conversations
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[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables \\(\nx(3 x-5)+6(2 x-3) \\equiv P x^{2}+Q x+R\n\\)\n\nWhat is the value of \\( R \\) ? \\( -3 \\)"
},
{
"from": "gpt",
"value": "Only multiplies the first term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Use direct proportion to solve non-unitary missing amounts in problems (e.g. recipes) Twelve rulers cost \\( 96 p \\).\nHow much do five rulers cost? \\( 89 p \\)"
},
{
"from": "gpt",
"value": "Subtracts rather than divides when scaling down in direct proportion problems"
}
] |
[
{
"from": "human",
"value": "Use direct proportion to solve non-unitary missing amounts in problems (e.g. recipes) Twelve rulers cost \\( 96 p \\).\nHow much do five rulers cost? \\( 8 p \\)"
},
{
"from": "gpt",
"value": "Finds unit price but doesn't multiply up for number in question"
}
] |
[
{
"from": "human",
"value": "Use direct proportion to solve non-unitary missing amounts in problems (e.g. recipes) Twelve rulers cost \\( 96 p \\).\nHow much do five rulers cost? \\( £ 4.80 \\)"
},
{
"from": "gpt",
"value": "Multiplies up without finding unit price in proportion question"
}
] |
[
{
"from": "human",
"value": "Convert from minutes to seconds Order the times from shortest to longest.\nA: 8 minutes\nB: 8 minutes 40 seconds\nC: 8 \\(\n\\frac{1}{2}\n\\) minutes\nD: 500 seconds \\( B, D, C, A \\)"
},
{
"from": "gpt",
"value": "Mixes up shortest and longest when ordering times"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.8532 \\) \\( 1 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.8532 \\) \\( 0.8 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.6=\\frac{3}{5}=? \\% \\) \\( 35 \\% \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a percentage by writing the numerator followed by the denominator"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.6=\\frac{3}{5}=? \\% \\) \\( 6 \\% \\)"
},
{
"from": "gpt",
"value": "Believes a decimal with one significant figure is a multiple of 10 when converted to a percentage, regardless of place value"
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality in the form x ≤ a or x ≥ b (and other sign arrangements) on a numberline Which of the following diagrams represents \\( x<-1 \\) or \\( x \\geq 2 \\) ? ![Number line from -5 to 5. Closed circle at -1 with arrow to the left. Open circle at 2 with arrow to the right. ]()"
},
{
"from": "gpt",
"value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning."
}
] |
[
{
"from": "human",
"value": "Find the reciprocal of a fraction What is the reciprocal of \\( -\\frac{1}{3} \\) ? \\( -0.333 \\ldots \\)"
},
{
"from": "gpt",
"value": "Has an incorrect assumption about the definition of a reciprocal"
}
] |
[
{
"from": "human",
"value": "Find the reciprocal of a fraction What is the reciprocal of \\( -\\frac{1}{3} \\) ? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Correctly finds the reciprocal of a number, but believes it should be opposite in sign to the original number."
}
] |
[
{
"from": "human",
"value": "Find the reciprocal of a fraction What is the reciprocal of \\( -\\frac{1}{3} \\) ? \\( \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "Makes the number negative when asked to find the reciprocal"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Which answer shows the following calculation using the correct algebraic convention?\n\n\\(\na+6+a+j+5+j+j\n\\) \\( 6+5+2 a+3 j \\)"
},
{
"from": "gpt",
"value": "Does not understand when like terms can be collected"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Which answer shows the following calculation using the correct algebraic convention?\n\n\\(\na+6+a+j+5+j+j\n\\) \\( 6+2 a+5+3 j \\)"
},
{
"from": "gpt",
"value": "Does not understand when like terms can be collected"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Which answer shows the following calculation using the correct algebraic convention?\n\n\\(\na+6+a+j+5+j+j\n\\) \\( 11+a^{2}+j^{3} \\)"
},
{
"from": "gpt",
"value": "Confuses collecting like terms with multiplication"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-8\" next to the bottom dash and \"4\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the dash that is 2 below the \"4\" label and 4 above the \"-8\" label. ]() \\( 2 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 1"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-8\" next to the bottom dash and \"4\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the dash that is 2 below the \"4\" label and 4 above the \"-8\" label. ]() \\( -4 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 1"
}
] |
[
{
"from": "human",
"value": "Identify parallel lines written in the form y = mx + c Tom and Katie are arguing about parallel lines.\n\nTom says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x}+\\mathbf{2} \\) are parallel. \n\nKatie says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{2 x}-\\mathbf{3} \\) are parallel.\n\nWho is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Believes switching the gradient and y-intercept gives a parallel line"
}
] |
[
{
"from": "human",
"value": "Identify parallel lines written in the form y = mx + c Tom and Katie are arguing about parallel lines.\n\nTom says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x}+\\mathbf{2} \\) are parallel. \n\nKatie says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{2 x}-\\mathbf{3} \\) are parallel.\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes switching the gradient and y-intercept gives a parallel line"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring multiplication or division, involving positive decimals Solve the equation:\n\\(\n0.15=0.5 p\n\\) \\( p=-0.35 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, subtracts instead of dividing"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring multiplication or division, involving positive decimals Solve the equation:\n\\(\n0.15=0.5 p\n\\) \\( p=\\frac{10}{3} \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate non linear real life graph Which of the following graphs is most likely to represent the change in journey time against average speed? ![A straight line graph starting at the origin and travelling right with a positive gradient.]()"
},
{
"from": "gpt",
"value": "Thinks the faster you travel the longer the time it will take"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate non linear real life graph Which of the following graphs is most likely to represent the change in journey time against average speed? ![A curved graph that starts at the origin. As you move right it travels steeply up, then levels off]()"
},
{
"from": "gpt",
"value": "Thinks the faster you travel the longer the time it will take"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate non linear real life graph Which of the following graphs is most likely to represent the change in journey time against average speed? ![A straight line graph starting partway up the y-axis and travelling right with a negative gradient until it hits the x-axis.]()"
},
{
"from": "gpt",
"value": "Believes a reciprocal graph can be a straight line"
}
] |
[
{
"from": "human",
"value": "Identify the mode from a frequency table This table shows the number of pets a group of students owns.\n\nWhat is the modal number of pets owned? \\begin{tabular}{|c|c|}\n\\hline Number of pets & Frequency \\\\\n\\hline \\( 0 \\) & \\( 9 \\) \\\\\n\\hline \\( 1 \\) & \\( 6 \\) \\\\\n\\hline \\( 2 \\) & \\( 3 \\) \\\\\n\\hline \\( 3 \\) & \\( 2 \\) \\\\\n\\hline \\( 4 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular} \\( 2 \\)"
},
{
"from": "gpt",
"value": "Finds the median instead of the mode"
}
] |
[
{
"from": "human",
"value": "Identify the mode from a frequency table This table shows the number of pets a group of students owns.\n\nWhat is the modal number of pets owned? \\begin{tabular}{|c|c|}\n\\hline Number of pets & Frequency \\\\\n\\hline \\( 0 \\) & \\( 9 \\) \\\\\n\\hline \\( 1 \\) & \\( 6 \\) \\\\\n\\hline \\( 2 \\) & \\( 3 \\) \\\\\n\\hline \\( 3 \\) & \\( 2 \\) \\\\\n\\hline \\( 4 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular} \\( 3 \\)"
},
{
"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 number of pets a group of students owns.\n\nWhat is the modal number of pets owned? \\begin{tabular}{|c|c|}\n\\hline Number of pets & Frequency \\\\\n\\hline \\( 0 \\) & \\( 9 \\) \\\\\n\\hline \\( 1 \\) & \\( 6 \\) \\\\\n\\hline \\( 2 \\) & \\( 3 \\) \\\\\n\\hline \\( 3 \\) & \\( 2 \\) \\\\\n\\hline \\( 4 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular} \\( 4 \\)"
},
{
"from": "gpt",
"value": "Believes when identifying the mode you look at all values, not just frequencies, for the highest number"
}
] |
[
{
"from": "human",
"value": "Enlarge a shape, with a centre of enlargement given, by a positive scale factor bigger than 1, where the centre of enlargement lies on the edge or outside of the object The triangle is enlarged by scale factor \\( 3 \\), with the centre of enlargement at \\( (1,0) \\).\nWhat are the new coordinates of the point marked \\( T \\) ? ![A coordinate grid with the x-axis going from -1 to 10 and the y-axis going from -1 to 7.\n3 points are plotted and joined with straight lines to form a triangle. The points are (1,1), (1,4) and (3,1). Point (3,1) is labelled as T.\nPoint (1,0) is also plotted.]() \\( (6,4) \\)"
},
{
"from": "gpt",
"value": "Added rather than multiplied by a scale factor"
}
] |
[
{
"from": "human",
"value": "Enlarge a shape, with a centre of enlargement given, by a positive scale factor bigger than 1, where the centre of enlargement lies on the edge or outside of the object The triangle is enlarged by scale factor \\( 3 \\), with the centre of enlargement at \\( (1,0) \\).\nWhat are the new coordinates of the point marked \\( T \\) ? ![A coordinate grid with the x-axis going from -1 to 10 and the y-axis going from -1 to 7.\n3 points are plotted and joined with straight lines to form a triangle. The points are (1,1), (1,4) and (3,1). Point (3,1) is labelled as T.\nPoint (1,0) is also plotted.]() \\( (9,3) \\)"
},
{
"from": "gpt",
"value": "Enlarges by the wrong centre of enlargement"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of this set of data?\n\\[\n5 \\mathrm{~cm}, 19 \\mathrm{~cm}, 6 \\mathrm{~cm}, 2 \\mathrm{~cm}\n\\] \\( 19 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Identifies the biggest value for the range"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of this set of data?\n\\[\n5 \\mathrm{~cm}, 19 \\mathrm{~cm}, 6 \\mathrm{~cm}, 2 \\mathrm{~cm}\n\\] \\( 3 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Thinks the range is just the first value subtracted from the last value, without ordering"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of this set of data?\n\\[\n5 \\mathrm{~cm}, 19 \\mathrm{~cm}, 6 \\mathrm{~cm}, 2 \\mathrm{~cm}\n\\] \\( 21 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "To find the range adds the biggest and smallest number rather than subtract"
}
] |
[
{
"from": "human",
"value": "Describe the solution to a graphical inequality involving a single diagonal line Which inequality is represented by the shaded region? ![Graph showing four quadrants with a straight line going from the top left to the bottom right. The line goes through (-4, 4) (-3, 3) (-2, 2) and so on]() \\( y>x \\)"
},
{
"from": "gpt",
"value": "Confuses the lines y=x and y=-x"
}
] |
[
{
"from": "human",
"value": "Describe the solution to a graphical inequality involving a single diagonal line Which inequality is represented by the shaded region? ![Graph showing four quadrants with a straight line going from the top left to the bottom right. The line goes through (-4, 4) (-3, 3) (-2, 2) and so on]() \\( y<-x \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Use brackets to write function machines as calculations Here is a function machine\n\\( input\\Rightarrow +2 \\Rightarrow \\times 3 \\Rightarrow output\\)\nThe input is \\( 5 \\).\nWhich calculation gives the correct output? \\( 5 \\times 3+2 \\)"
},
{
"from": "gpt",
"value": "Does not follow the arrows through a function machine, changes the order of the operations asked."
}
] |
[
{
"from": "human",
"value": "Use brackets to write function machines as calculations Here is a function machine\n\\( input\\Rightarrow +2 \\Rightarrow \\times 3 \\Rightarrow output\\)\nThe input is \\( 5 \\).\nWhich calculation gives the correct output? \\( 5(3+2) \\)"
},
{
"from": "gpt",
"value": "In a function machine, confuses an operation with the input"
}
] |
[
{
"from": "human",
"value": "Use brackets to write function machines as calculations Here is a function machine\n\\( input\\Rightarrow +2 \\Rightarrow \\times 3 \\Rightarrow output\\)\nThe input is \\( 5 \\).\nWhich calculation gives the correct output? \\( 5+2 \\times 3 \\)"
},
{
"from": "gpt",
"value": "Believes order of operations does not affect the answer to a calculation"
}
] |
[
{
"from": "human",
"value": "Given the area of a square, calculate a missing dimension A square has an area \\( 64 \\mathrm{~mm}^{2} \\)\n\nWhat is the length of one side of the square? \\( 16 \\mathrm{~mm} \\)"
},
{
"from": "gpt",
"value": "Calculates perimeter when asked for area"
}
] |
[
{
"from": "human",
"value": "Given the area of a square, calculate a missing dimension A square has an area \\( 64 \\mathrm{~mm}^{2} \\)\n\nWhat is the length of one side of the square? \\( 32 \\mathrm{~mm} \\)"
},
{
"from": "gpt",
"value": "Adds when calculating area instead of multiplying"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out the whole The ratio of cars to bikes in a housing estate is \\( 5: 2 \\)\nIf there are \\( \\mathbf{7 0} \\) cars, how many vehicles (cars and bikes) are there in total? \\( 72 \\)"
},
{
"from": "gpt",
"value": "Thinks the number in the ratio is the total"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = n This is the graph of\n\\[\ny=0.5 x-2\n\\]\n\nAccording to the graph, what is the solution to:\n\\[\n0.5 x-2=1\n\\] ![Graph showing straight line with y intercept (0,-2) and x intercept (4,0)]() \\( x=-1.5 \\)"
},
{
"from": "gpt",
"value": "Thinks they solve mx + c = a, by substituting in the value of a for x and therefore calculating ma + c"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = n This is the graph of\n\\[\ny=0.5 x-2\n\\]\n\nAccording to the graph, what is the solution to:\n\\[\n0.5 x-2=1\n\\] ![Graph showing straight line with y intercept (0,-2) and x intercept (4,0)]() \\( x=4 \\)"
},
{
"from": "gpt",
"value": "Believes the solution to mx + c = a is the x intercept of y = mx +c"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order a negative and a positive integer One of these pairs of numbers does not fit \nthe inequality \\( d \\leq h \\)\n\nCan you find which pair? \\( \\begin{array}{l}d=4 \\\\ h=4\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order a negative and a positive integer One of these pairs of numbers does not fit \nthe inequality \\( d \\leq h \\)\n\nCan you find which pair? \\( \\begin{array}{c}d=-4\\\\h=4\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order a negative and a positive integer One of these pairs of numbers does not fit \nthe inequality \\( d \\leq h \\)\n\nCan you find which pair? \\( \\begin{array}{c}d=-2 \\\\ h=2\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Given a midpoint and a coordinate work out the position of the other coordinate, where all the values are integers but at least one is negative Tom and Katie are arguing about midpoints.\n\\( M \\) is the midpoint between points \\( P \\) and \\( Q \\).\n\nTom says if you know the location of \\( M \\) only, then there is more than one possible location for \\( \\mathrm{P} \\) and \\( \\mathrm{Q} \\).\n\nKatie says if you only know the locations of \\( M \\) and \\( Q \\), then there is more than one possible location for \\( \\mathrm{P} \\).\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes there is more than one line which passes through a given pair of points"
}
] |
[
{
"from": "human",
"value": "Given a midpoint and a coordinate work out the position of the other coordinate, where all the values are integers but at least one is negative Tom and Katie are arguing about midpoints.\n\\( M \\) is the midpoint between points \\( P \\) and \\( Q \\).\n\nTom says if you know the location of \\( M \\) only, then there is more than one possible location for \\( \\mathrm{P} \\) and \\( \\mathrm{Q} \\).\n\nKatie says if you only know the locations of \\( M \\) and \\( Q \\), then there is more than one possible location for \\( \\mathrm{P} \\).\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Believes that one point is enough to specify a line"
}
] |
[
{
"from": "human",
"value": "Continue linear sequences expressed as patterns by drawing the next pattern How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequence. \nPattern 1 contains 3 squares in this arrangement :. \nPattern 2 contains 5 squares in this arrangement ::.\nPattern 3 contains 7 squares in this arrangement :::.]() \\( 8 \\)"
},
{
"from": "gpt",
"value": "When asked for the next term in the sequence adds one to the last term given, despite the sequence not going up in ones."
}
] |
[
{
"from": "human",
"value": "Continue linear sequences expressed as patterns by drawing the next pattern How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequence. \nPattern 1 contains 3 squares in this arrangement :. \nPattern 2 contains 5 squares in this arrangement ::.\nPattern 3 contains 7 squares in this arrangement :::.]() \\( 10 \\)"
},
{
"from": "gpt",
"value": "Does not notice all changes in a sequence of visual patterns"
}
] |
[
{
"from": "human",
"value": "Continue linear sequences expressed as patterns by drawing the next pattern How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequence. \nPattern 1 contains 3 squares in this arrangement :. \nPattern 2 contains 5 squares in this arrangement ::.\nPattern 3 contains 7 squares in this arrangement :::.]() \\( 14 \\)"
},
{
"from": "gpt",
"value": "Does not notice all changes in a sequence of visual patterns"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 50 \\mathrm{~m} \\) as a percentage of \\( 5 \\mathrm{~km} \\) ? \\( 100 \\% \\)"
},
{
"from": "gpt",
"value": "Has found the total as a percentage of the amount being asked"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 50 \\mathrm{~m} \\) as a percentage of \\( 5 \\mathrm{~km} \\) ? \\( 50 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks you need to just add a % sign to a number to make it a percentage"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 50 \\mathrm{~m} \\) as a percentage of \\( 5 \\mathrm{~km} \\) ? \\( 10 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100m and a km"
}
] |
[
{
"from": "human",
"value": "Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative Which of the following sketches could represent \\( y=4-2 x \\) ? ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis below the origin.]()"
},
{
"from": "gpt",
"value": "Believes that in y=mx+c, m is the y-intercept"
}
] |
[
{
"from": "human",
"value": "Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative Which of the following sketches could represent \\( y=4-2 x \\) ? ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis above the origin.]()"
},
{
"from": "gpt",
"value": "Believes that in y = mx+c, c is the gradient"
}
] |
[
{
"from": "human",
"value": "Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative Which of the following sketches could represent \\( y=4-2 x \\) ? ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis below the origin.]()"
},
{
"from": "gpt",
"value": "Believes that in y = mx+c, c is the gradient"
}
] |
[
{
"from": "human",
"value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 3 \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nKatie says \\( x \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Does not know how to identify common factors from algebraic terms"
}
] |
[
{
"from": "human",
"value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 3 \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nKatie says \\( x \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not know how to identify common factors from algebraic terms"
}
] |
[
{
"from": "human",
"value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 3 \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nKatie says \\( x \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not know how to identify common factors from algebraic terms"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention?\n\\(\n2 \\div(3+a \\times b)\n\\) \\( \\frac{2}{3}+a b \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention?\n\\(\n2 \\div(3+a \\times b)\n\\) \\( \\frac{2}{b(a+3)} \\)"
},
{
"from": "gpt",
"value": "Only multiplies the first term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention?\n\\(\n2 \\div(3+a \\times b)\n\\) \\( \\frac{2}{a \\times b+3} \\)"
},
{
"from": "gpt",
"value": "Does not realize we can omit the multiplication symbol in algebraic expressions"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data When finding the range of a data set, which step is never needed Check the units of your answer"
},
{
"from": "gpt",
"value": "Believes range does not need units"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data When finding the range of a data set, which step is never needed Write the numbers in ascending or descending order."
},
{
"from": "gpt",
"value": "When calculating the range does not reorder the data to find the largest number minus the smallest number"
}
] |
[
{
"from": "human",
"value": "Assign probabilities to single events using fractions A box contains \\( 10 \\) coloured counters.\n\n\\( 3 \\) of the counters are pink\n\n\\( 3 \\) of the counters are blue\n\nThe rest of the counters are green\n\nWhat is the probability of choosing a green counter? \\( 4 \\)"
},
{
"from": "gpt",
"value": "Forgets the denominator in probability"
}
] |
[
{
"from": "human",
"value": "Assign probabilities to single events using fractions A box contains \\( 10 \\) coloured counters.\n\n\\( 3 \\) of the counters are pink\n\n\\( 3 \\) of the counters are blue\n\nThe rest of the counters are green\n\nWhat is the probability of choosing a green counter? \\( \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "Thinks that probabilities of an event occurring or not occurring must be equal"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cuboid when the dimensions are given in different units Which of the following calculations would give the volume of this cuboid? ![A cuboid with dimensions 60mm, 7cm and 5cm]() \\( 7 \\times 5 \\times 60 \\)"
},
{
"from": "gpt",
"value": "Does not convert measurements to have the same units before calculating area or volume"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cuboid when the dimensions are given in different units Which of the following calculations would give the volume of this cuboid? ![A cuboid with dimensions 60mm, 7cm and 5cm]() \\( 7+5+6 \\)"
},
{
"from": "gpt",
"value": "Adds when calculating volume instead of multiplying"
}
] |
[
{
"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\nexpanded and simplified?\n\n\\(\n(p-3)(p+3) \\equiv p^{2} \\color{purple}\\triangle\\) \\(p\\)\\(\\color{green}\\bigcirc\n\\)\n \\(\\color{green}\\bigcirc\\) = +0 \n(no number term)"
},
{
"from": "gpt",
"value": "Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets"
}
] |
[
{
"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\nexpanded and simplified?\n\n\\(\n(p-3)(p+3) \\equiv p^{2} \\color{purple}\\triangle\\) \\(p\\)\\(\\color{green}\\bigcirc\n\\)\n \\(\\color{green}\\bigcirc\\) = +9"
},
{
"from": "gpt",
"value": "Believes multiplying a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Add column vectors each containing two elements \\( \\left(\\begin{array}{l}2 \\\\ 3\\end{array}\\right)+\\left(\\begin{array}{c}-1 \\\\ 0\\end{array}\\right)= \\) \\( \\left(\\begin{array}{c}-2 \\\\ 0\\end{array}\\right) \\)"
},
{
"from": "gpt",
"value": "When adding column vectors, multiplies rather than adds"
}
] |
[
{
"from": "human",
"value": "Recognise a quadratic graph from its shape Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() Who is correct? Only Tom"
},
{
"from": "gpt",
"value": "Only recognises the positive form of a quadratic graph"
}
] |
[
{
"from": "human",
"value": "Recognise a quadratic graph from its shape Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() Who is correct? Only Katie"
},
{
"from": "gpt",
"value": "Only recognises the negative form of a quadratic graph"
}
] |
[
{
"from": "human",
"value": "Recognise a quadratic graph from its shape Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() Who is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not recognise a quadratic graph"
}
] |
[
{
"from": "human",
"value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 40 \\mathrm{~cm}^{2} \\).\n\nWhat is the value of \\( a \\) ? ![A trapezium with the parallel sides labelled with 2cm and a and the height labelled with 8cm]() \\( 3 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when calculating the area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Calculate the square root of a number \\( \\sqrt{-16}=? \\) \\( -4 \\)"
},
{
"from": "gpt",
"value": "Can not square root a negative number"
}
] |
[
{
"from": "human",
"value": "Calculate the square root of a number \\( \\sqrt{-16}=? \\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "Can not square root a negative number"
}
] |
[
{
"from": "human",
"value": "Multiply amounts of money up to £10 Alicia wants to buy some bottles of water.\nEach bottle of water costs \\( £ 1.65 \\)\nAlicia has \\( £ 10 \\) to spend.\nWhat is the greatest number of bottles can she buy? \\( 7 \\)"
},
{
"from": "gpt",
"value": "Believes you can go above an amount of money when finding how much of something you can buy"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n3 n+2 \\geq 4 n-5\n\\] \\( -3 \\geq n \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n3 n+2 \\geq 4 n-5\n\\] \\( 1 \\geq n \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n3 n+2 \\geq 4 n-5\n\\] \\( n \\geq 7 \\)"
},
{
"from": "gpt",
"value": "Believes they can multiply/divide through by a negative number without changing the direction of the inequality"
}
] |
[
{
"from": "human",
"value": "Substitute into simple formulae given in words A theme park charges \\( £ 8 \\) entry fee and then \\( £ 3 \\) for every ride you go on.\nHeena goes on \\( 5 \\) rides.\nHow much does she pay in total? \\( £ 55 \\)"
},
{
"from": "gpt",
"value": "Combines variables with constants when writing a formula from a given situation"
}
] |
[
{
"from": "human",
"value": "Substitute into simple formulae given in words A theme park charges \\( £ 8 \\) entry fee and then \\( £ 3 \\) for every ride you go on.\nHeena goes on \\( 5 \\) rides.\nHow much does she pay in total? \\( £ 15 \\)"
},
{
"from": "gpt",
"value": "Does not add on the constant in a worded substitution problem"
}
] |
[
{
"from": "human",
"value": "Substitute into simple formulae given in words A theme park charges \\( £ 8 \\) entry fee and then \\( £ 3 \\) for every ride you go on.\nHeena goes on \\( 5 \\) rides.\nHow much does she pay in total? \\( £ 11 \\)"
},
{
"from": "gpt",
"value": "Does not consider the variable when evaluating an expression that requires substitution."
}
] |
[
{
"from": "human",
"value": "Increase a number by a given percentage mentally where the percent is a multiple of 10 Increase \\( 160 \\) by \\( 30 \\% \\) \\( 190 \\)"
},
{
"from": "gpt",
"value": "Added the values together instead of finding the percentage"
}
] |
[
{
"from": "human",
"value": "Increase a number by a given percentage mentally where the percent is a multiple of 10 Increase \\( 160 \\) by \\( 30 \\% \\) \\( 48 \\)"
},
{
"from": "gpt",
"value": "Found the percentage but forgot to add to 100%"
}
] |
[
{
"from": "human",
"value": "Increase a number by a given percentage mentally where the percent is a multiple of 10 Increase \\( 160 \\) by \\( 30 \\% \\) \\( 4800 \\)"
},
{
"from": "gpt",
"value": "Thinks when finding a percentage you multiply by the percentage being asked"
}
] |
[
{
"from": "human",
"value": "Continue a sequence involving triangle numbers Here are two consecutive triangle numbers: \\( 153,171, \\ldots \\) What is the next triangle number in the sequence? \\( 188 \\)"
},
{
"from": "gpt",
"value": "Believes the difference between triangle numbers decreases by 1 each time"
}
] |
[
{
"from": "human",
"value": "Continue a sequence involving triangle numbers Here are two consecutive triangle numbers: \\( 153,171, \\ldots \\) What is the next triangle number in the sequence? \\( 189 \\)"
},
{
"from": "gpt",
"value": "Believes the difference between triangle numbers remains the same"
}
] |
[
{
"from": "human",
"value": "Continue a sequence involving triangle numbers Here are two consecutive triangle numbers: \\( 153,171, \\ldots \\) What is the next triangle number in the sequence? \\( 324 \\)"
},
{
"from": "gpt",
"value": "Believes to find the next traingle number you add the previous two numbers together i.e. Fibonacci"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition and subtraction At the start of the day, there was \\( £ 1,456 \\) in the till. \\( £ 7,347 \\) was taken and \\( £ 4,377 \\) was handed out. How much money was left? \\( £ 13,180 \\)"
},
{
"from": "gpt",
"value": "Assumes they add all values in a worded problem, thereby not interpreting the problem correctly"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition and subtraction At the start of the day, there was \\( £ 1,456 \\) in the till. \\( £ 7,347 \\) was taken and \\( £ 4,377 \\) was handed out. How much money was left? \\( £ 2,970 \\)"
},
{
"from": "gpt",
"value": "In a worded problem, does not complete all calculations"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition and subtraction At the start of the day, there was \\( £ 1,456 \\) in the till. \\( £ 7,347 \\) was taken and \\( £ 4,377 \\) was handed out. How much money was left? \\( £ 10,268 \\)"
},
{
"from": "gpt",
"value": "When talking about money \"taken\" in a retail context, thinks that means take-away rather than add"
}
] |
[
{
"from": "human",
"value": "Recognise a quadratic graph from its shape Which of the following is an example of a quadratic graph? ![A graph showing a straight line from top left to bottom right.]()"
},
{
"from": "gpt",
"value": "Does not recognise a quadratic graph"
}
] |
[
{
"from": "human",
"value": "Recognise a quadratic graph from its shape Which of the following is an example of a quadratic graph? ![A graph showing a curve that starts in the bottom left, moves steeply up and right, levels off briefly, then continues steeply up and right.]()"
},
{
"from": "gpt",
"value": "Confuses cubic and quadratic graphs"
}
] |
[
{
"from": "human",
"value": "Recognise a quadratic graph from its shape Which of the following is an example of a quadratic graph? ![A graph with two curves. One curve is in the positive x, positive y quadrant. It starts at the top close to the y axis, as we move right it drops very quickly towards the x axis then levels off to travel almost parallel to the x axis.\nThe other curve is in the negative x, negative y quadrant. It starts at the top left close to the x axis, as we move right it drops very quickly towards the y axis then becomes almost vertical to travel almost parallel to the y axis. ]()"
},
{
"from": "gpt",
"value": "Confuses reciprocal and quadratic graphs"
}
] |
[
{
"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=8 \\\\ 3 x+y=14\\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\nTom"
},
{
"from": "gpt",
"value": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations."
}
] |
[
{
"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=8 \\\\ 3 x+y=14\\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": "Round numbers greater than 1 to two significant figures \\(\n180.5672\n\\)\n\nWhat is the second significant figure in the number above? \\( 7 \\)"
},
{
"from": "gpt",
"value": "Does not understand the first significant value is the first non-zero digit number"
}
] |