conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "Calculate the gradient on a linear section on a real life graph The cost of a taxi-ride is shown on the graph.\n\nWhat is the cost per mile? ![The graph is Cost (£) on the vertical axis and Distance (miles) on the horizontal axis. The graph is a straight line from (0, 2) to (5, ... |
[
{
"from": "human",
"value": "Calculate the gradient on a linear section on a real life graph The cost of a taxi-ride is shown on the graph.\n\nWhat is the cost per mile? ![The graph is Cost (£) on the vertical axis and Distance (miles) on the horizontal axis. The graph is a straight line from (0, 2) to (5, ... |
[
{
"from": "human",
"value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, double it, subtract 5, and the answer is \\( 23 \\).\n\nWhich of the following should replace the star? ![A function machine with ... |
[
{
"from": "human",
"value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, double it, subtract 5, and the answer is \\( 23 \\).\n\nWhich of the following should replace the star? ![A function machine with ... |
[
{
"from": "human",
"value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, double it, subtract 5, and the answer is \\( 23 \\).\n\nWhich of the following should replace the star? ![A function machine with ... |
[
{
"from": "human",
"value": "Use inequality notation to order fractions whose denominators are not multiples of the same number What sign would make this statement true?\n\\(\n\\frac{4}{6} ? \\frac{10}{15}\n\\) \\( < \\)"
},
{
"from": "gpt",
"value": "Believes that fractions with larger denomin... |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible\n\\(\n\\frac{5 m-10}{m^{2}+3 m-10}\n\\) \\( \\frac{5 m}{m^{2}+3 m} \\)"
},
{
"from": "gpt",
"value": "Simplifies a fraction by adding or subtracting t... |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible\n\\(\n\\frac{5 m-10}{m^{2}+3 m-10}\n\\) Does not simplify"
},
{
"from": "gpt",
"value": "Does not know how to simplify algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{2}{5} \\div 2\n\\) \\( \\frac{4}{5} \\)"
},
{
"from": "gpt",
"value": "when dividing a fraction by an integer, multiplies the numerator by the integer"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{2}{5} \\div 2\n\\) \\( \\frac{4}{10} \\)"
},
{
"from": "gpt",
"value": "When dividing a fraction by an integer, multiplies both the numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Interpret the gradient on a linear section on a real life graph Jadon decides to go for a run.\nThe graph on the right shows Jadon's speed in metres per second \\( (s) \\) over time in seconds\n\\( (t) \\).\n\nThe gradient of the negative sloping section of the graph is \\( 0.8 ... |
[
{
"from": "human",
"value": "Interpret the gradient on a linear section on a real life graph Jadon decides to go for a run.\nThe graph on the right shows Jadon's speed in metres per second \\( (s) \\) over time in seconds\n\\( (t) \\).\n\nThe gradient of the negative sloping section of the graph is \\( 0.8 ... |
[
{
"from": "human",
"value": "Sketch curves in the form (x + a)(x + b) indicating where they cross the axes \\( y=(x-8)(x-6) \\) \\( y=(x-8)(x-6) \\) Where does this curve intercept the \\( y \\) axis? Where does this curve intercept the \\( y \\) axis? \\( (0,-14) \\) \\( (0,-14) \\)"
},
{
"from": "... |
[
{
"from": "human",
"value": "Sketch curves in the form (x + a)(x + b) indicating where they cross the axes \\( y=(x-8)(x-6) \\) \\( y=(x-8)(x-6) \\) Where does this curve intercept the \\( y \\) axis? Where does this curve intercept the \\( y \\) axis? \\( \\begin{array}{c}(0,8) \\\\ \\text { and } \\\\ (0,... |
[
{
"from": "human",
"value": "Sketch curves in the form (x + a)(x + b) indicating where they cross the axes \\( y=(x-8)(x-6) \\) \\( y=(x-8)(x-6) \\) Where does this curve intercept the \\( y \\) axis? Where does this curve intercept the \\( y \\) axis? \\( (0,-48) \\) \\( (0,-48) \\)"
},
{
"from": "... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving roots Tom and Katie are discussing calculations involving square roots.\n\nTom says \\( \\sqrt{16}+\\sqrt{9}=5 \\)\n\nKatie says \\( \\sqrt{16+9}=5 \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gp... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving roots Tom and Katie are discussing calculations involving square roots.\n\nTom says \\( \\sqrt{16}+\\sqrt{9}=5 \\)\n\nKatie says \\( \\sqrt{16+9}=5 \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gp... |
[
{
"from": "human",
"value": "Find the nth term rule for an ascending fractional linear sequence \\( \\frac{1}{24}, \\frac{1}{12}, \\frac{1}{8}, \\frac{1}{6}, \\ldots \\) When calculating the nth-term rule of this sequence, what should replace the rectangle? ![nth-term rule:\n\\[\n\\frac{1}{24} n\n\\] follow... |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 Tom and Katie are trying to write calculations based on the diagram below.\n\nTom writes: \\( 15-20=-5 \\)\n\nKatie writes: \\( (-5)+20=15 \\)\n\nWho is correct? ![Number line with an arrow ma... |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 Tom and Katie are trying to write calculations based on the diagram below.\n\nTom writes: \\( 15-20=-5 \\)\n\nKatie writes: \\( (-5)+20=15 \\)\n\nWho is correct? ![Number line with an arrow ma... |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 Tom and Katie are trying to write calculations based on the diagram below.\n\nTom writes: \\( 15-20=-5 \\)\n\nKatie writes: \\( (-5)+20=15 \\)\n\nWho is correct? ![Number line with an arrow ma... |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence A sequence is formed using the rule\n\nSquare the position and add \\( 5 \\)\n\nWhat is the third term in the sequence? \\( 11 \\)"
},
{
"from": "gpt",
"value": ... |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence A sequence is formed using the rule\n\nSquare the position and add \\( 5 \\)\n\nWhat is the third term in the sequence? \\( 6 \\)"
},
{
"from": "gpt",
"value": "... |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for the curve y = x3 + c This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) ![\\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 2 \\) \\\\\n\\hline\\( y \\) & W \\\\\... |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for the curve y = x3 + c This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) ![\\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 2 \\) \\\\\n\\hline\\( y \\) & W \\\\\... |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for the curve y = x3 + c This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) ![\\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 2 \\) \\\\\n\\hline\\( y \\) & W \\\\\... |
[
{
"from": "human",
"value": "Calculate distance where speed and time are in the appropriate units This displacement-time graph shows \\( 10 \\) seconds of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 15 \\mathrm{~m} / \\mathrm{s} \\).\n\nWhat distance should replace the star? ![The ... |
[
{
"from": "human",
"value": "Calculate distance where speed and time are in the appropriate units This displacement-time graph shows \\( 10 \\) seconds of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 15 \\mathrm{~m} / \\mathrm{s} \\).\n\nWhat distance should replace the star? ![The ... |
[
{
"from": "human",
"value": "Calculate distance where speed and time are in the appropriate units This displacement-time graph shows \\( 10 \\) seconds of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 15 \\mathrm{~m} / \\mathrm{s} \\).\n\nWhat distance should replace the star? ![The ... |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.5=\\frac{1}{2}=? \\% \\) \\( 12 \\% \\)"
},
{
"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 \\( 0.5=\\frac{1}{2}=? \\% \\) \\( 2 \\% \\)"
},
{
"from": "gpt",
"value": "Converts fraction to percentage by putting % sign after the denominator"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Simplify, if possible:\n\\(\na \\times 4\n\\) \\( a 4 \\)"
},
{
"from": "gpt",
"value": "Writes the variable before the coefficient in an algebraic term"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Simplify, if possible:\n\\(\na \\times 4\n\\) \\( a^{4} \\)"
},
{
"from": "gpt",
"value": "Thinks multiplying a variable by a number is the same as raising that variable to the power of that number"
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is ![Triangle with base labelled b and perpendicular height labelled h]() \\( A=\\frac{1}{2}(b \\times h) \\) Rearrange this to mak... |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is ![Triangle with base labelled b and perpendicular height labelled h]() \\( A=\\frac{1}{2}(b \\times h) \\) Rearrange this to mak... |
[
{
"from": "human",
"value": "Given the distance travelled, complete missing values on a speed-time graph ![A speed-time graph. The vertical axis is labelled Speed (mph), with no scale labelled but 4 squares up is marked v.\nThe horizontal axis is labelled Time (hours) and the scale is 0, 1, 2, 3, 4 in even ... |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 4 \\) litres \\( = \\)_________ \\( \\mathrm{cm}^{3} \\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 1 cubic centimetre"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 4 \\) litres \\( = \\)_________ \\( \\mathrm{cm}^{3} \\) \\( 400 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 100 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 4 \\) litres \\( = \\)_________ \\( \\mathrm{cm}^{3} \\) \\( 40 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 10 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for finding the average speed is\n\n\\(\n\\text { speed }(S)=\\frac{\\text { distance }(D)}{\\text { time }(T)}\n\\)\n\nWhich of the following are not correct? \\( D=S T ... |
[
{
"from": "human",
"value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\( 2,2,4,7,10 \\) \\( 5 \\)"
},
{
"from": "gpt",
"value": "Finds the mean instead of the median"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\( 2,2,4,7,10 \\) \\( 2 \\)"
},
{
"from": "gpt",
"value": "Finds the mode instead of the median"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\( 2,2,4,7,10 \\) \\( 5.5 \\)"
},
{
"from": "gpt",
"value": "When finding the median for an odd numbered data set, find the midpoint of two values rath... |
[
{
"from": "human",
"value": "Identify when it is appropriate to use a line graph Which of the following situations would a line graph be the most appropriate to use? Showing the number of brothers and sisters children in a class have"
},
{
"from": "gpt",
"value": "Does not understand that a line... |
[
{
"from": "human",
"value": "Identify when it is appropriate to use a line graph Which of the following situations would a line graph be the most appropriate to use? Showing what time each member of a family went to bed last night"
},
{
"from": "gpt",
"value": "Does not understand that a line gr... |
[
{
"from": "human",
"value": "Identify when it is appropriate to use a line graph Which of the following situations would a line graph be the most appropriate to use? Showing the numbers of each type of animal in a zoo"
},
{
"from": "gpt",
"value": "Does not understand that a line graph shows a r... |
[
{
"from": "human",
"value": "Read values off a displacement-time graph This graph shows the displacement of a ball from a starting point at various times.\nHow far did the ball travel between \\( 1 \\) and \\( 2 \\) seconds? ![A displacement versus time graph]() This graph displacem from a start \\( 0.5 \\ ... |
[
{
"from": "human",
"value": "Read values off a displacement-time graph This graph shows the displacement of a ball from a starting point at various times.\nHow far did the ball travel between \\( 1 \\) and \\( 2 \\) seconds? ![A displacement versus time graph]() This graph displacem from a start \\( 2 \\ \\... |
[
{
"from": "human",
"value": "Read values off a displacement-time graph This graph shows the displacement of a ball from a starting point at various times.\nHow far did the ball travel between \\( 1 \\) and \\( 2 \\) seconds? ![A displacement versus time graph]() This graph displacem from a start \\( 2.5 \\ ... |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving negative integers Tom and Katie are arguing about a first step to solve this equation:\n\\(1-4 v=3-9 v\\)\n\nTom says you can write: \\( 1+5 v=3 \\)\n\nKatie says you can write: \\( -4 v=2-9 v \\)\n\nWho... |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 326 \\) rounded to the nearest \\( 10 \\) ? \\( 300 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 326 \\) rounded to the nearest \\( 10 \\) ? \\( 320 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 326 \\) rounded to the nearest \\( 10 \\) ? \\( 350 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units Paige, Kaci and David want to find the area of the school playground. They each do it a different way. Who is correct? ![A compound shape made up of two rectangles. D... |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units Paige, Kaci and David want to find the area of the school playground. They each do it a different way. Who is correct? ![A compound shape made up of two rectangles. D... |
[
{
"from": "human",
"value": "Carry out division problems involving one negative integer \\( 12 \\div(-4)= \\) \\( 3 \\)"
},
{
"from": "gpt",
"value": "Believes dividing a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n1,5,5,17,-6\n\\] \\( 5 \\)"
},
{
"from": "gpt",
"value": "Finds the mode rather than the range"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n1,5,5,17,-6\n\\] \\( 11 \\)"
},
{
"from": "gpt",
"value": "To find the range adds the biggest and smallest number rather than subtract"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n1,5,5,17,-6\n\\] \\( 16 \\)"
},
{
"from": "gpt",
"value": "Does not include negative numbers when calculating a range"
}
] |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape \\( Q \\) is an enlargement of shape \\( P \\).\nWhat calculation works out the constant of proportionality from shape \\( P \\) to shape \\( Q \\) ? ![To similar star sh... |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape \\( Q \\) is an enlargement of shape \\( P \\).\nWhat calculation works out the constant of proportionality from shape \\( P \\) to shape \\( Q \\) ? ![To similar star sh... |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape \\( Q \\) is an enlargement of shape \\( P \\).\nWhat calculation works out the constant of proportionality from shape \\( P \\) to shape \\( Q \\) ? ![To similar star sh... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division What does the following equal?\n\\[\n8-7+10 \\times 3\n\\] \\( -29 \\)"
},
{
"from": "gpt",
"value": "Applies BIDMAS in strict order (does not reali... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division What does the following equal?\n\\[\n8-7+10 \\times 3\n\\] \\( 33 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regar... |
[
{
"from": "human",
"value": "Distinguish between congruency and similarity Tom and Katie are discussing congruence and similarity. Who is correct? Tom says these two squares are congruent ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Katie says these two squa... |
[
{
"from": "human",
"value": "Distinguish between congruency and similarity Tom and Katie are discussing congruence and similarity. Who is correct? Tom says these two squares are congruent ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Katie says these two squa... |
[
{
"from": "human",
"value": "Distinguish between congruency and similarity Tom and Katie are discussing congruence and similarity. Who is correct? Tom says these two squares are congruent ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Katie says these two squa... |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Jo and Paul are arguing about how to fully describe the rotation from shape \\( P \\... |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Jo and Paul are arguing about how to fully describe the rotation from shape \\( P \\... |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Jo and Paul are arguing about how to fully describe the rotation from shape \\( P \\... |
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