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Maths Year 5 54 questions with answers

Year 5 maths: a question for each objective

The national curriculum lists what children are taught in maths in Year 5. 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 5 place value questions with the common mistakes

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

    Write this number in digits:

    "six hundred and ninety-eight thousand and thirty-four"

    Show the answer to question 1

    Answer: 698,034

    Why:

    Column by column, from the hundred thousands: 6, 9, 8, 0, 3, 4.

    In digits: 698,034. A zero keeps each empty column in its place.

  2. Objective: Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000

    Start at 211,469 and count on in steps of 10,000.

    What is the 7th number you say after 211,469?

    Show the answer to question 2

    Answer: 281,469

    Why:

    7 steps of 10,000 is 70,000.

    211,469 + 70,000 = 281,469.

  3. Objective: Interpret negative numbers in context; count forwards and backwards with positive and negative whole numbers, including through 0

    The thermometer shows the temperature at sunset.

    Overnight it falls by 12 degrees. What is the temperature then?

    ThermometerA thermometer. Its marks are numbered in degrees Celsius from −15 to 15, one every 5. Between each numbered mark and the next there are four unnumbered marks, equally spaced. The liquid comes up on the fourth unnumbered mark above 0. −15−10−5051015°C
    Show the answer to question 3

    Answer: -8 °C

    Why:

    The numbered marks go up in 5s. Four unnumbered marks split each gap into five equal steps, so each mark is 5 ÷ 5 = 1 °C.

    The top of the liquid is four marks above 0: 0 + 4 × 1 = 4 °C.

    Count down 12: 4 down to 0 is 4, then 8 more below 0 is −8 °C.

  4. Objective: Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000

    Round 907,422 to the nearest 10,000.

    • A 920,000
    • B 915,000
    • C 910,000
    • D 900,000
    Show the answer to question 4

    Answer: C · 910,000

    Why:

    Find the 10,000 column, then look at the digit immediately to its right: 5 or more rounds up. → 910,000

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

    A whole number rounded to the nearest 10,000 is 360,000.

    What is the largest number it could be?

    • A 364,999
    • B 365,000
    • C 364,998
    • D 364,997
    Show the answer to question 5

    Answer: A · 364,999

    Why:

    Every whole number from 355,000 up to 364,999 rounds to 360,000.

    355,000 rounds up, because its thousands digit is 5; 365,000 would round up to 370,000.

  6. Objective: Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals

    Write the year 595 in Roman numerals. Use CAPITAL letters.

    Show the answer to question 6

    Answer: DXCV

    Why:

    595 = DXCV.

  7. Objective: *(non-statutory but expected)* Recognise and describe linear number sequences, including with fractions and decimals, and state the term-to-term rule

    What is the rule for this sequence?

    40, 55, 70, 85, …

    • A Subtract 15
    • B Add 14
    • C Subtract 14
    • D Add 15
    Show the answer to question 7

    Answer: D · Add 15

    Why:

    From 40 to 55 the sequence goes up by 15, and it does so every time. The rule is "add 15".

Addition & subtraction

  1. Objective: Add and subtract whole numbers with more than 4 digits, including formal columnar methods Explained, with a worked example

    Kai says: 574,758 + 390,847 = 864,595.

    Kai is wrong. Which reason shows why?

    • A When a column comes to 10 or more, its last digit is written and the rest is dropped.
    • B In the ones, 8 + 7 is 15, so the 5 is written, as exchanging happens in taking away, not adding.
    • C Swapping the numbers in a sum keeps the total.
    • D Ten in a column makes 1 more in the next column to the left.
    Show the answer to question 8

    Answer: D · Ten in a column makes 1 more in the next column to the left.

    Why:

    Ten in a column makes 1 more in the next column to the left.

    "Swapping the numbers in a sum keeps the total." is true, but it does not show Kai is wrong.

  2. Objective: Add and subtract mentally with increasingly large numbers (e.g. 12,462 − 2,300 = 10,162)

    Work this out in your head:

    25,520 − 4,000 = ?

    Show the answer to question 9

    Answer: 21,520

    Why:

    Only the thousands change: 25 − 4 = 21 thousand, giving 21,520. No column method needed.

  3. Objective: Use rounding to check answers and determine, in context, appropriate levels of accuracy

    Estimate 339,261 − 161,930 by rounding both numbers to the nearest 1,000.

    What is your estimate?

    Show the answer to question 10

    Answer: 177,000

    Why:

    339,261 ≈ 339,000 and 161,930 ≈ 162,000.

    339,000 − 162,000 = 177,000.

    (The exact answer is 177,331, close enough to show the real answer is sensible.)

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

    A railway line runs from Camp to Castle, through Lake and Forest. The diagram shows three distances along it.

    How far is it from Lake to Forest?

    A route, not to scaleA route drawn as a straight line, not to scale, from Camp through Lake and Forest to Castle. The legs: from Camp to Lake, not labelled; from Lake to Forest, marked ?; from Forest to Castle, not labelled. A bracket above the line from Camp to Forest is labelled 425 km. A bracket below the line from Lake to Castle is labelled 455 km. A bracket above the line from Camp to Castle is labelled 635 km.?425 km455 km635 kmCampLakeForestCastleNot to scale
    Show the answer to question 11

    Answer: 245 km

    Why:

    Camp to Forest and Lake to Castle together: 425 + 455 = 880 km.

    That is the whole line with Lake to Forest counted twice: 880 − 635 = 245 km.

Multiplication & division

  1. Objective: Identify multiples and factors, find all factor pairs of a number, and common factors of two numbers

    Which of these numbers belong in the box under ‘not a multiple of 4’, beside ‘not a factor of 60’?

    Tick every one that is right.

    Carroll diagramA Carroll diagram: a table of four boxes. The two columns are headed ‘multiple of 4’ and ‘not a multiple of 4’; the two rows ‘factor of 60’ and ‘not a factor of 60’. Under ‘multiple of 4’, beside ‘factor of 60’: 20. Under ‘not a multiple of 4’, beside ‘factor of 60’: 30. Under ‘multiple of 4’, beside ‘not a factor of 60’: 64. Under ‘not a multiple of 4’, beside ‘not a factor of 60’: 7.multiple of 4not a multipleof 4factor of60not afactor of607206430
    • A 2
    • B 65
    • C 76
    • D 27
    • E 4
    Show the answer to question 12

    Answer: B, D · 65, 27

    Why:

    2: not a multiple of 4, factor of 60.

    4: multiple of 4, factor of 60.

    27: not a multiple of 4, not a factor of 60 ✓.

    65: not a multiple of 4, not a factor of 60 ✓.

    76: multiple of 4, not a factor of 60.

    The box under ‘not a multiple of 4’, beside ‘not a factor of 60’ holds the numbers that are ‘not a multiple of 4’ and ‘not a factor of 60’: 27, 65.

  2. Objective: Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

    Which of these is a prime factor of 20?

    • A 11
    • B 5
    • C 13
    • D 10
    Show the answer to question 13

    Answer: B · 5

    Why:

    20 = 2 × 2 × 5. A prime factor is a factor that is also prime, so 5 is one; 4 is a factor but not prime.

  3. Objective: Establish whether a number up to 100 is prime; recall prime numbers up to 19

    Is 87 a prime number?

    • A No
    • B Yes
    Show the answer to question 14

    Answer: A · No

    Why:

    No. 87 = 3 × 29, so it has other factors.

    Watch out for 87: it looks prime but is not.

  4. Objective: Multiply numbers up to 4 digits by a 1- or 2-digit number using formal written method, including long multiplication

    A school orders 21 boxes of paper. Each box holds 421 sheets.

    How many sheets is that?

    Show the answer to question 15

    Answer: 8,841

    Why:

    421 × 21:

    421 × 1 = 421

    421 × 20 = 8,420

    421 + 8,420 = 8,841

  5. Objective: Multiply and divide numbers mentally, drawing on known facts

    Fill the gap so that both sides are equal:

    36 ÷ 4 = 360 ÷ ?

    Show the answer to question 16

    Answer: 40

    Why:

    36 ÷ 4 = 9. 360 is 10 times 36, so divide by 10 times 4 to get 9 again: 360 ÷ 40 = 9.

  6. Objective: Divide numbers up to 4 digits by a 1-digit number using short division, and interpret remainders appropriately for the context (as remainder, fraction, decimal, or by rounding)

    1,377 ÷ 5 = ?

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

    Show the answer to question 17

    Answer: 275r2 (also accept 275 remainder 2)

    Why:

    Short division ("bus stop"): 1,377 ÷ 5 = 275 remainder 2.

  7. Objective: Multiply and divide whole numbers and decimals by 10, 100 and 1,000

    2,507 ÷ 10 = ?

    Show the answer to question 18

    Answer: 250.7

    Why:

    Dividing by 10 moves every digit 1 place to the right. Answer: 250.7.

  8. Objective: Recognise and use square and cube numbers, and the notation ² and ³

    Write every square number between 72 and 112.

    List them smallest first, separated by commas.

    Show the answer to question 19

    Answer: 81, 100

    Why:

    Square the whole numbers in turn: 9 × 9 = 81, 10 × 10 = 100.

    Those between 72 and 112: 81, 100.

  9. Objective: Solve problems using knowledge of factors, multiples, squares and cubes

    A square patio is made from 49 square tiles.

    How many tiles are along one side?

    • A 10 tiles
    • B 8 tiles
    • C 9 tiles
    • D 7 tiles
    Show the answer to question 20

    Answer: D · 7 tiles

    Why:

    A square has equal sides, so you need the number that times itself makes 49: 7 × 7 = 49.

  10. Objective: Solve problems involving all four operations combined, including understanding the meaning of the equals sign (e.g. 13 + 24 = 12 + 25; 33 = 5 × ?)

    A baker makes 12 trays of 15 bread rolls.

    92 of them are sold in the morning.

    The rest are put into bags of 8.

    How many bags are filled?

    • A 6
    • B 11
    • C 9
    • D 10
    Show the answer to question 21

    Answer: B · 11

    Why:

    12 × 15 = 180

    180 − 92 = 88

    88 ÷ 8 = 11

  11. Objective: Solve problems involving scaling by simple fractions and simple rates

    The table shows a recipe for pancakes for 2 people.

    How much plain flour is needed for 4 people?

    Pancakes for 2 people
    IngredientAmount
    Eggs2
    Plain flour125 g
    Milk300 ml
    Show the answer to question 22

    Answer: 250 g

    Why:

    4 people is 2 times 2 people: 125 × 2 = 250.

    250 g of plain flour.

Fractions, decimals & %

Six Year 5 fractions questions with the common mistakes

  1. Objective: Compare and order fractions whose denominators are all multiples of the same number

    Which is the largest?

    • A 1/4
    • B 2/3
    • C 3/4
    • D 11/12
    Show the answer to question 23

    Answer: D · 11/12

    Why:

    In 12ths: 1/4 = 3/12, 11/12 = 11/12, 2/3 = 8/12, 3/4 = 9/12. The largest is 11/12.

  2. Objective: Identify, name and write equivalent fractions, including tenths and hundredths Explained, with a worked example

    Write 6 tenths as a decimal.

    Show the answer to question 24

    Answer: 0.6 (also accept .6)

    Why:

    10 tenths make one whole, so 6 tenths = 6 ÷ 10 = 0.6.

    The last digit of 6 goes in the tenths column, the first place after the point.

  3. Objective: Recognise mixed numbers and improper fractions and convert between them Explained, with a worked example

    Write 5 2/3 as an improper fraction.

    Show the answer to question 25

    Answer: 17/3 · accept equivalent fractions

    Why:

    5 wholes = 5 × 3 = 15 thirds. Add the 2: 17/3.

  4. Objective: Add and subtract fractions with the same denominator, and denominators that are multiples of the same number

    Elif says: 3/5 + 1/10 = 4/15.

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

    Show the answer to question 26

    Answer: 7/10 · accept equivalent fractions · "No, 7/10" is right too; "No" on its own scores nothing

    Why:

    You cannot add the tops and the bottoms. Make the denominators the same first: 3/5 = 6/10, then 6/10 + 1/10 = 7/10.

    Elif's answer was not right: the correct answer is 7/10.

  5. Objective: Multiply proper fractions and mixed numbers by whole numbers

    Priya says: 3/4 × 6 = 18/24.

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

    Show the answer to question 27

    Answer: 4 1/2 (also accept 18/4) · accept equivalent fractions · "No, 4 1/2" is right too; "No" on its own scores nothing

    Why:

    Only the top is multiplied: 3/4 × 6 = 18/4 = 4 1/2. Multiplying both parts by 6 leaves the fraction the same size.

    Priya's answer was not right: the correct answer is 4 1/2.

  6. Objective: Read and write decimal numbers as fractions (0.71 = 71/100)

    Which fraction is equal to 0.68?

    • A 68/100
    • B 18/25
    • C 68/1000
    • D 68/10
    Show the answer to question 28

    Answer: A · 68/100

    Why:

    Two decimal places means hundredths: 0.68 = 68/100 (= 17/25).

  7. Objective: Recognise and use thousandths, relating to tenths, hundredths and decimal equivalents

    Write 545 thousandths as a decimal.

    Show the answer to question 29

    Answer: 0.545 (also accept .545)

    Why:

    1,000 thousandths make one whole, so 545 thousandths = 545 ÷ 1,000 = 0.545.

    The last digit of 545 goes in the thousandths column, the third place after the point.

  8. Objective: Round decimals with 2 d.p. to the nearest whole number and to 1 d.p.

    Round 15.76 to the nearest whole number.

    Show the answer to question 30

    Answer: 16

    Why:

    Look at the digit just after the place you are rounding to. → 16

  9. Objective: Read, write, order and compare numbers with up to 3 decimal places

    Which number lies between 0.1 and 0.15?

    • A 0.16
    • B 0.6
    • C 0.08
    • D 0.125
    Show the answer to question 31

    Answer: D · 0.125

    Why:

    0.1 = 0.1 and 0.15 = 0.15. 0.125 is between them.

  10. Objective: Solve problems involving number up to 3 d.p.

    The table shows the times in the 60 m race on sports day.

    How many seconds faster than Jonah was Noor?

    60 m race on sports day
    RunnerTime (seconds)
    Priya11.8
    Noor10.6
    Jonah12.1
    Yusuf11.0
    • A 0.15 seconds
    • B 1.5 seconds
    • C 1.4 seconds
    • D 1.3 seconds
    Show the answer to question 32

    Answer: B · 1.5 seconds

    Why:

    Jonah: 12.1 s. Noor: 10.6 s.

    12.1 − 10.6 = 1.5 seconds faster.

  11. Objective: Recognise the per cent symbol (%); understand per cent as parts per 100; write percentages as a fraction with denominator 100 and as a decimal

    Write 0.3 as a fraction.

    Show the answer to question 33

    Answer: 3/10 · accept equivalent fractions

    Why:

    3/10 = 30% = 0.3. These equivalences are worth knowing by heart. They save time in every percentage question.

  12. Objective: Solve problems requiring percentage and decimal equivalents of ½, ¼, ⅕, ⅖, ⅘ and fractions with a denominator that is a multiple of 10 or 25

    Write 20% as a fraction.

    Show the answer to question 34

    Answer: 1/5 · accept equivalent fractions

    Why:

    1/5 = 20% = 0.2. These equivalences are worth knowing by heart. They save time in every percentage question.

  13. Objective: *(expected fluency)* Complements of 1 with decimals (0.83 + 0.17 = 1); mentally add and subtract tenths

    1 − 0.82 = ?

    Show the answer to question 35

    Answer: 0.18

    Why:

    82 hundredths from 100 hundredths leaves 18 hundredths: 0.18. Check: the hundredths digits add to 10 and the tenths to 9.

Measurement

Six Year 5 measurement questions with the common mistakes

  1. Objective: Convert between different units of metric measure (km/m; cm/m; cm/mm; g/kg; l/ml) Explained, with a worked example

    How long is the worm, in centimetres?

    A ruler and a wormA piece of a ruler, broken off on the left, numbered in centimetres from 1 to 5, with a small mark for every millimetre and a longer mark halfway between each centimetre and the next. A worm lies along it. Its left end lines up with the mark numbered 1; its right end lines up with the longer mark halfway between 3 and 4. 12345 cm
    Show the answer to question 36

    Answer: 2.5 cm

    Why:

    Each centimetre is split into 10 millimetres. The right end is at 3 cm and 5 small marks, which is 35 mm.

    The worm starts at 1 cm, not at 0. 35 − 10 = 25 mm. 25 mm is 25 ÷ 10 = 2.5 cm.

  2. Objective: Understand and use approximate equivalences between metric and common imperial units (inches, pounds, pints)

    Roughly how many litres is 4 pints?

    • A about 2.3 litres
    • B about 4.6 litres
    • C about 4 litres
    • D about 9.2 litres
    Show the answer to question 37

    Answer: A · about 2.3 litres

    Why:

    Useful rough equivalences: 1 inch ≈ 2.5 cm, 1 pound ≈ 0.45 kg, 1 pint ≈ 0.57 litres. These are approximate, so "about" is the right word.

  3. Objective: Measure and calculate the perimeter of composite rectilinear shapes in cm and m

    Which has the largest perimeter?

    • A a rectangle 4 cm by 2 cm
    • B a square of side 7 cm
    • C an L-shape made from three 4 cm squares
    Show the answer to question 38

    Answer: C · an L-shape made from three 4 cm squares

    Why:

    Perimeters: a square of side 7 cm: 28 cm; an L-shape made from three 4 cm squares: 32 cm; a rectangle 4 cm by 2 cm: 12 cm.

  4. Objective: Calculate and compare the area of rectangles (including squares) using cm² and m²; estimate the area of irregular shapes

    A rectangle has an area of 77 cm².

    One side is 11 cm.

    How long is the other side?

    Show the answer to question 39

    Answer: 7 cm

    Why:

    Area ÷ known side = the other side: 77 ÷ 11 = 7 cm.

  5. Objective: Estimate volume (cm³ blocks, cuboids and cubes) and capacity

    A storage box is a cuboid 60 cm long, 20 cm wide and 30 cm high.

    1,000 cm³ holds 1 litre.

    How many litres does it hold when it is full?

    Show the answer to question 40

    Answer: 36 litres

    Why:

    Volume: 60 × 20 × 30 = 36,000 cm³.

    36,000 ÷ 1,000 = 36 litres.

  6. Objective: Solve problems involving converting between units of time

    Write 495 minutes as hours and minutes, like "2 hours 15 minutes".

    Show the answer to question 41

    Answer: 8 hours 15 minutes (also accept 8h15, 8hoursand15minutes, 8hours15minute)

    Why:

    495 ÷ 60 = 8 remainder 15 → 8 hours 15 minutes.

  7. Objective: Use all four operations to solve problems involving measure (length, mass, volume, money) using decimal notation, including scaling

    A class measured the height of a bean plant once a week. The table shows what they found.

    How much did it grow from week 3 to week 4?

    Height of a bean plant
    WeekHeight (cm)
    Week 13.3
    Week 29.0
    Week 313.4
    Week 419.5
    Week 525.4
    Show the answer to question 42

    Answer: 6.1 cm

    Why:

    Week 4: 19.5 cm. Week 3: 13.4 cm.

    19.5 − 13.4 = 6.1 cm.

  8. Objective: *(non-statutory, but FSCE-relevant)* Use perimeter/area relations to find unknown lengths: effectively simple algebra, e.g. 4 + 2b = 20

    All the sides of this hexagon are the same length. Its perimeter is 36 cm.

    How long is the side marked ?

    HexagonA hexagon with six straight sides, drawn to scale. Going round from the bottom left-hand corner, its sides go: right, marked ?, with one small mark across it; up and to the right, not labelled, with one small mark across it; up and to the left, not labelled, with one small mark across it; left, not labelled, with one small mark across it; down and to the left, not labelled, with one small mark across it; down and to the right, not labelled, with one small mark across it. Sides with the same number of small marks across them are equal. ?
    Show the answer to question 43

    Answer: 6 cm

    Why:

    A hexagon has 6 sides, all equal.

    36 ÷ 6 = 6 cm.

Geometry

  1. Objective: Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

    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, one square: the first column; in the second row, one square: the first column; in the third row, one square: the first column; in the fourth row, one square: the first column; in the fifth row, one square: the first column; in the sixth row, one square: the first 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, two squares: the first column and the second column; in the third row, one square: the first column. Net C: six equal squares: in the top row, two squares: the first column and the second column; in the second row, one square: the first column; in the third row, three squares: the first column, the second column and the third column. Net D: six equal squares: in the top row, one square: the second 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 second column.ABCD
    • A
    • B
    • C
    • D
    Show the answer to question 44

    Answer: D

    Why:

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

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

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

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

  2. Objective: Know angles are measured in degrees; estimate and compare acute, obtuse and reflex angles

    Put these angles in order, smallest first:

    175°, 15°, 300°, 55°

    Show the answer to question 45

    Answer: 15°,55°,175°,300° (also accept 15,55,175,300, 15, 55, 175, 300)

    Why:

    Degrees are just numbers: 15° < 55° < 175° < 300°.

  3. Objective: Draw given angles and measure them in degrees using a protractor

    Ava measures an obtuse angle with a protractor and writes down 50°.

    Ava has read the wrong scale.

    What is the angle really?

    Show the answer to question 46

    Answer: 130°

    Why:

    The two scales add to 180°, so the other scale reads 180 − 50 = 130°.

    50° is acute; the angle was obtuse, so 130° is the one that fits.

  4. Objective: Identify angles at a point / one whole turn (360°)

    Three angles meet at a point.

    Two of them are 84° and 58°.

    What is the third?

    Angles at a pointThree lines meeting at a point, making three angles all the way round. Two are 84° and 58°; the third is marked ?.84°58°?
    Show the answer to question 47

    Answer: 218°

    Why:

    Angles at a point add to 360° (a full turn).

    360 − 84 − 58 = 218°.

  5. Objective: Identify angles at a point on a straight line / half a turn (180°)

    Jonah says: one angle on a straight line is 66°, so the other angle is 66°.

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

    Show the answer to question 48

    Answer: 114° · "No, 114°" is right too; "No" on its own scores nothing

    Why:

    Angles on a straight line add to 180°, so the other angle is 180 − 66 = 114.

    Jonah's answer was not right: the correct answer is 114°.

  6. Objective: Identify other multiples of 90°

    Sana says: Two angles lie side by side on a straight line. One is 32°, so the other is 58°.

    Sana is wrong. Which reason shows why?

    Angles on a straight lineA straight line with another line coming out of it, making two angles side by side. One is 32°; the other is marked ?. 32° ?
    • A Angles on a straight line make one right angle: 90°.
    • B A straight line is a half turn, which is two right angles.
    • C The two angles on a straight line make a right angle together.
    • D A right angle is a quarter turn.
    Show the answer to question 49

    Answer: B · A straight line is a half turn, which is two right angles.

    Why:

    A straight line is a half turn, which is two right angles.

    "A right angle is a quarter turn." is true, but it does not show Sana is wrong.

  7. Objective: Use the properties of rectangles to deduce related facts and find missing lengths and angles

    A diagonal of a rectangle makes an angle of 33° with the long side.

    What angle does it make with the short side?

    Show the answer to question 50

    Answer: 57°

    Why:

    The corner of a rectangle is 90°, and the diagonal splits it: 90 − 33 = 57°.

  8. Objective: Distinguish between regular and irregular polygons by reasoning about equal sides and angles

    The same marks on two sides mean they are equal, a small square is a right angle and the same arcs mean equal angles.

    Which of the shapes P to T belong in the box under ‘all sides equal’, beside ‘not all angles equal’?

    Tick every one that is right.

    Carroll diagramA Carroll diagram: a table of four boxes. The two columns are headed ‘all sides equal’ and ‘not all sides equal’; the two rows ‘all angles equal’ and ‘not all angles equal’. Under ‘all sides equal’, beside ‘all angles equal’: shape N (three straight sides; no corner marked as a right angle; three corners with one arc (the same number of arcs, the same angle); three sides with one small mark across them (the same number of marks, the same length)). Under ‘not all sides equal’, beside ‘all angles equal’: shape G (six straight sides; no corner marked as a right angle; six corners with one arc (the same number of arcs, the same angle); three sides with one small mark, three sides with two small marks across them (the same number of marks, the same length)). Under ‘all sides equal’, beside ‘not all angles equal’: 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); four sides with one small mark across them (the same number of marks, the same length)). Under ‘not all sides equal’, beside ‘not all angles equal’: shape H (four straight sides; no corner marked as a right angle; two corners with one arc (the same number of arcs, the same angle); two sides with one small mark, two sides with two small marks across them (the same number of marks, the same length)). Under the table, to sort: shape P (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 small mark across them (the same number of marks, the same length)), shape Q (five straight sides; two corners marked as a right angle; two corners with one arc (the same number of arcs, the same angle); five sides with one small mark across them (the same number of marks, the same length)), shape R (four straight sides; four corners marked as a right angle; no angles marked with arcs; two sides with one small mark, two sides with two small marks across them (the same number of marks, the same length)), shape S (four straight sides; four corners marked as a right angle; no angles marked with arcs; two sides with one small mark, two sides with two small marks across them (the same number of marks, the same length)) and shape T (four straight sides; four corners marked as a right angle; no angles marked with arcs; two sides with one small mark, two sides with two small marks across them (the same number of marks, the same length)).all sidesequalnot all sidesequalall anglesequalnot allanglesequalJHNGPQRST
    • P
    • Q
    • R
    • S
    • T
    Show the answer to question 51

    Answer: Q

    Why:

    P: not all sides equal; not all angles equal.

    Q: all sides equal; not all angles equal ✓.

    R: not all sides equal; all angles equal.

    S: not all sides equal; all angles equal.

    T: not all sides equal; all angles equal.

  9. Objective: Identify, describe and represent the position of a shape after a reflection or translation, knowing the shape has not changed

    The triangle is reflected in the mirror line.

    Where is the image of corner C? Write it like (4, 7).

    Coordinate gridA coordinate grid. The x-axis is numbered from 0 to 10 and the y-axis from 0 to 10, with a gridline for every whole number and every gridline numbered. Points A at (3, 1), B at (1, 1) and C at (0, 4) are marked where gridlines cross. A triangle is drawn, its corners at A, B and C. A dashed mirror line runs straight up the grid through 4 on the x-axis.xy012345678910012345678910ABC
    Show the answer to question 52

    Answer: (8, 4) (also accept 8, 4)

    Why:

    The mirror line goes up the grid through 4 on the x-axis. C is at (0, 4), 4 squares to the left of the line.

    Its image is 4 squares the other side: 4 + 4 = 8.

    The y-coordinate does not change: the image of C is at (8, 4).

Statistics

  1. Objective: Solve comparison, sum and difference problems using a line graph

    The line graph shows how many people were in a café each hour.

    At what time were the most people in the café?

    Line graph: People in a caféA line graph. Number of people is up the side, from 0 to 60, with a line every 10, each line labelled; Time along the bottom: 09:00, 10:00, 11:00, 12:00, 13:00, 14:00. A point is marked at each, joined by straight lines. At 09:00 the point is on the line marked 30; At 10:00 the point is on the line marked 10; At 11:00 the point is on the line marked 50; At 12:00 the point is on the line marked 10; At 13:00 the point is halfway between 10 and 20; At 14:00 the point is on the line marked 60.People in a café 010203040506009:0010:0011:0012:0013:0014:00 TimeNumber of people
    • A 12:00
    • B 14:00
    • C 11:00
    • D 10:00
    Show the answer to question 53

    Answer: B · 14:00

    Why:

    The highest point is at 14:00: 60.

  2. Objective: Complete, read and interpret information in tables, including timetables

    The table shows the fruit a stall sold in two weeks.

    How many pieces of fruit were sold in week 2 altogether?

    Fruit sold
    FruitWeek 1Week 2
    Apples159
    Pears2030
    Plums3113
    • A 62
    • B 53
    • C 54
    • D 52
    Show the answer to question 54

    Answer: D · 52

    Why:

    Add the week 2 column: 9 + 30 + 13 = 52.

Answers

  1. 1. 698,034
  2. 2. 281,469
  3. 3. -8 °C
  4. 4. C · 910,000
  5. 5. A · 364,999
  6. 6. DXCV
  7. 7. D · Add 15
  8. 8. D · Ten in a column makes 1 more in the next column to the left.
  9. 9. 21,520
  10. 10. 177,000
  11. 11. 245 km
  12. 12. B, D · 65, 27
  13. 13. B · 5
  14. 14. A · No
  15. 15. 8,841
  16. 16. 40
  17. 17. 275r2 (also accept 275 remainder 2)
  18. 18. 250.7
  19. 19. 81, 100
  20. 20. D · 7 tiles
  21. 21. B · 11
  22. 22. 250 g
  23. 23. D · 11/12
  24. 24. 0.6 (also accept .6)
  25. 25. 17/3 · accept equivalent fractions
  26. 26. 7/10 · accept equivalent fractions · "No, 7/10" is right too; "No" on its own scores nothing
  27. 27. 4 1/2 (also accept 18/4) · accept equivalent fractions · "No, 4 1/2" is right too; "No" on its own scores nothing
  28. 28. A · 68/100
  29. 29. 0.545 (also accept .545)
  30. 30. 16
  31. 31. D · 0.125
  32. 32. B · 1.5 seconds
  33. 33. 3/10 · accept equivalent fractions
  34. 34. 1/5 · accept equivalent fractions
  35. 35. 0.18
  36. 36. 2.5 cm
  37. 37. A · about 2.3 litres
  38. 38. C · an L-shape made from three 4 cm squares
  39. 39. 7 cm
  40. 40. 36 litres
  41. 41. 8 hours 15 minutes (also accept 8h15, 8hoursand15minutes, 8hours15minute)
  42. 42. 6.1 cm
  43. 43. 6 cm
  44. 44. D
  45. 45. 15°,55°,175°,300° (also accept 15,55,175,300, 15, 55, 175, 300)
  46. 46. 130°
  47. 47. 218°
  48. 48. 114° · "No, 114°" is right too; "No" on its own scores nothing
  49. 49. B · A straight line is a half turn, which is two right angles.
  50. 50. 57°
  51. 51. Q
  52. 52. (8, 4) (also accept 8, 4)
  53. 53. B · 14:00
  54. 54. D · 52

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