conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "Given a term in an ascending integer linear sequence, use the nth term rule to find its position in that sequence Here are the first \\( 4 \\) terms of a sequence ![\\( \\begin{array}{lllll}11 & 15 & 19 & 23 & \\ldots\\end{array} \\)]() What position in the sequence is the numbe... |
[
{
"from": "human",
"value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... An octagon"
},
{
"from": "gpt",
"value": "Does not understand the naming structure of polygons"
}
] |
[
{
"from": "human",
"value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... A hexagon"
},
{
"from": "gpt",
"value": "Does not understand the naming structure of polygons"
}
] |
[
{
"from": "human",
"value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... A dodecagon"
},
{
"from": "gpt",
"value": "Does not understand the naming structure of polygons"
}
] |
[
{
"from": "human",
"value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Commutativity"
},
{
"from": "gpt",
"value": "Does not recognise the distributive property"
}
] |
[
{
"from": "human",
"value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Factors"
},
{
"from": "gpt",
"value": "Believes splitting a multiplication using the distributive property is the same as spli... |
[
{
"from": "human",
"value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Associativity"
},
{
"from": "gpt",
"value": "Does not recognise the distributive property"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+9 x+14 \\) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]() \\( (x+12) \\)"
},
{
"from": "gpt",
"value": "W... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+9 x+14 \\) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]() \\( (x-7) \\)"
},
{
"from": "gpt",
"value": "Be... |
[
{
"from": "human",
"value": "Convert between kg and g A \\( 0.5 \\) kilogram weight has \\( 10 \\) grams shaved off it.\n\nWhat is the mass of the weight that remains?\nGive your answer in grams. \\( 40 \\mathrm{~g} \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100g in a kilogram"
}
] |
[
{
"from": "human",
"value": "Divide a decimal by an integer \\( 0.1 \\div 4= \\) \\( 0.4 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than divides"
}
] |
[
{
"from": "human",
"value": "Divide a decimal by an integer \\( 0.1 \\div 4= \\) \\( 0.25 \\)"
},
{
"from": "gpt",
"value": "When dividing a decimal by a whole number, ignores decimal point and just divides the digits"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( -6 n+92 \\)"
},
{
"from": "gpt",
... |
[
{
"from": "human",
"value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( -6 n \\)"
},
{
"from": "gpt",
"v... |
[
{
"from": "human",
"value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( 6 n+92 \\)"
},
{
"from": "gpt",
... |
[
{
"from": "human",
"value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\sqrt[3]{\\frac{4 V \\pi}{3}} \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"va... |
[
{
"from": "human",
"value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\sqrt[3]{\\frac{4 V}{3 \\pi}} \\mathrm{cm} \\)"
},
{
"from": "gpt",
"val... |
[
{
"from": "human",
"value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\frac{3 \\sqrt[3]{V}}{4 \\pi} \\mathrm{cm} \\)"
},
{
"from": "gpt",
"val... |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, with all positive integers Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters. \nStep 1 is ... |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, with all positive integers Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters. \nStep 1 is ... |
[
{
"from": "human",
"value": "Solve linear simultaneous equations requiring no scaling of expressions Which of the following pairs of simultaneous equations would have no solutions?\n\\begin{array}{ccc} \nPair \\( 1 \\) & Pair \\( 2 \\) \\\\\n\\( 2 y-2 x=7 \\) & & \\( 2 x+2 y=7 \\) \\\\\n\\( 2 x-2 y=7 \\) & ... |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction \\( \\frac{6}{7} \\times \\frac{2}{3}=? \\) \\( \\frac{9}{7} \\)"
},
{
"from": "gpt",
"value": "Uses dividing fractions method for multiplying fractions"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction \\( \\frac{6}{7} \\times \\frac{2}{3}=? \\) \\( \\frac{8}{21} \\)"
},
{
"from": "gpt",
"value": "When multiplying fractions, adds the numerators and multiplies the denominators"
}
] |
[
{
"from": "human",
"value": "Substitute positive non-integer values into expressions involving powers or roots Jo and Paul are discussing quadratic equations.\n\nJo says there is no value of \\( x \\) that can make \\( (1-x)^{2} \\) negative.\n\nPaul says there is no value of \\( x \\) that can make \\( 1-x... |
[
{
"from": "human",
"value": "Substitute positive non-integer values into expressions involving powers or roots Jo and Paul are discussing quadratic equations.\n\nJo says there is no value of \\( x \\) that can make \\( (1-x)^{2} \\) negative.\n\nPaul says there is no value of \\( x \\) that can make \\( 1-x... |
[
{
"from": "human",
"value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) What should replace the circle when this expression is fully factorised? \\( 9 y^{2}+4 y \\equiv \\bigstar(\\triangle y+\\bigcirc) \\) \\( \\bigcirc=4 y \\)"
}... |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 60 \\)"
},
{
"from": "gpt",
"value": "Believes that addit... |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 50 \\)"
},
{
"from": "gpt",
"value": "When finding the di... |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 30 \\)"
},
{
"from": "gpt",
"value": "When finding the di... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form ax² - c Which of the following answers shows a correct factorisation of the expression below? \\( 2 x^{2}-50 \\) \\( 2\\left(x^{2}-25\\right) \\)"
},
{
"from": "gpt",
"value": "Does not recognise difference of two squares"... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form ax² - c Which of the following answers shows a correct factorisation of the expression below? \\( 2 x^{2}-50 \\) \\( 2(x-5)(x-5) \\)"
},
{
"from": "gpt",
"value": "Factorises difference of two squares with the same sign in... |
[
{
"from": "human",
"value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( 14 \\)"
},
{
"from": "gpt",
"value": "Ignores the negative signs when adding positive and negative numbers"
}
] |
[
{
"from": "human",
"value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( -14 \\)"
},
{
"from": "gpt",
"value": "When subtracting a negative number, subtracts the absolute value rather than adding it"
}
] |
[
{
"from": "human",
"value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( -2 \\)"
},
{
"from": "gpt",
"value": "When subtracting a negative thinks the answer must be negative "
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally I increase \\( £ 200 \\) by \\( 50 \\% \\).\nThen, I increase the new amount by \\( 10 \\% \\).\nWhat percentage of the original amount do I have now? \\( 155 \\% \\)"
},
{
"from": "gpt",
"value": "In repeated ... |
[
{
"from": "human",
"value": "Recognise cube numbers Which of these is a cube number? \\( 15 \\)"
},
{
"from": "gpt",
"value": "Thinks numbers are a multiple of their index"
}
] |
[
{
"from": "human",
"value": "Recognise cube numbers Which of these is a cube number? \\( 100 \\)"
},
{
"from": "gpt",
"value": "Mixes up square numbers and cube numbers"
}
] |
[
{
"from": "human",
"value": "Recognise cube numbers Which of these is a cube number? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Thinks numbers are a multiple of their index"
}
] |
[
{
"from": "human",
"value": "Identify and count the faces, vertices and edges of a 3D shape ![An orange cube]() How many faces does this cube have? \\( 12 \\)"
},
{
"from": "gpt",
"value": "Confuses the terms faces and edges"
}
] |
[
{
"from": "human",
"value": "Identify and count the faces, vertices and edges of a 3D shape ![An orange cube]() How many faces does this cube have? \\( 8 \\)"
},
{
"from": "gpt",
"value": "Confuses the terms faces and vertices"
}
] |
[
{
"from": "human",
"value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first... |
[
{
"from": "human",
"value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first... |
[
{
"from": "human",
"value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first... |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 1 decimal place Convert this fraction to a percentage\n\\(\n\\frac{27}{200}\n\\) \\( 27 \\% \\)"
},
{
"from": "gpt",
"value": "Does not understand a percentage is out of 100"
}
] |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 1 decimal place Convert this fraction to a percentage\n\\(\n\\frac{27}{200}\n\\) \\( 54 \\% \\)"
},
{
"from": "gpt",
"value": "Does not understand a percentage is out of 100"
}
] |
[
{
"from": "human",
"value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 1 \\) day? \\( 24 \\times 60 \\)"
},
{
"from": "gpt",
"value": "Converted hours to minutes instead of hours to seconds"
}
] |
[
{
"from": "human",
"value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 1 \\) day? \\( 12 \\times 60 \\times 60 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 12 hours in 1 day"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 2.507 \\)"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 2.50 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 3.00 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{|c|c|c|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline ... |
[
{
"from": "human",
"value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{|c|c|c|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline ... |
[
{
"from": "human",
"value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{|c|c|c|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline ... |
[
{
"from": "human",
"value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... no equal side lengths."
},
{
"from": "gpt",
"value": "Confuses isosceles and scalene triangles"
}
] |
[
{
"from": "human",
"value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... one pair of parallel sides."
},
{
"from": "gpt",
"value": "Does not know the meaning of the word parallel"
}
] |
[
{
"from": "human",
"value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... three equal angles."
},
{
"from": "gpt",
"value": "Confuses isosceles and equilateral triangles"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal 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 \\( P \\) ? ![A set of axes: x-axis from ... |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal 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 \\( P \\) ? ![A set of axes: x-axis from ... |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal 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 \\( P \\) ? ![A set of axes: x-axis from ... |
[
{
"from": "human",
"value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=6 x\n\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 0 \\) \\\\\n\\hline\n\... |
[
{
"from": "human",
"value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=6 x\n\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 0 \\) \\\\\n\\hline\n\... |
[
{
"from": "human",
"value": "Given a midpoint and a coordinate work out the position of the other coordinate, where at least one value is negative and at least one is a non-integer Here are two points and their midpoint.\nWhat should replace the triangle? ![The image is a set of axes with three points marke... |
[
{
"from": "human",
"value": "Given a midpoint and a coordinate work out the position of the other coordinate, where at least one value is negative and at least one is a non-integer Here are two points and their midpoint.\nWhat should replace the triangle? ![The image is a set of axes with three points marke... |
[
{
"from": "human",
"value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) Ori is expanding these three brackets:\n\\(\n(x+2)(x-4)(x-7)\n\\)\n\nHe finds it helpful to split the first bracket and view the problem as follows:\n\\(\nx(x-4)(x-7)+2(x-4)(x-7)\n\\)\n\nHe expands the brackets... |
[
{
"from": "human",
"value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in t... |
[
{
"from": "human",
"value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in t... |
[
{
"from": "human",
"value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in t... |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer What fraction replaces the question mark? ![A bar split into 5 equal parts, with two shaded. One of the shaded parts is labelled with a question mark.]() \\( \\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "Ident... |
[
{
"from": "human",
"value": "Answer decimal problems that require the use of BIDMAS Which calculation should you do first?\n\\(\n((0.5 \\div(0.2+0.4)-0.3) \\times 0.6)\n\\) \\( 0.5 \\div 0.2 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order... |
[
{
"from": "human",
"value": "Answer decimal problems that require the use of BIDMAS Which calculation should you do first?\n\\(\n((0.5 \\div(0.2+0.4)-0.3) \\times 0.6)\n\\) \\( 0.3 \\times 0.6 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from right to left regardless of priority ord... |
[
{
"from": "human",
"value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? \\( 12 \\times 6-(1+2) \\)"
},
{
"from": "gpt",
"value": "Performs subtraction in wrong order"
}
] |
[
{
"from": "human",
"value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? \\( 12 \\times(6-1+2) \\)"
},
{
"from": "gpt",
"value": "Applies BIDMAS in strict order (does not realize addition and sub... |
[
{
"from": "human",
"value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? Does not need brackets"
},
{
"from": "gpt",
"value": "Carries out operations from right to left regardless of priority ord... |
[
{
"from": "human",
"value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls a... |
[
{
"from": "human",
"value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls a... |
[
{
"from": "human",
"value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls a... |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow\\times 3\\rightarrow+4\\rightarrow4+3 a \\\\ a\\rightarrow \\times 3\\rightarrow+4\\rightarrow3(4+a)\\end{array} \... |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow+4 \\rightarrow\\times 3\\rightarrow4+3 a \\\\ a \\rightarrow\\times 3\\rightarrow+4\\rightarrow-3(4+a)\\end{array}... |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow4 \\rightarrow\\times 3\\rightarrow4+3 a \\\\ a\\rightarrow+4\\rightarrow\\times 3\\rightarrow3(4+a)\\end{array} \\... |
[
{
"from": "human",
"value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Confuses factors and multiples"
}
] |
[
{
"from": "human",
"value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 18 \\)"
},
{
"from": "gpt",
"value": "Identifies a common multiple of two numbers when asked to consider a common multiple of th... |
[
{
"from": "human",
"value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 20 \\)"
},
{
"from": "gpt",
"value": "Identifies a multiple of a number but not a common multiple of a group of numbers"
}
] |
[
{
"from": "human",
"value": "Carry out missing number subtraction problems involving negative integers \\( \\fbox{-5} \\) x\\( \\hspace{0.2cm} \\fbox{4} = \\hspace{0.2cm} \\fbox{-12} - \\hspace{0.2cm}\\fbox{ ? } \\) \\( -8 \\)"
},
{
"from": "gpt",
"value": "When subtracting a negative number, su... |
[
{
"from": "human",
"value": "Carry out missing number subtraction problems involving negative integers \\( \\fbox{-5} \\) x\\( \\hspace{0.2cm} \\fbox{4} = \\hspace{0.2cm} \\fbox{-12} - \\hspace{0.2cm}\\fbox{ ? } \\) \\( -32 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying a positive by a ... |
[
{
"from": "human",
"value": "Multiplication, division and power law of indices with positive integer powers \\(\\frac{\\left(5^{6}\\right)^{4}}{5^{2}} \\equiv 5^{n}\\)\n\nWhat is the value of \\( n \\) ? \\( 8 \\)"
},
{
"from": "gpt",
"value": "Thinks a power raised to a power leads to addition ... |
[
{
"from": "human",
"value": "Multiplication, division and power law of indices with positive integer powers \\(\\frac{\\left(5^{6}\\right)^{4}}{5^{2}} \\equiv 5^{n}\\)\n\nWhat is the value of \\( n \\) ? \\( 12 \\)"
},
{
"from": "gpt",
"value": "Believes when dividing numbers with the same base ... |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.8989 \\ldots \\)"
},
... |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.75 \\)"
},
{
"fr... |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.9 \\)"
},
{
"fro... |
[
{
"from": "human",
"value": "Identify factors of a number \\begin{tabular}{|c|c|c|}\n & Multiple of \\( 4 \\) & Not a multiple of \\( 4 \\) \\\\\n\\hline Factor of \\( 60 \\) & A & B \\\\\n\\hline Not a factor of \\( 60 \\) & C & D \\\\\n\\hline\n\\end{tabular} In which box should you place \\( \\mathb... |
[
{
"from": "human",
"value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( n, 2 n, 3 n \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of consecutive"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( 3 n, 2 n, n \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of consecutive"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( n, n+2, n+4 \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of consecutive"
}
] |
[
{
"from": "human",
"value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 18 \\)"
},
{
"from": "gpt",
"value": "Halves when asked to find the square root"
}
] |
[
{
"from": "human",
"value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 1296 \\)"
},
{
"from": "gpt",
"value": "Squares when asked to find the square root"
}
] |
[
{
"from": "human",
"value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 72 \\)"
},
{
"from": "gpt",
"value": "Mixes up square rooting and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 0.4 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 0.0256 \\)"
},
{
"from": "gpt",
"value": "Does not understand place value within a number"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 2.56 \\)"
},
{
"from": "gpt",
"value": "Does not understand place value within a number"
}
] |
[
{
"from": "human",
"value": "Given the sector angle on a pie chart, calculate the frequency of a group The pie chart shows the favourite subjects of children at a school.\n\nIf \\( 12 \\) students chose Science, how many chose French? ![A pie chart split into four parts, labelled with school subjects. The p... |
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