conversations listlengths 2 2 |
|---|
[
{
"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 te... |
[
{
"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 prob... |
[
{
"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 ti... |
[
{
"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 o... |
[
{
"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 arr... |
[
{
"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",
... |
[
{
"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",
... |
[
{
"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",... |
[
{
"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... |
[
{
"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... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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": "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": "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 unt... |
[
{
"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 \\) \... |
[
{
"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 \\) \... |
[
{
"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 \\) \... |
[
{
"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... |
[
{
"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... |
[
{
"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 fr... |
[
{
"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 numbe... |
[
{
"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) a... |
[
{
"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) a... |
[
{
"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",
... |
[
{
"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... |
[
{
"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",
... |
[
{
"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 n... |
[
{
"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": ... |
[
{
"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": "gp... |
[
{
"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 unde... |
[
{
"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 under... |
[
{
"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 und... |
[
{
"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 t... |
[
{
"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 t... |
[
{
"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... |
[
{
"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... |
[
{
"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... |
[
{
"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": "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": "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": "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": "g... |
[
{
"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"
},
{
"f... |
[
{
"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"
},
{
"f... |
[
{
"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 le... |
[
{
"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 ter... |
[
{
"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 ca... |
[
{
"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... |
[
{
"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": "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... |
[
{
"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": "D... |
[
{
"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 calculat... |
[
{
"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... |
[
{
"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... |
[
{
"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 addin... |
[
{
"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 sho... |
[
{
"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 sho... |
[
{
"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 sho... |
[
{
"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": "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... |
[
{
"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 ... |
[
{
"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 wi... |
[
{
"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 c... |
[
{
"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... |
[
{
"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 ... |
[
{
"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 th... |
[
{
"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 previ... |
[
{
"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 ad... |
[
{
"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 prob... |
[
{
"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 ab... |
[
{
"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",
... |
[
{
"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 ax... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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"
}
] |
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