conversations listlengths 2 2 |
|---|
[
{
"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 \\( v \\) the subject\n\\(F=\\frac{v^{2}}{r}\\) \\( v=\\sqrt{\\frac{F}{r}} \\)"
},
{
"from": "gpt",
"value": "When solving an equ... |
[
{
"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 \\( v \\) the subject\n\\(F=\\frac{v^{2}}{r}\\) \\( v=r \\sqrt{F} \\)"
},
{
"from": "gpt",
"value": "Does not reverse the order o... |
[
{
"from": "human",
"value": "Convert between cm and mm How many millimetres are there in \\( 1 \\) centimetre? \\( 0.1 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10 centimetres in 1 mm."
}
] |
[
{
"from": "human",
"value": "Convert between cm and mm How many millimetres are there in \\( 1 \\) centimetre? \\( 100 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100mm in a centimetre"
}
] |
[
{
"from": "human",
"value": "Convert between cm and mm How many millimetres are there in \\( 1 \\) centimetre? \\( 1000 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 1000mm in a centimetre"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division Tom and Katie are discussing the order of operations\nTom says: \\( 6+4-2 \\equiv 4-2+6 \\)\nKatie says: \\( 6+4 \\times 2 \\equiv 6 \\times 4+2 \\)\nWho is cor... |
[
{
"from": "human",
"value": "Find missing angles in a right-angled triangle Tom and Katie are arguing about triangles.\nTom says a triangle can have two right angles.\nKatie says only a scalene triangle can have a right angle.\nWho is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Does not co... |
[
{
"from": "human",
"value": "Find missing angles in a right-angled triangle Tom and Katie are arguing about triangles.\nTom says a triangle can have two right angles.\nKatie says only a scalene triangle can have a right angle.\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Does not k... |
[
{
"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 Tom and Katie are discussing calculations involving brackets\nTom says \\( a(b+c) \\equiv(b+c) \\times a \\)\nKatie says \\( a(b+c) \\equiv a b+c \\)\nWho ... |
[
{
"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 Tom and Katie are discussing calculations involving brackets\nTom says \\( a(b+c) \\equiv(b+c) \\times a \\)\nKatie says \\( a(b+c) \\equiv a b+c \\)\nWho ... |
[
{
"from": "human",
"value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. \"-4\" below the 2nd dash and \"5\" below the last d... |
[
{
"from": "human",
"value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. \"-4\" below the 2nd dash and \"5\" below the last d... |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 8 \\) out of \\( 20 \\) as a percentage? \\( 82 \\% \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a percentage by writing the numerator followed by the denominator"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 8 \\) out of \\( 20 \\) as a percentage? \\( 16 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks they double the numerator to turn a fraction into a percentage"
}
] |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside contains a letter and the inside contains a linear expression ![A blue, rectangle with each side labelled. The left side is labelled x and the right side 8. The top side is labelled 2x + 4 and the base 3x - 4.](... |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside contains a letter and the inside contains a linear expression ![A blue, rectangle with each side labelled. The left side is labelled x and the right side 8. The top side is labelled 2x + 4 and the base 3x - 4.](... |
[
{
"from": "human",
"value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) One of these equations has exactly one solution.\nWhich is it? \\( t^{2}-9=0 \\)"
},
{
"from": "gpt",
"value": "Factorises difference of two squares with the same sign in both brackets"
}
] |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence ![Square and then subtract \\( 4 \\)]() The first three terms of which sequence below is produced by this term-to-term rule? \\( -3,9,5 \\)"
},
{
"from": "gpt",
... |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence ![Square and then subtract \\( 4 \\)]() The first three terms of which sequence below is produced by this term-to-term rule? \\( -3,-13,-173 \\)"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence ![Square and then subtract \\( 4 \\)]() The first three terms of which sequence below is produced by this term-to-term rule? \\( -3,0,5 \\)"
},
{
"from": "gpt",
... |
[
{
"from": "human",
"value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 5 \\) red balls and \\( 4 \\) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks out two balls at the same t... |
[
{
"from": "human",
"value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 5 \\) red balls and \\( 4 \\) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks out two balls at the same t... |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of the parallelogram? ![A parallelogram with length 7cm, perpendicular height (marked by a right angle) 3cm, and slanted height 4cm. Not to scale]() \\( 22 \\mathrm{~cm}^{2} \... |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of the parallelogram? ![A parallelogram with length 7cm, perpendicular height (marked by a right angle) 3cm, and slanted height 4cm. Not to scale]() \\( 28 \\mathrm{~cm}^{2} \... |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of the parallelogram? ![A parallelogram with length 7cm, perpendicular height (marked by a right angle) 3cm, and slanted height 4cm. Not to scale]() \\( 84 \\mathrm{~cm}^{2} \... |
[
{
"from": "human",
"value": "Understand the non-commutativity of division Jacob makes a conjecture: If you have two different numbers, \\( P \\) and \\( Q \\), the order you divide does not matter. \\( P \\div Q=Q \\div P \\) Is Jacob's conjecture... Always true"
},
{
"from": "gpt",
"value": "Be... |
[
{
"from": "human",
"value": "Understand the non-commutativity of division Jacob makes a conjecture: If you have two different numbers, \\( P \\) and \\( Q \\), the order you divide does not matter. \\( P \\div Q=Q \\div P \\) Is Jacob's conjecture... Sometimes true"
},
{
"from": "gpt",
"value": ... |
[
{
"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? Pair \\( 1 \\)\n\\(\n\\begin{array}{l}\n-5 p+2 q=12 \\\\\n3 p-2 q=8\n\\end{array}... |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows how much a block of ice melted over time. ![Chart of water depth (cm) against time (minutes)]() What was the difference between the second minute and fourth minute? \\( 6 \\)"
},
{
"from": "gpt",
"value": ... |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows how much a block of ice melted over time. ![Chart of water depth (cm) against time (minutes)]() What was the difference between the second minute and fourth minute? \\( 9 \\mathrm{~cm} \\)"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows how much a block of ice melted over time. ![Chart of water depth (cm) against time (minutes)]() What was the difference between the second minute and fourth minute? \\( 2 \\mathrm{~cm} \\)"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer James is expanding these two brackets.\n\nWhat should he get when he multiplies the two terms indicated by the arrows? ![The brackets shown are (x-8)(x-2). The arrows are pointing at the -8 in the first bracket and... |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer James is expanding these two brackets.\n\nWhat should he get when he multiplies the two terms indicated by the arrows? ![The brackets shown are (x-8)(x-2). The arrows are pointing at the -8 in the first bracket and... |
[
{
"from": "human",
"value": "Round numbers to one decimal place \\( 154.1762 \\) to \\( 1 \\) decimal place is. \\( 154.1 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round numbers to one decimal place \\( 154.1762 \\) to \\( 1 \\) decimal place is. \\( 155.2 \\)"
},
{
"from": "gpt",
"value": "Rounds incorrectly by changing multiple place values"
}
] |
[
{
"from": "human",
"value": "Round numbers to one decimal place \\( 154.1762 \\) to \\( 1 \\) decimal place is. \\( 155.1 \\)"
},
{
"from": "gpt",
"value": "Rounds incorrectly by changing multiple place values"
}
] |
[
{
"from": "human",
"value": "Convert between m and km \\( 4000 m \\) is the same as ____ \\(km\\) \\( 400 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10m in a km"
}
] |
[
{
"from": "human",
"value": "Convert between m and km \\( 4000 m \\) is the same as ____ \\(km\\) \\( 400000 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than divides"
}
] |
[
{
"from": "human",
"value": "Convert between m and km \\( 4000 m \\) is the same as ____ \\(km\\) \\( 40 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100m and a km"
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors ![A coordinate grid with point V marked at (2,2) and point W marked at (-3,-1)]() Describe the movements to get from point \\( \\mathrm{V} \\) to point \\( \\mathrm{W} \\). Left \\( 4 \\) squares, ... |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors ![A coordinate grid with point V marked at (2,2) and point W marked at (-3,-1)]() Describe the movements to get from point \\( \\mathrm{V} \\) to point \\( \\mathrm{W} \\). Right \\( 5 \\) squares,... |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors ![A coordinate grid with point V marked at (2,2) and point W marked at (-3,-1)]() Describe the movements to get from point \\( \\mathrm{V} \\) to point \\( \\mathrm{W} \\). Left \\( 5 \\) squares, ... |
[
{
"from": "human",
"value": "Find 100 more than a given number What number is \\( 100 \\) more than \\( 28902 ? \\) \\( 2,890,200 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than adds when given the command word 'more'"
}
] |
[
{
"from": "human",
"value": "Find 100 more than a given number What number is \\( 100 \\) more than \\( 28902 ? \\) \\( 29,902 \\)"
},
{
"from": "gpt",
"value": "When adding powers of 10 adds onto the wrong column"
}
] |
[
{
"from": "human",
"value": "Find 100 more than a given number What number is \\( 100 \\) more than \\( 28902 ? \\) \\( 28,002 \\)"
},
{
"from": "gpt",
"value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit"
}
] |
[
{
"from": "human",
"value": "Recall the correct formula to calculate the length of a non-hypotenuse of a right-angled triangle in a 2D Pythagoras questions A right-angled tringle has sides a, b, and \\( c \\) as shown.\n\nChoose the formula for finding side a. ![Right-angled triangle with height a, base b a... |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Write \\( \\textbf{nineteen fifths} \\) as a mixed number fraction. \\( 4 \\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "When converting from an improper fraction to a mixed number, adds on the part left to m... |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Write \\( \\textbf{nineteen fifths} \\) as a mixed number fraction. \\( 19 \\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "Writes the numerator of an improper fraction as the number of wholes when converting t... |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Write \\( \\textbf{nineteen fifths} \\) as a mixed number fraction. \\( \\frac{19}{5} \\)"
},
{
"from": "gpt",
"value": "Confused mixed numbers with improper fractions"
}
] |
[
{
"from": "human",
"value": "Convert fractions less than 1 to terminating decimals of 1 decimal place What is \\( \\frac{4}{5} \\) as a decimal? \\( 0.5 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by using the denominator after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert fractions less than 1 to terminating decimals of 1 decimal place What is \\( \\frac{4}{5} \\) as a decimal? \\( 0.4 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by using only the numerator after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert fractions less than 1 to terminating decimals of 1 decimal place What is \\( \\frac{4}{5} \\) as a decimal? \\( 0.45 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by placing all values of the fraction after the decimal point"
}
] |
[
{
"from": "human",
"value": "Understand inequality notation Which of these statements show that \\( \\mathrm{t} \\) is greater than \\( 9 \\) ? \\( t<9 \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Understand inequality notation Which of these statements show that \\( \\mathrm{t} \\) is greater than \\( 9 \\) ? \\( t=9 \\)"
},
{
"from": "gpt",
"value": "Confuses inequality symbols with equality"
}
] |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 1 decimal place What percentage is represented by:\n\\(\n\\frac{3}{10}+ \\frac{7}{1000}\n\\) \\( 307 \\% \\)"
},
{
"from": "gpt",
"value": "Does not know that you can have a decimal percentage"
}
] |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 1 decimal place What percentage is represented by:\n\\(\n\\frac{3}{10}+ \\frac{7}{1000}\n\\) \\( 3.7 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks you just add a % sign to the numerator to make a fraction into a percentage"... |
[
{
"from": "human",
"value": "Convert from hours to minutes Hannah's journey to camp is \\( 3 \\) hours and \\( 26 \\) minutes.\nTori's journey to camp is \\( 204 \\) minutes.\nWhat is the difference in their journeys in minutes? \\( 122 \\) minutes"
},
{
"from": "gpt",
"value": "Answers as if th... |
[
{
"from": "human",
"value": "Convert from hours to minutes Hannah's journey to camp is \\( 3 \\) hours and \\( 26 \\) minutes.\nTori's journey to camp is \\( 204 \\) minutes.\nWhat is the difference in their journeys in minutes? \\( 410 \\) minutes"
},
{
"from": "gpt",
"value": "Adds instead of ... |
[
{
"from": "human",
"value": "Calculate the length of horizontal and vertical line segments ![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3,12) and (10,12) indicating the width.]() What is the width of this rectangle as i... |
[
{
"from": "human",
"value": "Calculate the length of horizontal and vertical line segments ![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3,12) and (10,12) indicating the width.]() What is the width of this rectangle as i... |
[
{
"from": "human",
"value": "Calculate the length of horizontal and vertical line segments ![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3,12) and (10,12) indicating the width.]() What is the width of this rectangle as i... |
[
{
"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|c|c|c|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( 4 \\) & \\( \\ \\) & \\(\\color{gold}\\bigs... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+5 p+4\n\\) \\( (p+2)(p+3) \\)"
},
{
"from": "gpt",
"value": "Believes that when factorising a quadratic, they can choose any two numbers that add to give the ... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+5 p+4\n\\) \\( (p+1)(p+5) \\)"
},
{
"from": "gpt",
"value": "Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in t... |
[
{
"from": "human",
"value": "Can calculate missing coordinates in a geometric shape ![A coordinate grid with a line segment from (0,2) to (3,1)]() The line segment is one side of a square.\n\nTom says a vertex of the square could be \\( (2,-2) \\).\n\nKatie says a vertex of the square could be \\( (1,5) \\)... |
[
{
"from": "human",
"value": "Can calculate missing coordinates in a geometric shape ![A coordinate grid with a line segment from (0,2) to (3,1)]() The line segment is one side of a square.\n\nTom says a vertex of the square could be \\( (2,-2) \\).\n\nKatie says a vertex of the square could be \\( (1,5) \\)... |
[
{
"from": "human",
"value": "Estimate the gradient at a point on a non-linear section of a real life graph The graph shows information about the velocity, \\( v \\mathrm{~m} / \\mathrm{s} \\), of a parachutist \\( t \\) seconds after leaving a plane.\n\nWhich of the following is the best estimate for the gr... |
[
{
"from": "human",
"value": "Estimate the gradient at a point on a non-linear section of a real life graph The graph shows information about the velocity, \\( v \\mathrm{~m} / \\mathrm{s} \\), of a parachutist \\( t \\) seconds after leaving a plane.\n\nWhich of the following is the best estimate for the gr... |
[
{
"from": "human",
"value": "Estimate the gradient at a point on a non-linear section of a real life graph The graph shows information about the velocity, \\( v \\mathrm{~m} / \\mathrm{s} \\), of a parachutist \\( t \\) seconds after leaving a plane.\n\nWhich of the following is the best estimate for the gr... |
[
{
"from": "human",
"value": "Identify the net of a prism Which is the correct net for this shape? ![Net of a cuboid]() ![Net of a triangular prism]()"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Identify the net of a prism Which is the correct net for this shape? ![Net of a cuboid]() ![Net of a cube]()"
},
{
"from": "gpt",
"value": "Mixes up cubes and cuboids"
}
] |
[
{
"from": "human",
"value": "Identify the net of a prism Which is the correct net for this shape? ![Net of a cuboid]() ![None of the above]()"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Perform calculator calculations with powers Which of the following would give you the correct value of \\( \\frac{1}{7} \\) on your calculator? ![A scientific calculator]() ![The number 1, then a calculator button labelled \\(-\\), then the number 7]()"
},
{
"from": "gpt... |
[
{
"from": "human",
"value": "Perform calculator calculations with powers Which of the following would give you the correct value of \\( \\frac{1}{7} \\) on your calculator? ![A scientific calculator]() ![The number 1, then a calculator button labelled \\(x^{\\square} \\), then the number 7]()"
},
{
... |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer \\( 5 \\times(-4)= \\) \\( 20 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Recognise visual representations of division times table facts ![Six groups of three dots]() Jo says the diagram above represents\n\\[\n3 \\div 18=6\n\\]\nPaul says the diagram represents \\( 6 \\times 3=18 \\)\nWho is correct? Both Jo and Paul"
},
{
"from": "gpt",
"... |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form (x + a)² + b \\(y= x^{2}+8x+2 \\)\n\nWrite in the form\n\\( (x+a)^{2}+b \\) \\( (x+4)^{2}+2 \\)"
},
{
"from": "gpt",
"value": "When completing the square in the form (x - a)^2 + b, believes b = the original ... |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form (x + a)² + b \\(y= x^{2}+8x+2 \\)\n\nWrite in the form\n\\( (x+a)^{2}+b \\) \\( (x+8)^{2}+2 \\)"
},
{
"from": "gpt",
"value": "When completing the square, believes the constant in the bracket is the coeffici... |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form (x + a)² + b \\(y= x^{2}+8x+2 \\)\n\nWrite in the form\n\\( (x+a)^{2}+b \\) \\( (x+4)^{2}-16 \\)"
},
{
"from": "gpt",
"value": "When completing the square in the form (x - a)^2 + b, believes b = -a^2 regardl... |
[
{
"from": "human",
"value": "Convert fractions less than 1 to terminating decimals of 2 decimal places \\( \\frac{6}{25}=? \\) \\( 0.625 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by placing all values of the fraction after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert fractions less than 1 to terminating decimals of 2 decimal places \\( \\frac{6}{25}=? \\) \\( 0.6 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by using only the numerator after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert fractions less than 1 to terminating decimals of 2 decimal places \\( \\frac{6}{25}=? \\) \\( 6.25 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by placing a decimal point between the numerator and denominator"
}
] |
[
{
"from": "human",
"value": "Order decimals with a different number of digits Which number is the greatest? \\( 6.079 \\)"
},
{
"from": "gpt",
"value": "When ordering integers, orders from the digits at the end of the number instead of the digits at the start"
}
] |
[
{
"from": "human",
"value": "Carry out the first stage in an iteration solution \\(x_{n+1}=\\sqrt{\\frac{1}{x_{n}+1}}\\)\n\nUsing a starting value of \\( x_{1}=0.5 \\), what is the value of \\( x_{2} \\) ? \\( 0.7419 \\ldots \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a ... |
[
{
"from": "human",
"value": "Interpret and carry out mental division using a bar model Find the value of \\( \\mathrm{M} \\). ![Horizontal blue bar divided into 5 equal sections. Every section is labelled with M. A curly bracket shows that 4 of the sections sum to 420.]() \\( 100 \\)"
},
{
"from": "... |
[
{
"from": "human",
"value": "Interpret and carry out mental division using a bar model Find the value of \\( \\mathrm{M} \\). ![Horizontal blue bar divided into 5 equal sections. Every section is labelled with M. A curly bracket shows that 4 of the sections sum to 420.]() \\( 1680 \\)"
},
{
"from": ... |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring addition or subtraction, involving negative integers Solve the equation:\n\\(\n-5=p+10\n\\) \\( p=5 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, with all positive integers Solve the equation:\n\\(20 t-5=5 t+10\\) \\( t=0 \\)"
},
{
"from": "gpt",
"value": "Believes that a number divided by itself equals 0"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, with all positive integers Solve the equation:\n\\(20 t-5=5 t+10\\) \\( t=-1 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, with all positive integers Solve the equation:\n\\(20 t-5=5 t+10\\) \\( t=\\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}... |
[
{
"from": "human",
"value": "Convert fractions to ratios James and Cameron are watching a film. They pause it with one sixth left to watch.\n\nWhat is the ratio for how much they have watched to how much they have yet to see? ![An image of a television]() 1:5"
},
{
"from": "gpt",
"value": "Gets ... |
[
{
"from": "human",
"value": "Convert fractions to ratios James and Cameron are watching a film. They pause it with one sixth left to watch.\n\nWhat is the ratio for how much they have watched to how much they have yet to see? ![An image of a television]() \\( 6: 1 \\)"
},
{
"from": "gpt",
"value... |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line The sum of angle \\( a \\) and \\( b \\) would be... ![A straight line split in to two angles, a and b.]() \\( 100^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 100 degrees"
... |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line The sum of angle \\( a \\) and \\( b \\) would be... ![A straight line split in to two angles, a and b.]() \\( 360^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 360 degrees"
... |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line The sum of angle \\( a \\) and \\( b \\) would be... ![A straight line split in to two angles, a and b.]() \\( 90^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 90 degrees"
}... |
[
{
"from": "human",
"value": "Given a midpoint and a coordinate work out the position of the other coordinate, where all the values are integers but at least one is negative Here are two points and their midpoint.\nWhat should replace the star? ![A set of axis including all four quadrants. Lilac circle marke... |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers \\( 2 \\times 3^{2}= \\) \\( 12 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers \\( 2 \\times 3^{2}= \\) \\( 36 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers \\( 2 \\times 3^{2}= \\) \\( 11 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is 1 Before Zain uses the quadratic formula to solve this equation, what must he do?\n\\(\np^{2}-16=p\n\\) Square root everything"
},
{
"from": "gpt",
"value": "Does not realise a quad... |
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