conversations listlengths 2 2 |
|---|
[
{
"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? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Does not understand the first significant value is the first non-zero digit number"
}
] |
[
{
"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? \\( 6 \\)"
},
{
"from": "gpt",
"value": "Identifies second decimal place value when asked for the second significant figure"
}
] |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable What do you need to do to eliminate the \\( q \\)s in each of these pairs of simultaneous equations?\n\\begin{array}{cc}\n Pair 1 & Pair 2 \\\\\n\\( 2p-4q=6 \\) & \\( 2p-4q=6 \\)\\\\... |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable What do you need to do to eliminate the \\( q \\)s in each of these pairs of simultaneous equations?\n\\begin{array}{cc}\n Pair 1 & Pair 2 \\\\\n\\( 2p-4q=6 \\) & \\( 2p-4q=6 \\)\\\\... |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis? \\( (3,5) \\)"
},
{
"from": "gpt",
"value": "Believes both the x and y co-ordinates of the x... |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis? \\( \\begin{array}{c}(-3,0) \\\\ \\text { and } \\\\ (-5,0)\\end{array} \\)"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis? \\( \\begin{array}{c}(3,5) \\\\ \\text { and } \\\\ (-3,-5)\\end{array} \\)"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]() \\( 46^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Confuses vertically opp... |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]() \\( 65^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Misinterprets the meani... |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know that a... |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\] \\( 0+1+3+4+7 \\div 5 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to r... |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\] \\( \\frac{1+3+4+7}{4} \\)"
},
{
"from": "gpt",
"value": "When asked for the mean of a list of... |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\] None of them"
},
{
"from": "gpt",
"value": "Does not know how to calculate the mean"
}
] |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\) \\( 1 \\frac{3}{5} \\)"
},
{
"from": "gpt",
"value": "Believes when changing an improper fraction to a mixed number you divide the numerator ... |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\) \\( 3 \\frac{2}{5} \\)"
},
{
"from": "gpt",
"value": "Believes the whole and remainder are the other way when changing an improper fraction t... |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\) \\( 13 \\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "Believes the number of wholes in a mixed number multiplies by the fraction part"
}
] |
[
{
"from": "human",
"value": "Use area to write algebraic expressions The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and b... |
[
{
"from": "human",
"value": "Use area to write algebraic expressions The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and b... |
[
{
"from": "human",
"value": "Use area to write algebraic expressions The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and b... |
[
{
"from": "human",
"value": "Convert from kilometers to miles \\( 3 \\) miles \\( \\approx 5 \\mathrm{~km} \\) \\( 30 \\mathrm{~km} \\approx \\square \\) miles \\( 28 \\)"
},
{
"from": "gpt",
"value": "Added rather than multiplied by a scale factor"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing mental multiplication strategies.\nTom says \\( 15 \\times 42=154 \\times 2 \\)\nKatie says \\( 15 \\times 42=(15 \\times 4)+(15 \\times 2) \\)\nWho is correct? Only Tom"
},
{
"fro... |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing mental multiplication strategies.\nTom says \\( 15 \\times 42=154 \\times 2 \\)\nKatie says \\( 15 \\times 42=(15 \\times 4)+(15 \\times 2) \\)\nWho is correct? Only Katie"
},
{
"f... |
[
{
"from": "human",
"value": "Convert from hours to minutes \\( 3 \\) hours is the same as ___________ minutes \\( 90 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 30 minutes in a hour"
}
] |
[
{
"from": "human",
"value": "Convert from hours to minutes \\( 3 \\) hours is the same as ___________ minutes \\( 30 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10 minutes in an hour"
}
] |
[
{
"from": "human",
"value": "Convert from hours to minutes \\( 3 \\) hours is the same as ___________ minutes \\( 300 \\)"
},
{
"from": "gpt",
"value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n18, \\quad 11, \\quad 4, \\quad \\ldots\n\\] \\( -7 \\)"
},
{
"from": "gpt",
"value": "Identifies the term-to-term rule rather than the next term"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n18, \\quad 11, \\quad 4, \\quad \\ldots\n\\] Not enough information"
},
{
"from": "gpt",
"value": "Does not know how to find the next term in a sequence"
}... |
[
{
"from": "human",
"value": "Change minutes into decimals of hours (e.g. 90 minutes = 1.5 hours) \\( 90 \\) minutes is the same as _________ hours \\( 9 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10 minutes in an hour"
}
] |
[
{
"from": "human",
"value": "Change minutes into decimals of hours (e.g. 90 minutes = 1.5 hours) \\( 90 \\) minutes is the same as _________ hours \\( 1.3 \\)"
},
{
"from": "gpt",
"value": "Answers as if there are 100 minutes in an hour when writing minutes as decimals"
}
] |
[
{
"from": "human",
"value": "Identify factors of a number \\[\n1,2,4,8\n\\]\nThese are the only factors of... \\( 16 \\)"
},
{
"from": "gpt",
"value": "Does not think a number can be a factor of itself"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{2}{3}-\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star? \\( 19 \\)"
},
{
"from": "gpt",
"value": "Forgets to change the numerators when finding ... |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{2}{3}-\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star? \\( 1 \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numer... |
[
{
"from": "human",
"value": "Understand inequality notation Which of the following shows \" \\( x \\) is greater than or equal to \\( 6 \\) \"? \\( x>6 \\)"
},
{
"from": "gpt",
"value": "When using inequality notation, thinks \"greater than/less than or equal to\" symbols are instead the \"great... |
[
{
"from": "human",
"value": "Understand inequality notation Which of the following shows \" \\( x \\) is greater than or equal to \\( 6 \\) \"? \\( x \\leq 6 \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cone where the dimensions are all given in the same units STEP \\( 2 \\)\n\nJessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right... |
[
{
"from": "human",
"value": "Calculate the volume of a cone where the dimensions are all given in the same units STEP \\( 2 \\)\n\nJessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right... |
[
{
"from": "human",
"value": "Multiply mixed number fractions in the form: Fraction × Integer \\(\n1 \\frac{2}{3} \\times 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 2 \\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "When multiplying mixed numbers, ... |
[
{
"from": "human",
"value": "Multiply mixed number fractions in the form: Fraction × Integer \\(\n1 \\frac{2}{3} \\times 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 2 \\frac{4}{6} \\)"
},
{
"from": "gpt",
"value": "When multiplying a fraction by a... |
[
{
"from": "human",
"value": "Calculate questions involving the power law of indices with positive integer powers \\( \\left(5^{4}\\right)^{3}= \\) \\( 5^{7} \\)"
},
{
"from": "gpt",
"value": "Has added the powers rather than multiplying them"
}
] |
[
{
"from": "human",
"value": "Calculate questions involving the power law of indices with positive integer powers \\( \\left(5^{4}\\right)^{3}= \\) \\( 125^{12} \\)"
},
{
"from": "gpt",
"value": "Has cubed the base number and the power"
}
] |
[
{
"from": "human",
"value": "Calculate questions involving the power law of indices with positive integer powers \\( \\left(5^{4}\\right)^{3}= \\) None of these options"
},
{
"from": "gpt",
"value": "Does not understand laws of indices"
}
] |
[
{
"from": "human",
"value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 2 \\) squares left and \\( 3 \\) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Po... |
[
{
"from": "human",
"value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 2 \\) squares left and \\( 3 \\) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Po... |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 3 or more decimal place to percentages How do you write \\( 0.909 \\) as a percentage? \\( 99 \\% \\)"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 3 or more decimal place to percentages How do you write \\( 0.909 \\) as a percentage? \\( 909 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks they just remove the decimal point when converting a decimal to a percentage"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\) \\( \\{x<-4\\} \\cup\\{x>4\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\) \\( \\{x<4\\} \\)"
},
{
"from": "gpt",
"value": "Does not think a square root can be negative"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\) \\( \\{-8<x<8\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Identify a prism from a diagram Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct? Only Tom"
},
... |
[
{
"from": "human",
"value": "Identify a prism from a diagram Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct? Only Katie"
},
... |
[
{
"from": "human",
"value": "Identify a prism from a diagram Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct? Both Tom and Kati... |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\) Reflection in the\n\\[\ny \\text {-axis }\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a re... |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\) Reflection in the line\n\\[\ny=x\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection ... |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\) Reflection in the line\n\\[\ny=-x\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection... |
[
{
"from": "human",
"value": "Recognise the angles on a straight line relationship ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true? \\( a+b=360^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 360 deg... |
[
{
"from": "human",
"value": "Recognise the angles on a straight line relationship ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true? \\( a=b \\)"
},
{
"from": "gpt",
"value": "Student thinks that any two angles along a straight line are e... |
[
{
"from": "human",
"value": "Recognise the angles on a straight line relationship ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true? \\( a+b=90^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Thinks there are 180 degrees in a full turn"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Here are the first \\( 4 \\) terms of a linear sequence. ![A sequence of 4 patterns, that are the first 4 terms of a sequence. The first pattern is a rec... |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 50.09-0.1= \\) \\( 50.99 \\)"
},
{
"from": "gpt",
"value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 50.09-0.1= \\) \\( 50.08 \\)"
},
{
"from": "gpt",
"value": "When subtracting decimals with a different number of decimal places, lines up the digits incorrectly"
}
] |
[
{
"from": "human",
"value": "Identify the regions on a double Venn diagram given in set notation Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle i... |
[
{
"from": "human",
"value": "Identify the regions on a double Venn diagram given in set notation Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle i... |
[
{
"from": "human",
"value": "Solve a linear equation using a function machine Look at the function machine. ![An image of two function machines. The first function machine has x as the input. The first function is divide by 3 and the second is +4. The output is 5. The second function machine is the reverse ... |
[
{
"from": "human",
"value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -3<x \\leq 1 \\) ? ![A number line with a hollow circle above -3 and an arrow coming out of it over the numbers -4, -5 etc and a filled in circle ab... |
[
{
"from": "human",
"value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -3<x \\leq 1 \\) ? ![A number line with a filled in circle above -3 connected to a hollow circle above 1.]()"
},
{
"from": "gpt",
"value... |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° Which diagram shows an angle of \\( 325^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (... |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° Which diagram shows an angle of \\( 325^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (... |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° Which diagram shows an angle of \\( 325^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (... |
[
{
"from": "human",
"value": "Recognise the notation for parallel lines The two lines marked are... ![Trapezium with parallel sides labelled]() Perpendicular"
},
{
"from": "gpt",
"value": "Confuses the meaning of parallel and perpendicular"
}
] |
[
{
"from": "human",
"value": "Recognise the notation for parallel lines The two lines marked are... ![Trapezium with parallel sides labelled]() Vertical"
},
{
"from": "gpt",
"value": "Does not recognise the notation for parallel sides"
}
] |
[
{
"from": "human",
"value": "Recognise the notation for parallel lines The two lines marked are... ![Trapezium with parallel sides labelled]() Equal"
},
{
"from": "gpt",
"value": "Does not recognise the notation for parallel sides"
}
] |
[
{
"from": "human",
"value": "Carry out the first stage in an iteration solution The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x_{n}{ }^{3}}{9}\\)\n\nIf \\( x_{0}=0 \\), what does \\( x_{1} \\) equal? ![A ... |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]() \\( A B \\) and \\( B C \\)"... |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]() \\( A B \\) and \\( D C \\)"... |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]() None of them"
},
{
"... |
[
{
"from": "human",
"value": "Given a line segment, calculate the gradient where the gradient is a positive integer What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]() \\( 0 \\)"
},
... |
[
{
"from": "human",
"value": "Given a line segment, calculate the gradient where the gradient is a positive integer What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]() \\( x \\)"
},
... |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\n\\( 60302 \\) Six hundred and thirty-two"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\n\\( 60302 \\) Six thousand three hundred and two"
},
{
"from": "gpt",
"value": "Confuses the ten thousands and thousands place value columns"
}
] |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\n\\( 60302 \\) Sixty thousand and thirty-two"
},
{
"from": "gpt",
"value": "Confuses the hundreds and tens place value columns"
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed Rearrange the following equation to make \\( \\omega \\) the subject \\( F=r \\omega^{2} \\) \\( \\omega=r F^{2} \\)"
},
{
"from": "gpt",
"value": "When solving an equati... |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed Rearrange the following equation to make \\( \\omega \\) the subject \\( F=r \\omega^{2} \\) \\( \\omega=\\sqrt{r F} \\)"
},
{
"from": "gpt",
"value": "When solving an eq... |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed Rearrange the following equation to make \\( \\omega \\) the subject \\( F=r \\omega^{2} \\) \\( \\omega=\\frac{\\sqrt{F}}{r} \\)"
},
{
"from": "gpt",
"value": "Does not ... |
[
{
"from": "human",
"value": "Divide mixed number fractions in the form: Fraction ÷ Integer \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 1 \\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "When the dividend is a mixed number ... |
[
{
"from": "human",
"value": "Divide mixed number fractions in the form: Fraction ÷ Integer \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 2 \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "When the dividend is a mixed number ... |
[
{
"from": "human",
"value": "Divide mixed number fractions in the form: Fraction ÷ Integer \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( \\frac{3}{4} \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}... |
[
{
"from": "human",
"value": "Identify a unit of time Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct? Only\nKatie"
},
{
"from": "gpt",
"value": "Mistakes unit of speed for unit of time... |
[
{
"from": "human",
"value": "Identify a unit of time Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Mistakes unit of speed for unit ... |
[
{
"from": "human",
"value": "Identify a unit of time Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not recognise a unit of tim... |
[
{
"from": "human",
"value": "Substitute negative integer values into formulae involving powers or roots \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ? \\( -243 \\)"
},
{
"from": "gpt",
"value": "Believes a negative power results in a negative answer"
}
] |
[
{
"from": "human",
"value": "Substitute negative integer values into formulae involving powers or roots \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ? \\( -\\frac{1}{243} \\)"
},
{
"from": "gpt",
"value": "Believes a negative power results in a negative answer"
}
] |
[
{
"from": "human",
"value": "Substitute negative integer values into formulae involving powers or roots \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ? \\( -15 \\)"
},
{
"from": "gpt",
"value": "Has multiplied the base number and the power"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 1 digit integers using long multiplication Charlotte is trying to solve this problem using long multiplication.\n\nWhat should replace the star as the tens digit in her final answer? \\( 538 \\times 7 \\) \\begin{tabular}{r|r|r|r|}\n\\(\\space\\) & \... |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 1 digit integers using long multiplication Charlotte is trying to solve this problem using long multiplication.\n\nWhat should replace the star as the tens digit in her final answer? \\( 538 \\times 7 \\) \\begin{tabular}{r|r|r|r|}\n\\(\\space\\) & \... |
[
{
"from": "human",
"value": "Prove statements involving positive and negative numbers Which of these could be used as a counter - example to disprove Katie's theory that \\( 2 n^{2}-1 \\) is positive? \\( 2(-2)^{2}-1 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a n... |
[
{
"from": "human",
"value": "Prove statements involving positive and negative numbers Which of these could be used as a counter - example to disprove Katie's theory that \\( 2 n^{2}-1 \\) is positive? \\( 2(-1)^{2}-1 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a n... |
[
{
"from": "human",
"value": "Solve linear simultaneous equations requiring a scaling of both expressions What is the value of \\( l \\) in these simultaneous equations?\n\\(\n\\begin{array}{l}\n2 l+3 m=13 \\\\\n3 l+4 m=17\n\\end{array}\n\\) \\( l=1 \\)"
},
{
"from": "gpt",
"value": "Believes sub... |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{1}{3} \\times(-6)= \\) \\( -\\frac{1}{18} \\)"
},
{
"from": "gpt",
"value": "When multiplying a fraction by an integer, multiplies the denominator instead of the numerator"
}
] |
[
{
"from": "human",
"value": "Represent an equation using a bar model Tom and Katie are discussing bar models. Tom says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l}\n\\hline \\( 5 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 5 x \\) \\begin{tabular}{l|... |
[
{
"from": "human",
"value": "Represent an equation using a bar model Tom and Katie are discussing bar models. Tom says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l}\n\\hline \\( 5 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 5 x \\) \\begin{tabular}{l|... |
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