
[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\[\nx+y=8\n\\]\nWhich pair of numbers fits the equation? \\( \\begin{array}{l}x=8 \\\\ y=1\\end{array} \\)" }, { "from": "gpt", "value": "Changes the given operation when substituting" } ]
[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\[\nx+y=8\n\\]\nWhich pair of numbers fits the equation? \\( \\begin{array}{c}x=-8 \\\\ y=1\\end{array} \\)" }, { "from": "gpt", "value": "substitutes incorrectly" } ]
[ { "from": "human", "value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 509,570 \\) ? \\( 50.957 \\)" }, { "from": "gpt", "value": "Divides rather than subtracts when given the command 'less than'" } ]
[ { "from": "human", "value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 509,570 \\) ? \\( 409,570 \\)" }, { "from": "gpt", "value": "When subtracting a power of 10, subtracts from the wrong column" } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-x+3 y\\) \\( 5 x+5 y \\)" }, { "from": "gpt", "value": "When collecting like terms, assigns positivity or negativity incorrectly." } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-x+3 y\\) \\( 7 x+5 y \\)" }, { "from": "gpt", "value": "When collecting like terms, treats subtractions as if they are additions" } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-x+3 y\\) \\( 7 x+y \\)" }, { "from": "gpt", "value": "When collecting like terms, assigns positivity or negativity incorrectly." } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables Simplify the following by collecting like terms. \\( \\frac{2}{3} k^{2}+\\frac{1}{6} k^{2}-\\frac{1}{3} k^{2}+\\frac{5}{6} k^{2} \\) \\( 2 k^{2} \\)" }, { "from": "gpt", "value": "When collecting like terms, assigns positivity or negativity incorrectly." } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables Simplify the following by collecting like terms. \\( \\frac{2}{3} k^{2}+\\frac{1}{6} k^{2}-\\frac{1}{3} k^{2}+\\frac{5}{6} k^{2} \\) \\( \\frac{1}{3} k^{2}+k^{2} \\)" }, { "from": "gpt", "value": "Does not think that a variable with no coefficient has a coefficient of 1." } ]
[ { "from": "human", "value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\[\n2, \\quad 0.2, \\quad 0.02, \\quad 0.002\n\\] \\( 0.22 \\)" }, { "from": "gpt", "value": "When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle" } ]
[ { "from": "human", "value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\[\n2, \\quad 0.2, \\quad 0.02, \\quad 0.002\n\\] \\( 0.44 \\)" }, { "from": "gpt", "value": "Does not divide by 2 when finding midpoint" } ]
[ { "from": "human", "value": "Identify the mode from a frequency table This table shows the ages of people on a university running team.\n\nWhat is the modal age? \\begin{tabular}{\|c\|c\|l\|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} \\( 19.5 \\)" }, { "from": "gpt", "value": "Finds the median instead of the mode" } ]
[ { "from": "human", "value": "Identify the mode from a frequency table This table shows the ages of people on a university running team.\n\nWhat is the modal age? \\begin{tabular}{\|c\|c\|l\|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} \\( 7 \\)" }, { "from": "gpt", "value": "Believes the mode is the frequency rather than the value/group" } ]
[ { "from": "human", "value": "Identify the mode from a frequency table This table shows the ages of people on a university running team.\n\nWhat is the modal age? \\begin{tabular}{\|c\|c\|l\|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} \\( 21 \\)" }, { "from": "gpt", "value": "Believes when identifying the mode you look at all values, not just frequencies, for the highest number" } ]
[ { "from": "human", "value": "Multiply 2 digit integers by 2 digit integers using long multiplication \\( \\begin{array}{r}\\quad58 \\\\ \\times 22 \\\\ \\hline\\end{array} \\) What number will be in the ones/units column of the final answer? \\( 0 \\)" }, { "from": "gpt", "value": "Has treated this like an addition problem and added the ones column." } ]
[ { "from": "human", "value": "Multiply 2 digit integers by 2 digit integers using long multiplication \\( \\begin{array}{r}\\quad58 \\\\ \\times 22 \\\\ \\hline\\end{array} \\) What number will be in the ones/units column of the final answer? \\( 1 \\)" }, { "from": "gpt", "value": "Has written the value of the 'ones' column as the answer, withiut using the numbers in the question." } ]
[ { "from": "human", "value": "Write numbers greater than 1 in standard form \\[\n300200\n\\]\nWrite this number using standard form \\( 3.2 \\times 10^{5} \\)" }, { "from": "gpt", "value": "When changing a number to standard form omits zero's of significance " } ]
[ { "from": "human", "value": "Write numbers greater than 1 in standard form \\[\n300200\n\\]\nWrite this number using standard form \\( 3.002 \\times 10^{6} \\)" }, { "from": "gpt", "value": "When writing standard form does not give the correct power of ten" } ]
[ { "from": "human", "value": "Write numbers greater than 1 in standard form \\[\n300200\n\\]\nWrite this number using standard form \\( 3.2 \\times 10^{6} \\)" }, { "from": "gpt", "value": "When changing a number to standard form omits zero's of significance " } ]
[ { "from": "human", "value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative What is the midpoint of \\( (4,3) \\) and \\( (1,-5) \\) ? \\( (5,-2) \\)" }, { "from": "gpt", "value": "Does not divide by 2 when finding midpoint" } ]
[ { "from": "human", "value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative What is the midpoint of \\( (4,3) \\) and \\( (1,-5) \\) ? Impossible as you can't have a decimal coordinate" }, { "from": "gpt", "value": "Does not understand that coordinates can be decimals" } ]
[ { "from": "human", "value": "Generate an ascending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n4 n+3\n\\] \\( 4 \\)" }, { "from": "gpt", "value": "When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n." } ]
[ { "from": "human", "value": "Generate an ascending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n4 n+3\n\\] \\( 3 \\)" }, { "from": "gpt", "value": "Thinks the first term in a sequence is the term before the sequence begins (0th term)" } ]
[ { "from": "human", "value": "Divide algebraic fractions involving non-linear expressions STEP \\( 3 \\)\n\nWhich of the options is the final answer, expressed as simply as possible?\n\\(\n\\begin{aligned}\n& \\frac{3 x+1}{3} \\div \\frac{9 x^{2}-1}{12} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{9 x^{2}-1} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{(3 x-1)(3 x+1)}\n\\end{aligned}\n\\) \\( \\frac{12}{9 x-1} \\)" }, { "from": "gpt", "value": "Only applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction" } ]
[ { "from": "human", "value": "Divide algebraic fractions involving non-linear expressions STEP \\( 3 \\)\n\nWhich of the options is the final answer, expressed as simply as possible?\n\\(\n\\begin{aligned}\n& \\frac{3 x+1}{3} \\div \\frac{9 x^{2}-1}{12} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{9 x^{2}-1} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{(3 x-1)(3 x+1)}\n\\end{aligned}\n\\) \\( \\frac{4(3 x+1)}{(3 x-1)(3 x+1)} \\)" }, { "from": "gpt", "value": "When simplifying an algebraic fraction, only looks for number factors" } ]
[ { "from": "human", "value": "Divide algebraic fractions involving non-linear expressions STEP \\( 3 \\)\n\nWhich of the options is the final answer, expressed as simply as possible?\n\\(\n\\begin{aligned}\n& \\frac{3 x+1}{3} \\div \\frac{9 x^{2}-1}{12} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{9 x^{2}-1} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{(3 x-1)(3 x+1)}\n\\end{aligned}\n\\) \\( \\frac{5}{3 x} \\)" }, { "from": "gpt", "value": "Simplifies a fraction by adding or subtracting the same amount from the numerator and denominator" } ]
[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Julie wants to estimate the answer to this calculation by rounding each number to \\( 1 \\) significant figure.\n\n\\[\n87.4 \\times 0.3727\n\\]\n\nWhat number should replace \\( \\mathbf{8 7 . 4} \\) in her estimation? \\( 87 \\)" }, { "from": "gpt", "value": "Rounded to wrong degree of accuracy (2sf not 1sf)" } ]
[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Julie wants to estimate the answer to this calculation by rounding each number to \\( 1 \\) significant figure.\n\n\\[\n87.4 \\times 0.3727\n\\]\n\nWhat number should replace \\( \\mathbf{8 7 . 4} \\) in her estimation? \\( 88 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Julie wants to estimate the answer to this calculation by rounding each number to \\( 1 \\) significant figure.\n\n\\[\n87.4 \\times 0.3727\n\\]\n\nWhat number should replace \\( \\mathbf{8 7 . 4} \\) in her estimation? \\( 80 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+5 p+6\n\\) \\( (p+6)(p+1) \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+5 p+6\n\\) \\( (p+6)(p-1) \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x" } ]
[ { "from": "human", "value": "Given information about one part, work out other parts Josh and Lucy share some money in the ratio \\( 3: 7 \\)\n\nJosh receives \\( £ 84 \\).\n\nHow much money does Lucy receive? \\( £ 58.80 \\)" }, { "from": "gpt", "value": "In ratio question where one side of ratio is given, treats that as the total" } ]
[ { "from": "human", "value": "Given information about one part, work out other parts Josh and Lucy share some money in the ratio \\( 3: 7 \\)\n\nJosh receives \\( £ 84 \\).\n\nHow much money does Lucy receive? \\( £ 28 \\)" }, { "from": "gpt", "value": "Finds one part of a ratio but doesn't multiply that by the number of parts needed" } ]
[ { "from": "human", "value": "Given information about one part, work out other parts Josh and Lucy share some money in the ratio \\( 3: 7 \\)\n\nJosh receives \\( £ 84 \\).\n\nHow much money does Lucy receive? \\( £ 36 \\)" }, { "from": "gpt", "value": "Gets order of ratio wrong" } ]
[ { "from": "human", "value": "Order negative decimals with the same number of digits Here are the depths below sea level of \\( 3 \\) creatures:\nTuna: \\( -2.6 m \\)\nRay: \\( -6 m \\)\nLing: \\( -1.5 \\mathrm{~m} \\)\nArrange their depths in ascending order, starting with the deepest \\( 1^{\\text {st }} \\) Tuna\n\\( 2^{\\text {nd }} \\) Ling\n\\( 3^{\\text {rd }} \\) Ray" }, { "from": "gpt", "value": "Thinks the more digits a number has the greater it is, regardless of place value" } ]
[ { "from": "human", "value": "Order negative decimals with the same number of digits Here are the depths below sea level of \\( 3 \\) creatures:\nTuna: \\( -2.6 m \\)\nRay: \\( -6 m \\)\nLing: \\( -1.5 \\mathrm{~m} \\)\nArrange their depths in ascending order, starting with the deepest \\( \\begin{array}{l}1^{\\text {st }} \\text { Ling } \\\\ 2^{\\text {nd }} \\text { Tuna } \\\\ 3^{\\text {rd }} \\text { Ray }\\end{array} \\)" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]
[ { "from": "human", "value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Amy is trying to work out the distance between these two points: \\( (2,-5) \\) and \\( (-7,1) \\) She labels them like this: \\( \\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (2, & -5) & (-7, & 1)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) What does the first bracket equal? \\( (-5)^{2} \\)" }, { "from": "gpt", "value": "When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored " } ]
[ { "from": "human", "value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Amy is trying to work out the distance between these two points: \\( (2,-5) \\) and \\( (-7,1) \\) She labels them like this: \\( \\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (2, & -5) & (-7, & 1)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) What does the first bracket equal? \\( (9)^{2} \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]
[ { "from": "human", "value": "Calculate the mean as an average from a list of data What is the mean of this set of data?\n\\[\n5, \\quad 2, \\quad 0, \\quad 2, \\quad 3\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "When asked for the mean of a list of data, gives the mode" } ]
[ { "from": "human", "value": "Calculate the mean as an average from a list of data What is the mean of this set of data?\n\\[\n5, \\quad 2, \\quad 0, \\quad 2, \\quad 3\n\\] \\( 3 \\)" }, { "from": "gpt", "value": "When asked for the mean of a list of data, does not count any zeros in the data when working out what to divide by" } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2(a-5)\\) " }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\(a \\Rightarrow -5 \\Rightarrow \\times2\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow -5 \\Rightarrow \\times2\\Rightarrow 2(a-5)\\) " }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\(a \\Rightarrow -5 \\Rightarrow \\times2 \\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2(a-5)\\) " }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "Recall the formulae for the trigonometric ratios \\(\n\\bigstar=\\frac{\\text { Hypotenuse }}{\\text { Opposite }}\n\\)\n\nWhat should replace the star? \\( \\sin (\\theta) \\)" }, { "from": "gpt", "value": "Confuses order of sides in a trigonometric ratio" } ]
[ { "from": "human", "value": "Recall the formulae for the trigonometric ratios \\(\n\\bigstar=\\frac{\\text { Hypotenuse }}{\\text { Opposite }}\n\\)\n\nWhat should replace the star? \\( \\cos (\\theta) \\)" }, { "from": "gpt", "value": "Uses cos when sin is required" } ]
[ { "from": "human", "value": "Recall the formulae for the trigonometric ratios \\(\n\\bigstar=\\frac{\\text { Hypotenuse }}{\\text { Opposite }}\n\\)\n\nWhat should replace the star? \\( \\tan (\\theta) \\)" }, { "from": "gpt", "value": "Uses tan when sin is required" } ]
[ { "from": "human", "value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable Tom and Katie are discussing this pair of simultaneous equations: \\( \\begin{array}{l}3 x-2 y=15 \\\\ x+2 y=20\\end{array} \\) Tom says if you add the two equations together you will eliminate a variable\n\nKatie says if you subtract the two equations together you will eliminate a variable\n\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Subtracts simultaneous equations when addition is required" } ]
[ { "from": "human", "value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable Tom and Katie are discussing this pair of simultaneous equations: \\( \\begin{array}{l}3 x-2 y=15 \\\\ x+2 y=20\\end{array} \\) Tom says if you add the two equations together you will eliminate a variable\n\nKatie says if you subtract the two equations together you will eliminate a variable\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "When solving simultaneous equations thinks that identical terms in given equations can be eliminated by either adding or subtracting." } ]
[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card \n\\( \\frac{1}{6} \\) of \\( A \\) is \\( 12 \\) \nWhat is \\( \\frac{1}{8} \\) of \\( A \\) ? ![A pink rounded rectangle with a capital A typed inside]() \\( 0.25 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]
[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card \n\\( \\frac{1}{6} \\) of \\( A \\) is \\( 12 \\) \nWhat is \\( \\frac{1}{8} \\) of \\( A \\) ? ![A pink rounded rectangle with a capital A typed inside]() \\( 4 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]
[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card \n\\( \\frac{1}{6} \\) of \\( A \\) is \\( 12 \\) \nWhat is \\( \\frac{1}{8} \\) of \\( A \\) ? ![A pink rounded rectangle with a capital A typed inside]() \\( 72 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]

[ { "from": "human", "value": "Recognise and name an identity Which of the following is the most appropriate name for this:\n\\(p-3 \\equiv-(3-p)\\) Equation" }, { "from": "gpt", "value": "Confuses an equation with an identity" } ]

[ { "from": "human", "value": "Recognise and name an identity Which of the following is the most appropriate name for this:\n\\(p-3 \\equiv-(3-p)\\) Expression" }, { "from": "gpt", "value": "\nHas incorrect belief about the meaning of \"expression\"" } ]

[ { "from": "human", "value": "Recognise and name an identity Which of the following is the most appropriate name for this:\n\\(p-3 \\equiv-(3-p)\\) Formula" }, { "from": "gpt", "value": "\nHas incorrect belief about the meaning of \"formula\"" } ]

[ { "from": "human", "value": "Identify the outcomes of a single event This is a fair spinner.\n\nHow many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]() \\( 3 \\)" }, { "from": "gpt", "value": "Confuses all possible outcomes with options available" } ]

[ { "from": "human", "value": "Identify the outcomes of a single event This is a fair spinner.\n\nHow many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]() \\( 1 \\)" }, { "from": "gpt", "value": "Fails to consider all possible outcomes" } ]

[ { "from": "human", "value": "Identify the outcomes of a single event This is a fair spinner.\n\nHow many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]() \\( 1,3 \\) or \\( 5 \\)" }, { "from": "gpt", "value": "Lists outcomes rather than counts how many outcomes" } ]

[ { "from": "human", "value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) Which of the following answers shows a correct expansion of the expression below? \\( (x-2)^{3} \\) \\( x^{3}-8 \\)" }, { "from": "gpt", "value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets" } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Tom and Katie are discussing the output of this 2-step function machine ![A two step function machine with x as the input. The first functions is x5 and the second function says 'subtracted from 8'. The output is blank.]() Tom says the output is \\( \\mathbf{5} \\boldsymbol{x}-\\mathbf{8} \\)\n\nKatie says the output is \\( \\mathbf{8}-\\mathbf{5} \\boldsymbol{x} \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Has not noticed the difference between 'subtract' and 'subtract from'" } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Tom and Katie are discussing the output of this 2-step function machine ![A two step function machine with x as the input. The first functions is x5 and the second function says 'subtracted from 8'. The output is blank.]() Tom says the output is \\( \\mathbf{5} \\boldsymbol{x}-\\mathbf{8} \\)\n\nKatie says the output is \\( \\mathbf{8}-\\mathbf{5} \\boldsymbol{x} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Has not noticed the difference between 'subtract' and 'subtract from'" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer Jamie is counting up in threes. He starts at \\( -14 \\).\n\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -26 \\)" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer Jamie is counting up in threes. He starts at \\( -14 \\).\n\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -29 \\)" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 100 What is \\( \\mathbf{1 6 5 1 . 4 3} \\) rounded to the nearest hundred? \\( 2000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 100 What is \\( \\mathbf{1 6 5 1 . 4 3} \\) rounded to the nearest hundred? \\( 1600 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 100 What is \\( \\mathbf{1 6 5 1 . 4 3} \\) rounded to the nearest hundred? \\( 1650 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Use a protractor to measure angles between 90° and 180° What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]() \\( 15^{\\circ} \\)" }, { "from": "gpt", "value": "Reads the wrong scale on the protractor when measuring obtuse angles" } ]

[ { "from": "human", "value": "Use a protractor to measure angles between 90° and 180° What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]() \\( 0^{\\circ} \\)" }, { "from": "gpt", "value": "Reads 0 on protractor as size of angle when angle is not in usual orientation" } ]

[ { "from": "human", "value": "Use a protractor to measure angles between 90° and 180° What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]() This is not an angle" }, { "from": "gpt", "value": "Thinks angles can only be measured when one line is horizontal" } ]

[ { "from": "human", "value": "Convert fractions to two digit integer percentages Convert this fraction to a percentage\n\\( \\frac{4}{5} \\) \\( 45 \\% \\)" }, { "from": "gpt", "value": "Converts a fraction to a percentage by writing the numerator followed by the denominator" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 n^{2}-9 \\) \\( 6 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 n^{2}-9 \\) \\( 9 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks a term will be a factor" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 n^{2}-9 \\) \\( n \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]

[ { "from": "human", "value": "Mark a point in the second quadrant of a 2D grid having been given its coordinates, where both values are integers Which region describes where \\( \\boldsymbol{x}>\\mathbf{0} \\) and \\( \\boldsymbol{y}<\\mathbf{0} \\) ? ![A set of axis showing all four quadrants. y axis from -3 to 3 and x axis from -3 to 3]() D" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Identify and represent sets using set notation Tom and Katie are discussing the probability spinner\n\nTom says the sample space can be written as: \\( S=\\{5,6\\} \\)\n\nKatie says the sample space can be written as: \\( S=\\{5,5,6,6,6\\} \\)\nWho do you agree with? ![A circle divided into 5 equal sections. 3 of the sections are labelled with a purple number 6. 2 of the sections are labelled with a blue number 5.]() Only Katie" }, { "from": "gpt", "value": "Believes a sample space should show repeated outcomes, not just unique possible outcomes." } ]

[ { "from": "human", "value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation In which region would \\( x=-5.3 \\) belong? ![A Venn diagram made up of two overlapping circles. One circle is labelled x+5.3 is less than or equal to 0 and the other circle is labelled -(5.3+x)/2 is greater than 0.\nA is in the x+5.3 is less than or equal to 0 circle only.\nB is in the overlap of the two circles.\nC is in the -(5.3+x)/2 is great than 0 circle only.\nD is outside both circles.]() B" }, { "from": "gpt", "value": "Believes greater than/less than symbols include end values" } ]

[ { "from": "human", "value": "Convert between kg and tonne \\( 3000 \\mathrm{~kg} \\) is the same as \\( ___ \\) tonnes \\( 30 \\)" }, { "from": "gpt", "value": "Thinks there are 100kg in a tonne" } ]

[ { "from": "human", "value": "Convert between kg and tonne \\( 3000 \\mathrm{~kg} \\) is the same as \\( ___ \\) tonnes \\( 300 \\)" }, { "from": "gpt", "value": "Thinks there are 10kg in a tonne" } ]

[ { "from": "human", "value": "Convert between kg and tonne \\( 3000 \\mathrm{~kg} \\) is the same as \\( ___ \\) tonnes \\( 3000000 \\)" }, { "from": "gpt", "value": "Multiplies rather than divides" } ]

[ { "from": "human", "value": "Calculate the square root of a number What is the square root of sixteen? \\( 8 \\)" }, { "from": "gpt", "value": "Halves when asked to find the square root" } ]

[ { "from": "human", "value": "Calculate the square root of a number What is the square root of sixteen? \\( 32 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Calculate the square root of a number What is the square root of sixteen? \\( 256 \\)" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\[\n73975\n\\] \\( 80000 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\[\n73975\n\\] \\( 7 \\)" }, { "from": "gpt", "value": "Forgotten placeholders when rounding to significant figures" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\[\n73975\n\\] \\( 74000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Given a situation sketch an appropriate real life graph A taxi company has a \\( £ 1.50 \\) fixed charge and then charges \\( 60 p \\) per mile. Sam correctly sketches a graph to show the cost of different length journeys with the company. Which of the following graphs would best match Sam's sketch? ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive vertical axis and travels horizontally right.]()" }, { "from": "gpt", "value": "Believes a horizontal line can show a constant rate of change" } ]

[ { "from": "human", "value": "Given a situation sketch an appropriate real life graph A taxi company has a \\( £ 1.50 \\) fixed charge and then charges \\( 60 p \\) per mile. Sam correctly sketches a graph to show the cost of different length journeys with the company. Which of the following graphs would best match Sam's sketch? ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at the origin and travels in a straight line right and upwards.]()" }, { "from": "gpt", "value": "Assumes that a graph always starts at the origin" } ]

[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for the curve y = x3 + c Tom and Katie are discussing the table of values for \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 27 \\) \\\\\n\\hline\n\\end{tabular} Tom says the star could be \\( 3 \\).\n\nKatie says the star could be \\( -3 \\).\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Thinks multiplying two or more negative numbers together always gives a positive answer, regardless of how many negative numbers there are in the sum" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p+5)(p-4) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=+1 \\)" }, { "from": "gpt", "value": "Adds instead of multiplying when expanding bracket" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p+5)(p-4) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=+20 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Find 100 less than a given number What number is \\( 100 \\) less than \\( 876,099 ? \\) \\( 876.099 \\)" }, { "from": "gpt", "value": "Divides rather than subtracts when given the command 'less than'" } ]

[ { "from": "human", "value": "Find 100 less than a given number What number is \\( 100 \\) less than \\( 876,099 ? \\) \\( 875,099 \\)" }, { "from": "gpt", "value": "When subtracting a power of 10, subtracts from the wrong column" } ]

[ { "from": "human", "value": "Divide two decimals with a different number of decimal places \\( 50.09 \\div 0.1= \\) \\( 50.009 \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]

[ { "from": "human", "value": "Divide two decimals with a different number of decimal places \\( 50.09 \\div 0.1= \\) \\( 500.09 \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]

[ { "from": "human", "value": "Divide two decimals with a different number of decimal places \\( 50.09 \\div 0.1= \\) \\( 5.009 \\)" }, { "from": "gpt", "value": "Believes dividing by 0.1 is the same as dividing by 10" } ]

[ { "from": "human", "value": "Change decimals of hours into minutes \\( 0.6 \\) hours \\( = _____\\) minutes \\( 6 \\)" }, { "from": "gpt", "value": "Thinks there are 10 minutes in an hour" } ]

[ { "from": "human", "value": "Change decimals of hours into minutes \\( 0.6 \\) hours \\( = _____\\) minutes \\( 60 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]

[ { "from": "human", "value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]() \\( 290^{\\circ} \\)" }, { "from": "gpt", "value": "Incorrectly identifies angles as vertically opposite" } ]

[ { "from": "human", "value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]() \\( 50^{\\circ} \\)" }, { "from": "gpt", "value": "Does not know that angles around a point sum to 360" } ]

[ { "from": "human", "value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]() \\( 45^{\\circ} \\)" }, { "from": "gpt", "value": "Does not know that angles around a point sum to 360" } ]

[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\[\nx+y=8\n\\]\nWhich pair of numbers fits the equation? \\( \\begin{array}{l}x=10 \\\\ y=2\\end{array} \\)" }, { "from": "gpt", "value": "Changes the given operation when substituting" } ]

[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\[\nx+y=8\n\\]\nWhich pair of numbers fits the equation? \\( \\begin{array}{l}x=8 \\\\ y=1\\end{array} \\)" }, { "from": "gpt", "value": "Changes the given operation when substituting" } ]

[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\[\nx+y=8\n\\]\nWhich pair of numbers fits the equation? \\( \\begin{array}{c}x=-8 \\\\ y=1\\end{array} \\)" }, { "from": "gpt", "value": "substitutes incorrectly" } ]

[ { "from": "human", "value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 509,570 \\) ? \\( 50.957 \\)" }, { "from": "gpt", "value": "Divides rather than subtracts when given the command 'less than'" } ]

[ { "from": "human", "value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 509,570 \\) ? \\( 409,570 \\)" }, { "from": "gpt", "value": "When subtracting a power of 10, subtracts from the wrong column" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-x+3 y\\) \\( 5 x+5 y \\)" }, { "from": "gpt", "value": "When collecting like terms, assigns positivity or negativity incorrectly." } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-x+3 y\\) \\( 7 x+5 y \\)" }, { "from": "gpt", "value": "When collecting like terms, treats subtractions as if they are additions" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-x+3 y\\) \\( 7 x+y \\)" }, { "from": "gpt", "value": "When collecting like terms, assigns positivity or negativity incorrectly." } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables Simplify the following by collecting like terms. \\( \\frac{2}{3} k^{2}+\\frac{1}{6} k^{2}-\\frac{1}{3} k^{2}+\\frac{5}{6} k^{2} \\) \\( 2 k^{2} \\)" }, { "from": "gpt", "value": "When collecting like terms, assigns positivity or negativity incorrectly." } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables Simplify the following by collecting like terms. \\( \\frac{2}{3} k^{2}+\\frac{1}{6} k^{2}-\\frac{1}{3} k^{2}+\\frac{5}{6} k^{2} \\) \\( \\frac{1}{3} k^{2}+k^{2} \\)" }, { "from": "gpt", "value": "Does not think that a variable with no coefficient has a coefficient of 1." } ]

[ { "from": "human", "value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\[\n2, \\quad 0.2, \\quad 0.02, \\quad 0.002\n\\] \\( 0.22 \\)" }, { "from": "gpt", "value": "When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle" } ]

[ { "from": "human", "value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\[\n2, \\quad 0.2, \\quad 0.02, \\quad 0.002\n\\] \\( 0.44 \\)" }, { "from": "gpt", "value": "Does not divide by 2 when finding midpoint" } ]

[ { "from": "human", "value": "Identify the mode from a frequency table This table shows the ages of people on a university running team.\n\nWhat is the modal age? \\begin{tabular}{|c|c|l|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} \\( 19.5 \\)" }, { "from": "gpt", "value": "Finds the median instead of the mode" } ]

[ { "from": "human", "value": "Identify the mode from a frequency table This table shows the ages of people on a university running team.\n\nWhat is the modal age? \\begin{tabular}{|c|c|l|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} \\( 7 \\)" }, { "from": "gpt", "value": "Believes the mode is the frequency rather than the value/group" } ]

[ { "from": "human", "value": "Identify the mode from a frequency table This table shows the ages of people on a university running team.\n\nWhat is the modal age? \\begin{tabular}{|c|c|l|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} \\( 21 \\)" }, { "from": "gpt", "value": "Believes when identifying the mode you look at all values, not just frequencies, for the highest number" } ]

[ { "from": "human", "value": "Multiply 2 digit integers by 2 digit integers using long multiplication \\( \\begin{array}{r}\\quad58 \\\\ \\times 22 \\\\ \\hline\\end{array} \\) What number will be in the ones/units column of the final answer? \\( 0 \\)" }, { "from": "gpt", "value": "Has treated this like an addition problem and added the ones column." } ]

[ { "from": "human", "value": "Multiply 2 digit integers by 2 digit integers using long multiplication \\( \\begin{array}{r}\\quad58 \\\\ \\times 22 \\\\ \\hline\\end{array} \\) What number will be in the ones/units column of the final answer? \\( 1 \\)" }, { "from": "gpt", "value": "Has written the value of the 'ones' column as the answer, withiut using the numbers in the question." } ]

[ { "from": "human", "value": "Write numbers greater than 1 in standard form \\[\n300200\n\\]\nWrite this number using standard form \\( 3.2 \\times 10^{5} \\)" }, { "from": "gpt", "value": "When changing a number to standard form omits zero's of significance " } ]

[ { "from": "human", "value": "Write numbers greater than 1 in standard form \\[\n300200\n\\]\nWrite this number using standard form \\( 3.002 \\times 10^{6} \\)" }, { "from": "gpt", "value": "When writing standard form does not give the correct power of ten" } ]

[ { "from": "human", "value": "Write numbers greater than 1 in standard form \\[\n300200\n\\]\nWrite this number using standard form \\( 3.2 \\times 10^{6} \\)" }, { "from": "gpt", "value": "When changing a number to standard form omits zero's of significance " } ]

[ { "from": "human", "value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative What is the midpoint of \\( (4,3) \\) and \\( (1,-5) \\) ? \\( (5,-2) \\)" }, { "from": "gpt", "value": "Does not divide by 2 when finding midpoint" } ]

[ { "from": "human", "value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative What is the midpoint of \\( (4,3) \\) and \\( (1,-5) \\) ? Impossible as you can't have a decimal coordinate" }, { "from": "gpt", "value": "Does not understand that coordinates can be decimals" } ]

[ { "from": "human", "value": "Generate an ascending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n4 n+3\n\\] \\( 4 \\)" }, { "from": "gpt", "value": "When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n." } ]

[ { "from": "human", "value": "Generate an ascending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n4 n+3\n\\] \\( 3 \\)" }, { "from": "gpt", "value": "Thinks the first term in a sequence is the term before the sequence begins (0th term)" } ]

[ { "from": "human", "value": "Divide algebraic fractions involving non-linear expressions STEP \\( 3 \\)\n\nWhich of the options is the final answer, expressed as simply as possible?\n\\(\n\\begin{aligned}\n& \\frac{3 x+1}{3} \\div \\frac{9 x^{2}-1}{12} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{9 x^{2}-1} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{(3 x-1)(3 x+1)}\n\\end{aligned}\n\\) \\( \\frac{12}{9 x-1} \\)" }, { "from": "gpt", "value": "Only applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction" } ]

[ { "from": "human", "value": "Divide algebraic fractions involving non-linear expressions STEP \\( 3 \\)\n\nWhich of the options is the final answer, expressed as simply as possible?\n\\(\n\\begin{aligned}\n& \\frac{3 x+1}{3} \\div \\frac{9 x^{2}-1}{12} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{9 x^{2}-1} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{(3 x-1)(3 x+1)}\n\\end{aligned}\n\\) \\( \\frac{4(3 x+1)}{(3 x-1)(3 x+1)} \\)" }, { "from": "gpt", "value": "When simplifying an algebraic fraction, only looks for number factors" } ]

[ { "from": "human", "value": "Divide algebraic fractions involving non-linear expressions STEP \\( 3 \\)\n\nWhich of the options is the final answer, expressed as simply as possible?\n\\(\n\\begin{aligned}\n& \\frac{3 x+1}{3} \\div \\frac{9 x^{2}-1}{12} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{9 x^{2}-1} \\\\\n= & \\frac{3 x+1}{3} \\times \\frac{12}{(3 x-1)(3 x+1)}\n\\end{aligned}\n\\) \\( \\frac{5}{3 x} \\)" }, { "from": "gpt", "value": "Simplifies a fraction by adding or subtracting the same amount from the numerator and denominator" } ]

[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Julie wants to estimate the answer to this calculation by rounding each number to \\( 1 \\) significant figure.\n\n\\[\n87.4 \\times 0.3727\n\\]\n\nWhat number should replace \\( \\mathbf{8 7 . 4} \\) in her estimation? \\( 87 \\)" }, { "from": "gpt", "value": "Rounded to wrong degree of accuracy (2sf not 1sf)" } ]

[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Julie wants to estimate the answer to this calculation by rounding each number to \\( 1 \\) significant figure.\n\n\\[\n87.4 \\times 0.3727\n\\]\n\nWhat number should replace \\( \\mathbf{8 7 . 4} \\) in her estimation? \\( 88 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Julie wants to estimate the answer to this calculation by rounding each number to \\( 1 \\) significant figure.\n\n\\[\n87.4 \\times 0.3727\n\\]\n\nWhat number should replace \\( \\mathbf{8 7 . 4} \\) in her estimation? \\( 80 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+5 p+6\n\\) \\( (p+6)(p+1) \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+5 p+6\n\\) \\( (p+6)(p-1) \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x" } ]

[ { "from": "human", "value": "Given information about one part, work out other parts Josh and Lucy share some money in the ratio \\( 3: 7 \\)\n\nJosh receives \\( £ 84 \\).\n\nHow much money does Lucy receive? \\( £ 58.80 \\)" }, { "from": "gpt", "value": "In ratio question where one side of ratio is given, treats that as the total" } ]

[ { "from": "human", "value": "Given information about one part, work out other parts Josh and Lucy share some money in the ratio \\( 3: 7 \\)\n\nJosh receives \\( £ 84 \\).\n\nHow much money does Lucy receive? \\( £ 28 \\)" }, { "from": "gpt", "value": "Finds one part of a ratio but doesn't multiply that by the number of parts needed" } ]

[ { "from": "human", "value": "Given information about one part, work out other parts Josh and Lucy share some money in the ratio \\( 3: 7 \\)\n\nJosh receives \\( £ 84 \\).\n\nHow much money does Lucy receive? \\( £ 36 \\)" }, { "from": "gpt", "value": "Gets order of ratio wrong" } ]

[ { "from": "human", "value": "Order negative decimals with the same number of digits Here are the depths below sea level of \\( 3 \\) creatures:\nTuna: \\( -2.6 m \\)\nRay: \\( -6 m \\)\nLing: \\( -1.5 \\mathrm{~m} \\)\nArrange their depths in ascending order, starting with the deepest \\( 1^{\\text {st }} \\) Tuna\n\\( 2^{\\text {nd }} \\) Ling\n\\( 3^{\\text {rd }} \\) Ray" }, { "from": "gpt", "value": "Thinks the more digits a number has the greater it is, regardless of place value" } ]

[ { "from": "human", "value": "Order negative decimals with the same number of digits Here are the depths below sea level of \\( 3 \\) creatures:\nTuna: \\( -2.6 m \\)\nRay: \\( -6 m \\)\nLing: \\( -1.5 \\mathrm{~m} \\)\nArrange their depths in ascending order, starting with the deepest \\( \\begin{array}{l}1^{\\text {st }} \\text { Ling } \\\\ 2^{\\text {nd }} \\text { Tuna } \\\\ 3^{\\text {rd }} \\text { Ray }\\end{array} \\)" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]

[ { "from": "human", "value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Amy is trying to work out the distance between these two points: \\( (2,-5) \\) and \\( (-7,1) \\) She labels them like this: \\( \\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (2, & -5) & (-7, & 1)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) What does the first bracket equal? \\( (-5)^{2} \\)" }, { "from": "gpt", "value": "When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored " } ]

[ { "from": "human", "value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Amy is trying to work out the distance between these two points: \\( (2,-5) \\) and \\( (-7,1) \\) She labels them like this: \\( \\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (2, & -5) & (-7, & 1)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) What does the first bracket equal? \\( (9)^{2} \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]

[ { "from": "human", "value": "Calculate the mean as an average from a list of data What is the mean of this set of data?\n\\[\n5, \\quad 2, \\quad 0, \\quad 2, \\quad 3\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "When asked for the mean of a list of data, gives the mode" } ]

[ { "from": "human", "value": "Calculate the mean as an average from a list of data What is the mean of this set of data?\n\\[\n5, \\quad 2, \\quad 0, \\quad 2, \\quad 3\n\\] \\( 3 \\)" }, { "from": "gpt", "value": "When asked for the mean of a list of data, does not count any zeros in the data when working out what to divide by" } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2(a-5)\\) " }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\(a \\Rightarrow -5 \\Rightarrow \\times2\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow -5 \\Rightarrow \\times2\\Rightarrow 2(a-5)\\) " }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\(a \\Rightarrow -5 \\Rightarrow \\times2 \\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2(a-5)\\) " }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "Recall the formulae for the trigonometric ratios \\(\n\\bigstar=\\frac{\\text { Hypotenuse }}{\\text { Opposite }}\n\\)\n\nWhat should replace the star? \\( \\sin (\\theta) \\)" }, { "from": "gpt", "value": "Confuses order of sides in a trigonometric ratio" } ]

[ { "from": "human", "value": "Recall the formulae for the trigonometric ratios \\(\n\\bigstar=\\frac{\\text { Hypotenuse }}{\\text { Opposite }}\n\\)\n\nWhat should replace the star? \\( \\cos (\\theta) \\)" }, { "from": "gpt", "value": "Uses cos when sin is required" } ]

[ { "from": "human", "value": "Recall the formulae for the trigonometric ratios \\(\n\\bigstar=\\frac{\\text { Hypotenuse }}{\\text { Opposite }}\n\\)\n\nWhat should replace the star? \\( \\tan (\\theta) \\)" }, { "from": "gpt", "value": "Uses tan when sin is required" } ]

[ { "from": "human", "value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable Tom and Katie are discussing this pair of simultaneous equations: \\( \\begin{array}{l}3 x-2 y=15 \\\\ x+2 y=20\\end{array} \\) Tom says if you add the two equations together you will eliminate a variable\n\nKatie says if you subtract the two equations together you will eliminate a variable\n\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Subtracts simultaneous equations when addition is required" } ]

[ { "from": "human", "value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable Tom and Katie are discussing this pair of simultaneous equations: \\( \\begin{array}{l}3 x-2 y=15 \\\\ x+2 y=20\\end{array} \\) Tom says if you add the two equations together you will eliminate a variable\n\nKatie says if you subtract the two equations together you will eliminate a variable\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "When solving simultaneous equations thinks that identical terms in given equations can be eliminated by either adding or subtracting." } ]

[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card \n\\( \\frac{1}{6} \\) of \\( A \\) is \\( 12 \\) \nWhat is \\( \\frac{1}{8} \\) of \\( A \\) ? ![A pink rounded rectangle with a capital A typed inside]() \\( 0.25 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]

[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card \n\\( \\frac{1}{6} \\) of \\( A \\) is \\( 12 \\) \nWhat is \\( \\frac{1}{8} \\) of \\( A \\) ? ![A pink rounded rectangle with a capital A typed inside]() \\( 4 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]

[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card \n\\( \\frac{1}{6} \\) of \\( A \\) is \\( 12 \\) \nWhat is \\( \\frac{1}{8} \\) of \\( A \\) ? ![A pink rounded rectangle with a capital A typed inside]() \\( 72 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]