Checkpoint Mathematics 0845 — Stage 6 Coverage Practice (Fractions, Geometry, Data & more)

Cambridge Primary Checkpoint Mathematics — Stage 6 coverage-gap practice (calculator allowed)

Questions

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Question 1 of 27

1 A: Fractions — Write each fraction in its simplest form.

6/8 =

20/100 =

Working:

6/8 — divide top and bottom by 2 → 3/4.
20/100 — divide top and bottom by 20 → 1/5.

LO: 6Nn26 — reduce fractions to their simplest form.

Answer: 3/4, 1/5

2 A: Fractions — Write each improper fraction as a mixed number.

11/4 = ____

9/2 = ____

11/4 = 9/2 =

Working: divide the top by the bottom; the remainder is the fraction.

11/4 — 11 ÷ 4 = 2 remainder 3 → 2 3/4.
9/2 — 9 ÷ 2 = 4 remainder 1 → 4 1/2.

LO: 6Nn25 — change an improper fraction to a mixed number.

Answer: 2 3/4, 4 1/2

3 A: Fractions — Match each fraction to the percentage that is equal to it.

1/2 → ____

1/4 → ____

3/4 → ____

1/5 → ____

1/10 → ____

1/2 →

1/4 →

3/4 →

1/5 →

1/10 →

Working: A percentage is the number of parts in every 100. 1/2 = 50 in 100 = 50%; 1/4 = 25%; 3/4 = 75%; 1/5 = 20 in 100 = 20%; 1/10 = 10%.

LO: 6Nn28 — express 1/2, 1/4, 1/3, 1/10, 1/100 as percentages.

4 A: Fractions — Write each fraction as a decimal.

3/4 =

1/5 =

Working: a fraction means 'top divided by bottom'.

3/4 — 3 ÷ 4 → 0.75.
1/5 — 1 ÷ 5 → 0.2.

LO: 6Nn27 — convert a vulgar fraction to a decimal using division.

Answer: 0.75, 0.2

5 A: Fractions — Which sign makes this true? 3/4 □ 7/8

< (less than) > (greater than) = (equal to)

Working: Make the bottoms the same. 3/4 = 6/8. Compare 6/8 with 7/8: 6/8 is smaller, so 3/4 is less than 7/8.

LO: 6Nn21 — compare fractions with the same or related denominators.

Answer: < (less than)

6 A: Ratio & proportion — A recipe for 4 people uses 200 g of flour. How much flour is needed for 6 people?

Flour needed = g

Working: Find the amount for 1 person first: 200 ÷ 4 = 50 g each. Then for 6 people: 50 × 6 = 300 g.

LO: 6Nn30 / 6Ps7 — solve simple problems involving ratio and direct proportion.

Answer: 300

7 A: Percentages — A coat costs $40. In a sale it is reduced by 25 per cent. Work out how much money is taken off.

Money taken off = $

Working: 25 per cent is one quarter. One quarter of $40 = 40 ÷ 4 = $10 off.

LO: 6Ps8 / 6Nn29 — solve simple word problems involving percentages, e.g. discounts.

Answer: 10

8 A: Percentages — In a class, 3/10 of the children walk to school. Written as a percentage, what is this?

3/10 = per cent

Working: 3/10 means 3 in every 10, which is the same as 30 in every 100 — so 30 per cent.

LO: 6Nn28 — express tenths as percentages.

Answer: 30

9 B: Factors — Select ALL the numbers that are factors of 24.

3 4 6 8 5 9

Working: A factor divides exactly with no remainder. 24 ÷ 3 = 8, 24 ÷ 4 = 6, 24 ÷ 6 = 4, 24 ÷ 8 = 3 — all factors. 24 ÷ 5 and 24 ÷ 9 leave a remainder, so 5 and 9 are not factors.

LO: 6Nn6 — find factors of two-digit numbers.

Answer: 3; 4; 6; 8

10 B: Multiples — Write the LOWEST number that is a multiple of BOTH 4 and 6.

Lowest common multiple =

Working: Multiples of 4: 4, 8, 12, 16… Multiples of 6: 6, 12, 18… The lowest number in both lists is 12.

LO: 6Nn7 — find common multiples.

Answer: 12

11 B: Divisibility — Select ALL the numbers that divide exactly by 4.

16 24 36 18 30

Working: A number divides by 4 if halving it twice gives a whole number (or if the last two digits make a multiple of 4). 16, 24 and 36 divide by 4 exactly; 18 and 30 do not.

LO: 6Nc3 — know and apply tests of divisibility by 2, 4, 5, 10, 25 and 100.

Answer: 16; 24; 36

12 B: Rounding decimals — Round the number 3.47.

3.47 to the nearest tenth =

3.47 to the nearest whole number =

Working: look at the digit just after the place you are rounding to.

Nearest tenth — the hundredths digit is 7 (5 or more), so round up: 3.4 → 3.5.
Nearest whole number — the tenths digit is 4 (less than 5), so round down → 3.

LO: 6Nn9 — round a two-decimal-place number to the nearest tenth or whole number.

Answer: 3.5, 3

13 B: Estimation — Which is the best estimate for 412 × 19, found by rounding each number first?

8000 800 80 000 600

Working: Round to easy numbers: 412 ≈ 400 and 19 ≈ 20. Then 400 × 20 = 8000. (The exact answer, 7828, is close to this estimate.)

LO: 6Nn10 / 6Pt5 — make and justify estimates and approximations.

Answer: 8000

14 C: Angles — Three angles meet at a point. They are 120°, 90° and a°. Calculate angle a.

a = degrees

Three angles meeting at a point: 120, 90 and a

Working: the angles around a point add up to 360°. 360 − 120 − 90 = 150°.

LO: 6Gs6 — calculate angles in a triangle or around a point.

Answer: 150

15 C: Angles — Match each angle to the correct group.

45° → ____

90° → ____

120° → ____

200° → ____

45° →

90° →

120° →

200° →

Working: An acute angle is less than 90° (45°); a right angle is exactly 90°; an obtuse angle is between 90° and 180° (120°); a reflex angle is more than 180° (200°).

LO: 6Gs5 — recognise and draw acute and obtuse angles (extended to right and reflex).

16 C: Quadrilaterals — Match each description to the quadrilateral it matches.

Four right angles; opposite sides equal → ____

Four equal sides; no right angles → ____

Opposite sides parallel and equal; no right angles → ____

Exactly one pair of parallel sides → ____

Four right angles; opposite sides equal →

Four equal sides; no right angles →

Opposite sides parallel and equal; no right angles →

Exactly one pair of parallel sides →

A rectangle, rhombus, parallelogram and trapezium

Working:

Rectangle — four right angles; opposite sides equal.
Rhombus — four equal sides; no right angles.
Parallelogram — opposite sides parallel and equal; no right angles.
Trapezium — exactly one pair of parallel sides.

LO: 6Gs3 — identify and classify quadrilaterals by sides and angles.

17 C: Coordinates — Point P is at (−3, 2). Point Q is 5 squares to the RIGHT of P, on the same row. Write the coordinates of Q.

Q is at ( , )

Grid showing P at minus 3, 2 and an arrow 5 right to Q at 2, 2

Working:

x-coordinate — 5 squares right adds 5: −3 + 5 → 2.
y-coordinate — same row, so unchanged → 2.

So Q is (2, 2).

LO: 6Gp1 — read and plot co-ordinates in all four quadrants.

Answer: 2, 2

18 C: Reflection — The point (3, 2) is reflected in the y-axis (the vertical line through 0). Where does it land?

(−3, 2) (3, −2) (−3, −2) (3, 2)

Point 3,2 reflected across the y-axis to minus 3,2

Working: reflecting in the y-axis flips left–right: the x-coordinate changes sign and the y-coordinate stays the same. (3, 2) → (−3, 2).

LO: 6Gp2 — predict where a point will be after one reflection.

Answer: (−3, 2)

19 C: Polygons — A polygon is a closed 2D shape with straight sides. Which of these shapes is NOT a polygon?

Circle Pentagon Hexagon Triangle

Working: A circle has a curved edge, not straight sides, so it is not a polygon. A pentagon, hexagon and triangle all have straight sides.

LO: 6Gs1 — classify polygons and understand whether a 2D shape is a polygon or not.

Answer: Circle

20 D: Capacity — Convert between litres and millilitres. (1 litre = 1000 ml)

2.5 litres = ml

750 ml = litres

Working: 1 litre = 1000 ml.

2.5 litres → ml — multiply by 1000 → 2500 ml.
750 ml → litres — divide by 1000 → 0.75 litres.

LO: 6Ml2 — convert between units of measurement (l and ml).

Answer: 2500, 0.75

21 D: Time — Which is the LATER time: quarter to four, or 3:40?

Quarter to four 3:40 They are the same time

Working: Quarter to four means 15 minutes before 4 o'clock, which is 3:45. 3:45 is later than 3:40.

LO: 6Mt3 — compare times on digital and analogue clocks, e.g. realise quarter to four is later than 3:40.

Answer: Quarter to four

22 D: Time intervals — In a year that is NOT a leap year, February has 28 days. How many days are there from 28 February to 5 March?

Number of days =

Working: The day after 28 February is 1 March (there is no 29th in this year). Counting on: 1, 2, 3, 4, 5 March — that is 5 days after 28 February.

LO: 6Mt6 / 6Mt7 — use a calendar to calculate time intervals in days, weeks or months.

Answer: 5

23 D: Area — An L-shaped floor is made of two rectangles: one is 5 m by 3 m, and the other is 2 m by 2 m. What is the total area of the floor?

Total area = square metres

An L-shape split into a 5 by 3 rectangle and a 2 by 2 rectangle

Working: split the L into two rectangles and add their areas.

Bottom rectangle: 5 × 3 = 15 m².
Top rectangle: 2 × 2 = 4 m².

Total = 15 + 4 = 19 m².

LO: 6Ma3 — area of compound shapes split into rectangles.

Answer: 19

24 E: Reading a table — A 'ready-reckoner' converts dollars to euros: 5 dollars = 4 euros, 10 dollars = 8 euros, 15 dollars = 12 euros. Use the pattern to answer.

How many euros do you get for 20 dollars? euros

Working: Every 5 dollars gives 4 euros (so 1 dollar = 0.8 euros). 20 dollars is 4 lots of 5 dollars, so 4 × 4 = 16 euros.

LO: 6Dh1 — extract and interpret data from tables, e.g. a price ready-reckoner for currency conversion.

Answer: 16

25 E: Median — Five children scored these marks in a quiz: 5, 9, 3, 7, 6. Find the median (middle) score.

Median =

Working: Put the scores in order first: 3, 5, 6, 7, 9. The median is the middle value — the third of five — which is 6.

LO: 6Dh3 — begin to find the median and mean of a set of data.

Answer: 6

26 E: Probability — On a scale from 0 (impossible) to 1 (certain), what is the probability of getting heads when you flip a fair coin?

1/2 1 1/6

Working: A fair coin has two equally likely outcomes — heads or tails. Heads is one of the two, so the probability is 1 out of 2 = 1/2 (0.5).

LO: 6Db1 — use the language of probability for events with equally likely outcomes.

Answer: 1/2

27 E: Probability — Match each event to how likely it is to happen.

Rolling an 8 on an ordinary 1–6 dice → ____

A tossed coin landing on heads → ____

It will rain somewhere next month → ____

The sun will rise tomorrow morning → ____

Rolling an 8 on an ordinary 1–6 dice →

A tossed coin landing on heads →

It will rain somewhere next month →

The sun will rise tomorrow morning →

Working: An ordinary dice has no 8, so rolling an 8 is impossible. A coin landing heads is an even chance (1/2). Rain somewhere next month is likely. The sun rising tomorrow is certain.

LO: 6Db1 — use the language associated with probability to assess likelihood.

Checkpoint Mathematics 0845 — Stage 6 Coverage Practice (Fractions, Geometry, Data & more)

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