conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "Perform calculations with temperature when given in the same units Which statement about the temperatures \\( -5^{\\circ} \\mathrm{C} \\) and \\( 2^{\\circ} \\mathrm{C} \\) is true? \\( 2^{\\circ} \\mathrm{C} \\) is \\( 7^{\\circ} \\mathrm{C} \\) colder than\n\\[\n-5^{\\circ} \\... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? \\( 7+6 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from right t... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? \\( 10-8 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left t... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? It doesn't matter: you get the same answer"
},
{
"from": "gpt",
"value": "Beli... |
[
{
"from": "human",
"value": "Convert between cm³ and l \\( 500000 \\mathrm{~cm}^{3} \\) is the same as ______ litres \\( 5 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 10 000 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Convert between cm³ and l \\( 500000 \\mathrm{~cm}^{3} \\) is the same as ______ litres \\( 5000 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 100 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Equation"
},
{
"from": "gpt",
"value": "Confuses a variable with an equation"
}
] |
[
{
"from": "human",
"value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Term"
},
{
"from": "gpt",
"value": "Confuses a term with a variable"
}
] |
[
{
"from": "human",
"value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Expression"
},
{
"from": "gpt",
"value": "Confuses an expression with a variable"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\nz+5\n\\] \\( 5 z \\)"
},
{
"from": "gpt",
"value": "Does not realise that two letters together, or a number and letter toge... |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\nz+5\n\\] \\( z^{5} \\)"
},
{
"from": "gpt",
"value": "Believes addition of terms and powers of terms are equivalent e.g. a ... |
[
{
"from": "human",
"value": "Identify or mark lines of symmetry on a shape Which shape has a line of symmetry? ![A Trapezium above the label \"A\"; A shape which is a circle with a 90 degree sector removed above the label \"B\"; A crescent (moon) shape above the label \"C\"; the words \"All of them\" above ... |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a re... |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a re... |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a re... |
[
{
"from": "human",
"value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() Acute"
},
{
"from": "gpt",
"value": "Confuses obtuse and acute angles"
}
] |
[
{
"from": "human",
"value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() Reflex"
},
{
"from": "gpt",
"value": "Does not understand that an obtuse angle is between 90 and 180 degrees"
}
] |
[
{
"from": "human",
"value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() A right angle"
},
{
"from": "gpt",
"value": "Does not understand that an obtuse angle is between 90 and 180 degrees"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coor... |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coor... |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coor... |
[
{
"from": "human",
"value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"-4\" written inside it and the ... |
[
{
"from": "human",
"value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"-4\" written inside it and the ... |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=0 \\)"
},
{
"from": "gpt",
"value": "Believes the solution of mx + c = 0 is x =0"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=1 \\)"
},
{
"from": "gpt",
"value": "Believes they solve mx + c = 0 by substituting in x = 0"
... |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=-0.4 \\)"
},
{
"from": "gpt",
"value": "Believes the solution of mx + c = 0 is x = m"
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -1 \\leq x<3 \\) ? ![Number line with numbers from -5 to 5. Above the -1 is a blue, filled circle with an arrow to the left. Above the 3 is an open,... |
[
{
"from": "human",
"value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -1 \\leq x<3 \\) ? ![Number line with numbers from -5 to 5. Above the -1 is an open, unfilled circle and above the 3 is a green, filled circle. The... |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Expand:\n\\[\n3(p-1)\n\\] \\( 3 p-1 \\)"
},
{
"from": "gpt",
"value": "Only multiplies the first term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Expand:\n\\[\n3(p-1)\n\\] \\( p-3 \\)"
},
{
"from": "gpt",
"value": "Only multiplies second term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Expand:\n\\[\n3(p-1)\n\\] \\( 3 p-2 \\)"
},
{
"from": "gpt",
"value": "When expanding brackets, multiplies out the first term correctly but add... |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle... |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle... |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle... |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( +200 \\) then \\( +1 \\)"
},
{
"from": "gpt",
"value": "Does not understand the ... |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( -200 \\) then \\( -1 \\)"
},
{
"from": "gpt",
"value": "Does not understand the ... |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( +200 \\) then \\( -1 \\)"
},
{
"from": "gpt",
"value": "Does not understand the ... |
[
{
"from": "human",
"value": "Interpret numbers in a frequency table \\begin{tabular}{|c|c|c|}\n\\hline TVs & Frequency & TVs \\( \\times \\) Frequency \\\\\n\\hline \\( 0 \\) & \\( 3 \\) & \\( 0 \\) \\\\\n\\hline \\( 1 \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline \\( 2 \\) & \\( 8 \\) & \\( 16 \\) \\\\\n\\hlin... |
[
{
"from": "human",
"value": "Interpret numbers in a frequency table \\begin{tabular}{|c|c|c|}\n\\hline TVs & Frequency & TVs \\( \\times \\) Frequency \\\\\n\\hline \\( 0 \\) & \\( 3 \\) & \\( 0 \\) \\\\\n\\hline \\( 1 \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline \\( 2 \\) & \\( 8 \\) & \\( 16 \\) \\\\\n\\hlin... |
[
{
"from": "human",
"value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Radius"
},
{
"from": "gpt",
"value": "Confuses diameter and radius"
}
] |
[
{
"from": "human",
"value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Arc"
},
{
"from": "gpt",
"value": "Confuses arc and diameter"
}
] |
[
{
"from": "human",
"value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Circumference"
},
{
"from": "gpt",
"value": "Confuses circumference and diameter"
}
] |
[
{
"from": "human",
"value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( 3: 4 \\)"
},
{
"from": "gpt",
"value": "When writing ratio from diagram, writes total as one side"
}
] |
[
{
"from": "human",
"value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( \\frac{3}{4} \\)"
},
{
"from": "gpt",
"value": "When writing fraction from diagram, writes total as denominator"
}
] |
[
{
"from": "human",
"value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( \\frac{270}{360} \\)"
},
{
"from": "gpt",
"value": "When writing fraction from diagram, writes total as denominator"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to one significant figure Jo and Paul are arguing about rounding.\n\nJo says \\( \\mathbf{9 9 . 9 6} \\) rounded to \\( 1 \\) significant figure is \\( \\mathbf{1 0 0} \\)\n\nPaul says \\( \\mathbf{9 9 . 9 6} \\) rounded to \\( 1 \\) decimal place is... |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Tom and Katie are discussing rearranging \\( t=\\sqrt{u+9} \\) to make \\( u \\) the subject\nTom says a correct first line of working could be: \\( t=\\sqrt{u}+3 \\)\nKati... |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Tom and Katie are discussing rearranging \\( t=\\sqrt{u+9} \\) to make \\( u \\) the subject\nTom says a correct first line of working could be: \\( t=\\sqrt{u}+3 \\)\nKati... |
[
{
"from": "human",
"value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 0.3 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of divides"
}
] |
[
{
"from": "human",
"value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 0.025 \\)"
},
{
"from": "gpt",
"value": "When dividing a decimal by an integer, divides by the wrong power of 10 when reinserting the decimal."
}
] |
[
{
"from": "human",
"value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 1 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than divides"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hli... |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hli... |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hli... |
[
{
"from": "human",
"value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 95365 \\) \\( 10000 \\)"
},
{
"from": "gpt",
"value": "When rounding up from a 9, does not add one on to the digit to the left"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 95365 \\) \\( 90000 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.15 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.154 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.253 \\)"
},
{
"from": "gpt",
"value": "Rounds incorrectly by changing multiple place values"
}
] |
[
{
"from": "human",
"value": "Convert between cm³ and mm³ \\( 1 \\mathrm{~cm}^{3} \\) is the same as _______ \\( \\mathrm{mm}^{3} \\) \\( 10 \\)"
},
{
"from": "gpt",
"value": "Does not cube the conversion factor when converting cubed units"
}
] |
[
{
"from": "human",
"value": "Convert between cm³ and mm³ \\( 1 \\mathrm{~cm}^{3} \\) is the same as _______ \\( \\mathrm{mm}^{3} \\) \\( 100 \\)"
},
{
"from": "gpt",
"value": "Does not cube the conversion factor when converting cubed units"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 0.64 \\mathrm{~m}^{2} \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, divides by the wrong ... |
[
{
"from": "human",
"value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 1.12 \\mathrm{~m}^{2} \\)"
},
{
"from": "gpt",
"value": "Calculates perimeter when asked for area"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 0.56 \\mathrm{~m}^{2} \\)"
},
{
"from": "gpt",
"value": "Adds when calculating area instead of multiplyin... |
[
{
"from": "human",
"value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 1 \\) hexagon\n\\( 6 \\) triangles"
},
{
"from": "gpt",
"value": "Confuses pyramid with prism"
}
] |
[
{
"from": "human",
"value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 1 \\) hexagon\n\\( 6 \\) rectangles"
},
{
"from": "gpt",
"value": "Confuses pyramid with prism"
}
] |
[
{
"from": "human",
"value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 2 \\) hexagons\n\\( 6 \\) triangles"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 3 \\)"
},... |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 5 \\)"
},... |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 9 \\)"
},... |
[
{
"from": "human",
"value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) digits"
},
{
... |
[
{
"from": "human",
"value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) multiples"
},
... |
[
{
"from": "human",
"value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) reciprocal"
},
... |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hl... |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hl... |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hl... |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)](... |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)](... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+6 x+8 \\) we need two numbers that: Add to give \\( 6 x \\) and multiply to give \\( 8 \\)"
},
{
"from": "gpt",
"value": "When factorising into double brackets, believes the sum of th... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+6 x+8 \\) we need two numbers that: Add to give \\( 8 \\) and multiply to give \\( 6 \\)"
},
{
"from": "gpt",
"value": "Does not know that to factorise a quadratic expression, to find... |
[
{
"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=\\{1,2\\} \\)\n\nKatie says the sample space can be written as: \\( S=\\{1,1,2,2,2\\} \\)\nWho do you agree with? ![Circle di... |
[
{
"from": "human",
"value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() Equation"
},
{
"from": "gpt",
"value": "Confuses a formula with an equation"
}
] |
[
{
"from": "human",
"value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() Variable"
},
{
"from": "gpt",
"value": "Confuses a variable with a formula"
}
] |
[
{
"from": "human",
"value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() Expression"
},
{
"from": "gpt",
"value": "Confuses a formula with an expression"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 650 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 600 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 630 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Determine if a given point lies on a line Tom and Katie are arguing about points on the line\n\\[\ny=2 x-3\n\\]\n\nTom says \\( (5,7) \\) lies on the line \\( \\boldsymbol{y}=\\mathbf{2} \\boldsymbol{x}-\\mathbf{3} \\)\n\nKatie says \\( (-5,-7) \\) lies on the line \\( \\boldsym... |
[
{
"from": "human",
"value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{|l|l|l|l|l|l|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabul... |
[
{
"from": "human",
"value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{|l|l|l|l|l|l|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabul... |
[
{
"from": "human",
"value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{|l|l|l|l|l|l|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabul... |
[
{
"from": "human",
"value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=1 \\)"
},
{
... |
[
{
"from": "human",
"value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=9 \\)"
},
{
... |
[
{
"from": "human",
"value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=-9 \\)"
},
{... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - bx - c Tom and Katie are arguing about factorising. Tom says \\( x^{2}+5 x+6 \\equiv(x+3)(x+2) \\) \nKatie says \\( x^{2}-5 x-6 \\equiv(x-3)(x-2) \\) \nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": ... |
[
{
"from": "human",
"value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 90 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 90.7 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 92 \\)"
},
{
"from": "gpt",
"value": "Rounds incorrectly by changing multiple place values"
}
] |
[
{
"from": "human",
"value": "Carry out addition problems involving one negative integer Peter is counting up in threes. He starts at \\( -16 \\)\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -28 \\)"
},
{
"from": "gpt",
"value": "Counts on in the wrong direction on a number line"
}... |
[
{
"from": "human",
"value": "Carry out addition problems involving one negative integer Peter is counting up in threes. He starts at \\( -16 \\)\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -31 \\)"
},
{
"from": "gpt",
"value": "Counts on in the wrong direction on a number line"
}... |
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