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Maths Year 6 49 questions with answers

Year 6 maths: a question for each objective

The national curriculum lists what children are taught in maths in Year 6. Here is each objective in its own words, by strand, with one question on it, its answer and how to find it.

Questions written by Remelia for the objectives of the national curriculum for England; not taken from any test paper.

The strands

Try each question before opening its answer. Printed, the questions come first and the answers on a sheet of their own.

Number & place value

Six Year 6 place value questions with the common mistakes

  1. Objective: Read, write, order and compare numbers up to 10,000,000; determine the value of each digit Explained, with a worked example

    Which sign goes in the box: <, > or =?

    5,000,000 + 500 + 60 + 5 □ 5,000,565

    • A <
    • B >
    • C =
    Show the answer to question 1

    Answer: C · =

    Why:

    5,000,000 + 500 + 60 + 5 = 5,000,565.

    Compare 5,000,565 with 5,000,565 from the millions column down: every digit is the same.

    So 5,000,000 + 500 + 60 + 5 = 5,000,565.

  2. Objective: Round any whole number to a required degree of accuracy

    Round 157,777 to the nearest 10,000.

    Show the answer to question 2

    Answer: 160,000

    Why:

    To the nearest 10,000: look at the digit just to the right of the ten thousands digit. 5 or more rounds up, 4 or less rounds down: 160,000.

  3. Objective: Use negative numbers in context and calculate intervals across 0

    At 6 am the temperature was −4°C.

    The thermometer shows the temperature at 2 pm the same day. By how many degrees did it rise?

    ThermometerA thermometer. Its marks are numbered in degrees Celsius from −20 to 30, one every 10. Between each numbered mark and the next there are four unnumbered marks, equally spaced. The liquid comes up on the first unnumbered mark above 10. −20−100102030°C
    Show the answer to question 3

    Answer: 16 °C

    Why:

    The numbered marks go up in 10s. Four unnumbered marks split each gap into five equal steps, so each mark is 10 ÷ 5 = 2 °C.

    The top of the liquid is one mark above 10: 10 + 1 × 2 = 12 °C.

    From −4 up to 0 is 4, then up to 12 is 12 more: 4 + 12 = 16 degrees.

  4. Objective: Solve number and practical problems involving all of the above

    At noon the temperature in a town in Norway was 7°C.

    By midnight it had fallen by 13 degrees.

    What was the temperature at midnight?

    Show the answer to question 4

    Answer: -6 °C

    Why:

    Falling 13 degrees from 7°C crosses 0: 7 degrees down to 0, then 6 more gives −6°C.

Calculation (4 operations)

Six Year 6 calculation questions with the common mistakes

  1. Objective: Multiply multi-digit numbers up to 4 digits by a two-digit number using long multiplication

    2,235 × 48 = ?

    Round 2,235 to the nearest thousand and 48 to the nearest ten, then multiply. Which is the estimate?

    • A 200,000
    • B 100,000
    • C 150,000
    • D 1,000,000
    Show the answer to question 5

    Answer: B · 100,000

    Why:

    2,235 rounds to 2,000 and 48 to 50.

    2,000 × 50 = 100,000. (The exact answer is 107,280.)

  2. Objective: Divide numbers up to 4 digits by a two-digit number using long division, interpreting remainders as whole numbers, fractions, or by rounding

    A school takes 221 pupils and adults on a trip to the seaside. Each coach has 70 seats.

    Everyone needs a seat. How many coaches are needed?

    Show the answer to question 6

    Answer: 4

    Why:

    221 ÷ 70 = 3 remainder 11.

    Round up: 3 coaches carry 210 people, and the 11 people left over still need a coach, so 4 coaches.

  3. Objective: Divide up to 4 digits by a two-digit number using short division where appropriate, interpreting remainders in context

    The schools in a town send 212 children to a swimming gala by minibus. Each minibus carries 16 children.

    The minibuses are filled one at a time, each one full before the next is used.

    How many children are on the last minibus?

    • A 4
    • B 3
    • C 5
    • D 2
    Show the answer to question 7

    Answer: A · 4

    Why:

    212 ÷ 16 = 13 remainder 4.

    The remainder: 13 minibuses are full, with 208 children, so 212 − 208 = 4 children on the last minibus.

  4. Objective: Perform mental calculations including mixed operations and large numbers

    Which sign goes in the box: <, > or =?

    800 ÷ 5 □ 8,000 ÷ 50

    • A <
    • B >
    • C =
    Show the answer to question 8

    Answer: C · =

    Why:

    8,000 is 800 × 10. 50 is 5 × 10 too, so the answers are the same: 800 ÷ 5 = 160.

    So 800 ÷ 5 = 8,000 ÷ 50.

  5. Objective: Identify common factors, common multiples and prime numbers

    Is this statement always true, sometimes true or never true?

    "Two different prime numbers have a common factor bigger than 1."

    • A Always true
    • B Sometimes true
    • C Never true
    Show the answer to question 9

    Answer: C · Never true

    Why:

    A prime has no factors but 1 and itself, so two different primes share only the factor 1.

  6. Objective: Use knowledge of the order of operations (BIDMAS) to carry out calculations with all four operations

    Theo worked out 77 − 9 × 7 like this:

    77 − 9 = 68

    68 × 7 = 476

    What should the answer be?

    • A 14
    • B 15
    • C 114
    • D 24
    Show the answer to question 10

    Answer: A · 14

    Why:

    Multiplication comes before subtraction, so Theo did the steps in the wrong order.

    9 × 7 = 63, then 77 − 63 = 14.

  7. Objective: Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use and why

    A walk is 5,339 m long.

    Amir walks 3,035 m, then goes back 567 m to pick up a dropped glove.

    Which calculation finds how far Amir has left to walk?

    • A 3,035 + 567 − 5,339
    • B 5,339 − 3,035 − 567
    • C 5,339 + 3,035 − 567
    • D 5,339 − 3,035 + 567
    Show the answer to question 11

    Answer: D · 5,339 − 3,035 + 567

    Why:

    Start with the whole, take away what went, and add back what returned: 5,339 − 3,035 + 567 = 2,871.

  8. Objective: Solve problems involving addition, subtraction, multiplication and division

    1,062 ÷ 23 = ?

    Give your answer with a remainder, like "24 r 3".

    Show the answer to question 12

    Answer: 46r4 (also accept 46 remainder 4)

    Why:

    Build a table of 23 first, then divide.

    1,062 ÷ 23 = 46 remainder 4.

  9. Objective: Use estimation to check answers and determine an appropriate degree of accuracy in context

    2,293 ÷ 8 = ?

    Round 2,293 to the nearest thousand, then divide. Which is the estimate?

    • A 25
    • B 125
    • C 2,500
    • D 250
    Show the answer to question 13

    Answer: D · 250

    Why:

    2,293 rounds to 2,000.

    2,000 ÷ 8 = 250. (The exact answer is 286.63.)

Fractions, decimals & %

Six Year 6 fractions questions with the common mistakes

  1. Objective: Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

    Jonah says: 8/64 in its simplest form is 4/32.

    Is Jonah right? Write the correct answer, not just yes or no.

    Show the answer to question 14

    Answer: 1/8 · "No, 1/8" is right too; "No" on its own scores nothing

    Why:

    The highest common factor of 8 and 64 is 8.

    Divide both by it: 1/8.

    Jonah's answer was not right: the correct answer is 1/8.

  2. Objective: Compare and order fractions, including fractions > 1

    Which sign goes in the box: <, > or =?

    19/8 □ 2 5/6

    • A =
    • B >
    • C <
    Show the answer to question 15

    Answer: C · <

    Why:

    19/8 = 2 3/8. Both have 2 wholes, so compare 3/8 with 5/6: with denominator 24 they are 9/24 and 20/24.

    So 19/8 < 2 5/6.

  3. Objective: Add and subtract fractions with different denominators and mixed numbers, using equivalent fractions

    A bag holds 3 5/6 kg of flour.

    Zainab uses 1 1/3 kg.

    How much flour is left in the bag?

    Give your answer as a mixed number or a fraction, in its simplest form.

    Show the answer to question 16

    Answer: 2 1/2 kg (also accept 5/2)

    Why:

    As improper fractions over 6: 23/6 and 8/6.

    Take away: 15/6, which simplifies to 5/2, or 2 1/2.

  4. Objective: Multiply pairs of proper fractions, giving the answer in its simplest form (¼ × ½ = ⅛)

    What fraction is missing?

    4/7 × ? = 28/56

    Write it in its simplest form.

    Show the answer to question 17

    Answer: 7/8

    Why:

    Tops: 4 × 7 = 28. Bottoms: 7 × 8 = 56.

    So the missing fraction is 7/8.

  5. Objective: Divide proper fractions by whole numbers (⅓ ÷ 2 = ⅙)

    2/5 of a length of rope is cut into 3 equal pieces.

    What fraction of the whole rope is each piece?

    Write it in its simplest form.

    Show the answer to question 18

    Answer: 2/15

    Why:

    2/5 ÷ 3: the pieces get 3 times smaller, so the denominator is 5 × 3 = 15.

    Each gets 2/15.

  6. Objective: Associate a fraction with division and calculate decimal equivalents (⅜ = 0.375)

    Write 1/20 as a decimal.

    • A 0.05
    • B 0.5
    • C 0.04
    • D 0.06
    Show the answer to question 19

    Answer: A · 0.05

    Why:

    A fraction is a division: 1 ÷ 20 = 0.05.

  7. Objective: Identify the value of each digit to 3 d.p.; multiply and divide by 10, 100, 1,000 giving answers to 3 d.p. Explained, with a worked example

    8.44 × 7 = ?

    Show the answer to question 20

    Answer: 59.08

    Why:

    Ignore the decimal point: 844 × 7 = 5908.

    There were 2 decimal places, so put them back: 59.08.

  8. Objective: Multiply one-digit numbers with up to 2 d.p. by whole numbers

    8.88 × 5 = ?

    Show the answer to question 21

    Answer: 44.4 (also accept 44.40)

    Why:

    Ignore the decimal point: 888 × 5 = 4440.

    There were 2 decimal places, so put them back: 44.4.

  9. Objective: Use written division where the answer has up to 2 d.p.

    Use short division to work out 46.17 ÷ 9.

    Show the answer to question 22

    Answer: 5.13

    Why:

    46.17 ÷ 9 = 5.13.

    Check: 5.13 × 9 = 46.17.

  10. Objective: Solve problems requiring answers rounded to a specified degree of accuracy

    A 4 m length of rope is cut into 9 equal pieces.

    How long is each piece, in metres, to 1 decimal place?

    Show the answer to question 23

    Answer: 0.4

    Why:

    4 ÷ 9 = 0.444…

    To 1 decimal place, look at the next digit: 0.4.

  11. Objective: Recall and use equivalences between simple fractions, decimals and percentages in different contexts

    What percentage of the hexagons are shaded?

    Hexagons, some shadedTwenty hexagons, all the same size, in two rows of ten. In the top row, ten are shaded. In the second row, nine are shaded.
    • A 85%
    • B 90%
    • C 95%
    • D 19%
    Show the answer to question 24

    Answer: C · 95%

    Why:

    19 of the 20 hexagons are shaded: 19/20.

    20 parts make 100%, so each part is 100 ÷ 20 = 5%.

    19 × 5 = 95%.

Ratio & proportion

  1. Objective: Solve problems involving the relative sizes of two quantities, finding missing values by integer multiplication and division

    A cycle path goes from A to C through B. AB : BC = 2 : 3.

    How long is AB?

    A route, not to scaleA route drawn as a straight line, not to scale, from A through B to C. The legs: from A to B, marked ?; from B to C, not labelled. A bracket above the line from A to C is labelled 15 km.?15 kmABCNot to scale
    • A 9 km
    • B 3 km
    • C 6 km
    • D 12 km
    Show the answer to question 25

    Answer: C · 6 km

    Why:

    There are 2 + 3 = 5 equal parts in AC. One part is 15 ÷ 5 = 3 km.

    AB is 2 parts: 2 × 3 = 6 km.

  2. Objective: Solve problems involving the calculation of percentages (e.g. 15% of 360) and the use of percentages for comparison

    What is 55% of 900?

    Show the answer to question 26

    Answer: 495

    Why:

    10% of 900 = 90; 5% = 45; 1% = 9.

    Build 55%: 495.

  3. Objective: Solve problems involving similar shapes where the scale factor is known or can be found

    A postcard is 10 cm wide and 15 cm tall.

    It is enlarged to make a poster 40 cm wide and 60 cm tall.

    What is the scale factor of the enlargement?

    Show the answer to question 27

    Answer: 4

    Why:

    Divide a side of the poster by the matching side of the postcard: 40 ÷ 10 = 4.

    Check with the other pair: 60 ÷ 15 = 4. Both sides are 4 times as long, so the scale factor is 4.

  4. Objective: Solve problems involving unequal sharing and grouping using fractions and multiples

    Noor and Dara share 162 pebbles. Noor gets 5 times as many as Dara.

    How many pebbles does Dara get?

    Show the answer to question 28

    Answer: 27

    Why:

    Dara has 1 part and Noor has 5 parts: 6 parts altogether.

    One part = 162 ÷ 6 = 27.

    Dara gets 27; Noor gets 5 × 27 = 135.

Algebra

  1. Objective: Use simple formulae

    Here are some values of x and y:

    x: 1, 2, 3, 4

    y: 14, 19, 24, 29

    Which formula connects x and y?

    • A y = 5x + 9
    • B y = 4x + 9
    • C y = x + 19
    • D y = 4x + 10
    Show the answer to question 29

    Answer: A · y = 5x + 9

    Why:

    y goes up by 5 each time x goes up by 1, so the formula starts y = 5x.

    When x = 1: 5 × 1 + 9 = 14, so y = 5x + 9.

    Check x = 4: 5 × 4 + 9 = 29.

  2. Objective: Generate and describe linear number sequences

    Here is a sequence:

    3, 9, 15, 21, …

    What is the 18th term?

    • A 105
    • B 95
    • C 104
    • D 205
    Show the answer to question 30

    Answer: A · 105

    Why:

    The sequence goes up in 6s, so the rule is 6n − 3.

    Term 18 = 6 × 18 − 3 = 105.

  3. Objective: Express missing number problems algebraically

    Ivan has n sweets.

    Priya has 8 fewer than 4 times as many sweets as Ivan.

    Which expression shows how many sweets Priya has?

    • A n + 8 + 4
    • B 4n + 8
    • C 8n + 4
    • D 4n − 8
    Show the answer to question 31

    Answer: D · 4n − 8

    Why:

    4 times n is 4n; 8 fewer is 4n − 8.

    Check with n = 3: the words give 4, and so does 4n − 8.

  4. Objective: Find pairs of numbers that satisfy an equation with two unknowns

    x + y = 33 and x − y = 5.

    What is x?

    Show the answer to question 32

    Answer: 19

    Why:

    Add the two equations: the y's cancel, so 2x = 33 + 5 = 38 and x = 19.

    Then y = 33 − 19 = 14.

    Check: 19 − 14 = 5.

  5. Objective: Enumerate possibilities of combinations of two variables

    An ice cream van sells 3 flavours of ice cream and 3 toppings. Each ice cream has one flavour and one topping.

    How many different ice creams are there?

    Show the answer to question 33

    Answer: 9

    Why:

    Each of the 3 flavours of ice cream can go with each of the 3 toppings: 3 × 3 = 9.

    Listing them flavour by flavour gives the same count.

Measurement

Six Year 6 measurement questions with the common mistakes

  1. Objective: Solve problems involving calculation and conversion of units of measure, using decimals to 3 d.p. Explained, with a worked example

    Convert 603 ml into litres.

    Show the answer to question 34

    Answer: 0.603 litres

    Why:

    1,000 ml = 1 litre, so 603 ÷ 1,000 = 0.603 litres.

  2. Objective: Convert between standard units of length, mass, volume and time, smaller→larger and larger→smaller, to 3 d.p. Explained, with a worked example

    Convert 3,053 g into kg.

    Show the answer to question 35

    Answer: 3.053 kg

    Why:

    1,000 g = 1 kg, so 3,053 ÷ 1,000 = 3.053 kg.

  3. Objective: Convert between miles and kilometres

    Using 5 miles ≈ 8 km, which of these distances is the longest?

    • A 55 miles
    • B 48 km
    • C 68 km
    • D 45 miles
    Show the answer to question 36

    Answer: A · 55 miles

    Why:

    Put them all in km. 55 miles ≈ 55 ÷ 5 × 8 = 88 km; 45 miles ≈ 45 ÷ 5 × 8 = 72 km.

    In km: 88, 48, 68, 72.

    The longest is 55 miles.

  4. Objective: Recognise that shapes with the same area can have different perimeters, and vice versa

    Is this always true, sometimes true or never true?

    "If you double the length and the width of a rectangle, its perimeter doubles."

    • A Sometimes true
    • B Always true
    • C Never true
    Show the answer to question 37

    Answer: B · Always true

    Why:

    Always true. Every side is twice as long, so the distance round is twice as long: 3 cm by 2 cm has a perimeter of 10 cm, and 6 cm by 4 cm has 20 cm.

  5. Objective: Recognise when it is possible to use formulae for area and volume

    A triangle has a base of 6 cm and a perpendicular height of 4 cm.

    Which calculation gives its area?

    TriangleA triangle with a base of 6 cm. Its height, 4 cm, is drawn dashed from the top corner straight down to the base. 6 cm 4 cm
    • A 6 × 4 ÷ 2
    • B 6 + 4 ÷ 2
    • C 6 × 4
    • D 6 × 4 × 2
    Show the answer to question 38

    Answer: A · 6 × 4 ÷ 2

    Why:

    A triangle is half of a rectangle with the same base and height: area = base × height ÷ 2.

    6 × 4 ÷ 2 = 12 cm².

  6. Objective: Calculate the area of parallelograms and triangles

    A parallelogram has a base of 14 cm and a perpendicular height of 5 cm.

    What is its area?

    Show the answer to question 39

    Answer: 70 cm²

    Why:

    Area of a parallelogram = base × perpendicular height = 14 × 5 = 70 cm².

    Not the slanted side, but the straight-up height.

  7. Objective: Calculate, estimate and compare the volume of cubes and cuboids in cm³ and m³, extending to mm³ and km³

    A box shaped like a cuboid has a volume of 500 cm³.

    Its base is 10 cm by 10 cm.

    How tall is the box?

    Show the answer to question 40

    Answer: 5 cm

    Why:

    Volume = length × width × height.

    The base is 10 × 10 = 100 cm², so the height is 500 ÷ 100 = 5 cm.

Geometry

  1. Objective: Draw 2-D shapes using given dimensions and angles

    How many vertices does a cuboid have?

    • A 7
    • B 5
    • C 8
    • D 6
    Show the answer to question 41

    Answer: C · 8

    Why:

    A cuboid: 6 faces, 12 edges, 8 vertices.

    Check with Euler's rule, faces + vertices − edges = 2: 6 + 8 − 12 = 2. ✓

  2. Objective: Recognise, describe and build simple 3-D shapes, including making nets

    Which of these nets fold to make a cube?

    Tick every one that is right.

    NetsFour nets, lettered A, B, C and D. Net A: six equal squares: in the top row, two squares: the second column and the third column; in the second row, two squares: the first column and the second column; in the third row, two squares: the first column and the second column. Net B: six equal squares: in the top row, three squares: the first column, the second column and the third column; in the second row, one square: the second column; in the third row, one square: the second column; in the fourth row, one square: the second column. Net C: six equal squares: in the top row, one square: the second column; in the second row, two squares: the first column and the second column; in the third row, two squares: the second column and the third column; in the fourth row, one square: the second column. Net D: six equal squares: in the top row, one square: the first column; in the second row, four squares: the first column, the second column, the third column and the fourth column; in the third row, one square: the third column.ABCD
    • A
    • B
    • C
    • D
    Show the answer to question 42

    Answer: B, C, D

    Why:

    A does not: two of its squares land on the same face of the cube, and one face is left open.

    B folds into a cube: every square lands on a face of its own.

    C folds into a cube: every square lands on a face of its own.

    D folds into a cube: every square lands on a face of its own.

  3. Objective: Compare and classify shapes by properties and sizes; find unknown angles in any triangle, quadrilateral and regular polygon

    A small square is a right angle, the same arcs mean equal angles and the same arrowheads mean parallel sides.

    One shape is in the wrong box of the Carroll diagram. Which one?

    Carroll diagramA Carroll diagram: a table of four boxes. The two columns are headed ‘all angles equal’ and ‘not all angles equal’; the two rows ‘has a pair of parallel sides’ and ‘no parallel sides’. Under ‘all angles equal’, beside ‘has a pair of parallel sides’: shape H (four straight sides; four corners marked as a right angle; no angles marked with arcs; two sides with one arrowhead, two sides with two arrowheads (the same number of arrowheads, parallel)). Under ‘not all angles equal’, beside ‘has a pair of parallel sides’: shape G (five straight sides; two corners marked as a right angle; two corners with one arc (the same number of arcs, the same angle); two sides with one arrowhead (the same number of arrowheads, parallel)). Under ‘all angles equal’, beside ‘no parallel sides’: shape J (four straight sides; no corner marked as a right angle; two corners with one arc, two corners with two arcs (the same number of arcs, the same angle); two sides with one arrowhead, two sides with two arrowheads (the same number of arrowheads, parallel)). Under ‘not all angles equal’, beside ‘no parallel sides’: shape L (four straight sides; no corner marked as a right angle; no angles marked with arcs; no sides marked parallel).all anglesequalnot all anglesequalhas a pairofparallelsidesnoparallelsidesJHGL
    • G
    • H
    • J
    • L
    Show the answer to question 43

    Answer: J

    Why:

    Shape J is in the box under ‘all angles equal’, beside ‘no parallel sides’. Its corners are not all marked the same: it goes under ‘not all angles equal’. Two of its sides have the same arrowheads, so they are parallel: it goes beside ‘has a pair of parallel sides’.

    So it belongs in the box under ‘not all angles equal’, beside ‘has a pair of parallel sides’. G, H and L are each where they belong.

  4. Objective: Illustrate and name parts of circles (radius, diameter, circumference) and know the diameter is twice the radius

    What is the name for the distance all the way round the edge of a circle?

    • A radius
    • B circumference
    • C centre
    • D diameter
    Show the answer to question 44

    Answer: B · circumference

    Why:

    That is the circumference.

    The radius goes from the centre to the edge; the diameter goes right across through the centre and is twice the radius; the circumference is the distance round.

  5. Objective: Recognise angles that meet at a point, are on a straight line, or are vertically opposite, and find missing angles

    Three angles sit side by side on a straight line.

    They are 80°, x and 3x.

    What is x?

    Show the answer to question 45

    Answer: 25°

    Why:

    Angles on a straight line add up to 180°: 180 − 80 = 100.

    x and 3x make 4x, so x = 100 ÷ 4 = 25°.

  6. Objective: Describe positions on the full coordinate grid (all four quadrants)

    A, B and C are three corners of a square. The sides from A to B and from B to C are drawn.

    What are the coordinates of the fourth corner, D? Write them like (3, −4).

    Coordinate grid with four quadrantsA coordinate grid. The x-axis is numbered from −6 to 6 and the y-axis from −6 to 6, with a gridline for every whole number and every gridline numbered, the numbers along the bottom and the left-hand edge. The axes cross at 0 in the middle, making four quadrants. Points A at (6, 0), B at (5, 3) and C at (2, 2) are marked where gridlines cross. Straight lines join A, B and C, in that order.xy−6−5−4−3−2−10123456−6−5−4−3−2−10123456ABC
    Show the answer to question 46

    Answer: (3, −1) (also accept 3, -1, 3, −1)

    Why:

    D is opposite B. The side from B to A goes 1 right and 3 down; the side from C to D goes the same way.

    From C (2, 2): 2 + 1 = 3 across, 2 − 3 = −1 up. D is at (3, −1).

  7. Objective: Draw and translate simple shapes on the coordinate plane and reflect them in the axes

    The triangle is translated 2 right and 3 up.

    Where is corner B now? Write it like (2, −5).

    Coordinate grid with four quadrantsA coordinate grid. The x-axis is numbered from −6 to 6 and the y-axis from −6 to 6, with a gridline for every whole number and every gridline numbered, the numbers along the bottom and the left-hand edge. The axes cross at 0 in the middle, making four quadrants. Points A at (−5, −6), B at (−1, −6) and C at (−4, −2) are marked where gridlines cross. A triangle is drawn, its corners at A, B and C.xy−6−5−4−3−2−10123456−6−5−4−3−2−10123456ABC
    Show the answer to question 47

    Answer: (1, −3) (also accept 1, -3, 1, −3)

    Why:

    B is at (−1, −6).

    Right changes the x-coordinate: −1 + 2 = 1.

    Up changes the y-coordinate: −6 + 3 = −3.

    B is now at (1, −3). The triangle is the same size and shape: only its place has changed.

Statistics

  1. Objective: Interpret and construct pie charts and line graphs and use them to solve problems

    The line graph shows the temperature every three hours on a winter day.

    What was the temperature at 21:00?

    Line graph: Temperature on a winter dayA line graph. Temperature (°C) is up the side, from −8 to 2, with a line every 2, each line labelled; Time along the bottom: 00:00, 03:00, 06:00, 09:00, 12:00, 15:00, 18:00, 21:00. A point is marked at each, joined by straight lines. At 00:00 the point is halfway between −6 and −4; At 03:00 the point is on the line marked −2; At 06:00 the point is halfway between −2 and 0; At 09:00 the point is on the line marked 0; At 12:00 the point is halfway between 0 and 2; At 15:00 the point is on the line marked −2; At 18:00 the point is on the line marked −4; At 21:00 the point is halfway between −8 and −6.Temperature on a winter day −8−6−4−20200:0003:0006:0009:0012:0015:0018:0021:00 TimeTemperature (°C)
    Show the answer to question 48

    Answer: -7 °C

    Why:

    At 21:00 the point is halfway between −8 and −6: −7°C.

  2. Objective: Calculate and interpret the mean as an average

    The mean of 4 numbers is 11.

    3 of them are 10, 8 and 6.

    What is the other number?

    Show the answer to question 49

    Answer: 20

    Why:

    The 4 numbers add up to 4 × 11 = 44.

    The 3 you know add up to 10 + 8 + 6 = 24.

    44 − 24 = 20.

Answers

  1. 1. C · =
  2. 2. 160,000
  3. 3. 16 °C
  4. 4. -6 °C
  5. 5. B · 100,000
  6. 6. 4
  7. 7. A · 4
  8. 8. C · =
  9. 9. C · Never true
  10. 10. A · 14
  11. 11. D · 5,339 − 3,035 + 567
  12. 12. 46r4 (also accept 46 remainder 4)
  13. 13. D · 250
  14. 14. 1/8 · "No, 1/8" is right too; "No" on its own scores nothing
  15. 15. C · <
  16. 16. 2 1/2 kg (also accept 5/2)
  17. 17. 7/8
  18. 18. 2/15
  19. 19. A · 0.05
  20. 20. 59.08
  21. 21. 44.4 (also accept 44.40)
  22. 22. 5.13
  23. 23. 0.4
  24. 24. C · 95%
  25. 25. C · 6 km
  26. 26. 495
  27. 27. 4
  28. 28. 27
  29. 29. A · y = 5x + 9
  30. 30. A · 105
  31. 31. D · 4n − 8
  32. 32. 19
  33. 33. 9
  34. 34. 0.603 litres
  35. 35. 3.053 kg
  36. 36. A · 55 miles
  37. 37. B · Always true
  38. 38. A · 6 × 4 ÷ 2
  39. 39. 70 cm²
  40. 40. 5 cm
  41. 41. C · 8
  42. 42. B, C, D
  43. 43. J
  44. 44. B · circumference
  45. 45. 25°
  46. 46. (3, −1) (also accept 3, -1, 3, −1)
  47. 47. (1, −3) (also accept 1, -3, 1, −3)
  48. 48. -7 °C
  49. 49. 20

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