📝 Grade 5 Practice Paper 2

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⏱ 45 Minutes
✏️ 40 Marks
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📋 25 Questions
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Section A — Number & Proportion (14 marks)

Q11 mark

Find the LCM (Lowest Common Multiple) of 6 and 8.

✅ 24
Q21 mark

Find the HCF (Highest Common Factor) of 24 and 36.

✅ 12
Q32 marks

Calculate: 2/3 + 5/12

Give your answer as a fraction. Write the numerator (denominator = 12).

✅ 2/3 = 8/12. 8/12 + 5/12 = 13/12. Numerator = 13
Q42 marks

Calculate: 3/4 − 1/3

Give as a fraction (denominator = 12). Write the numerator.

✅ 9/12 − 4/12 = 5/12. Numerator = 5
Q52 marks

In a class of 32 students, 75% passed the test. How many students passed?

✅ 75% of 32 = 0.75 × 32 = 24
Q62 marks

A bike costs £360. It is on sale with 15% off. What is the sale price?

✅ 15% of 360 = 54. Sale price = 360 − 54 = £306
Q72 marks

A sequence starts: 4, 9, 14, 19, 24, ...
(a) What is the term-to-term rule? (Answer: add ___)

(b) What is the 10th term?

✅ (a) Add 5   (b) 4 + (9×5) = 4+45 = 49
Q82 marks

The formula for speed is: Speed = Distance ÷ Time.
A car travels 180 km in 3 hours. What is its speed in km/h?

✅ 180 ÷ 3 = 60 km/h

Section B — Decimals & Data (10 marks)

Q91 mark

Round 6.783 to 2 decimal places.

✅ 6.78
Q102 marks

Calculate: 4.6 × 0.3

✅ 1.38
Q112 marks

Data set: 8, 12, 15, 9, 11, 13, 8, 14
(a) Find the mean (give to 1 d.p. if needed).

(b) Find the range.

✅ Sum = 90, n = 8. Mean = 11.25 (accept 11.3). Range = 15−8 = 7
Q122 marks

A pie chart shows 200 students' favourite fruits. The 'Apple' sector is 90°.
How many students chose apple?

✅ 90/360 × 200 = 1/4 × 200 = 50
Q133 marks

Bar chart data — Shop sales per day: Mon=45, Tue=38, Wed=52, Thu=49, Fri=60, Sat=72, Sun=34.
(a) Total sales for the week?

(b) Mean daily sales?

(c) How many more on Saturday than Tuesday?

✅ (a) 350   (b) 50   (c) 34

Section C — Geometry & Measures (10 marks)

Q142 marks

A regular hexagon has perimeter 54 cm. What is one side length?

✅ 54 ÷ 6 = 9 cm
Q152 marks

A compound shape is made of a rectangle (8cm × 5cm) with a triangle on top (base 8cm, height 4cm).
Find the total area.

✅ Rectangle = 40, Triangle = ½×8×4 = 16. Total = 56 cm²
Q162 marks

A swimming pool is 25 m long, 12 m wide and 2 m deep.
(a) Volume of the pool in m³?

(b) 1 m³ = 1000 litres. How many litres does the pool hold?

✅ (a) 600 m³   (b) 600,000 litres
Q171 mark

A train departs at 09:45 and arrives at 12:20. How long is the journey? Give the answer in minutes.

✅ 2h 35min = 155 minutes
Q183 marks

A rectangle has perimeter 38 cm. The length is 5 cm more than the width.
Find the length and width.

✅ 2(2w+5)=38 → 4w+10=38 → 4w=28 → w=7. Width=7cm, Length=12cm

Section D — Probability & Problem Solving (6 marks)

Q191 mark

A bag contains 3 red, 5 blue and 2 yellow counters. What is P(blue)?
Write as a fraction — give the numerator (denominator = 10).

✅ 5/10 = 1/2. Numerator = 5
Q201 mark

P(rain) = 3/8. What is P(no rain)? Write as a fraction — give the numerator (denominator = 8).

✅ 1 − 3/8 = 5/8. Numerator = 5
Q212 marks

A function machine: INPUT → ×3 → −7 → OUTPUT.
(a) Input = 5. What is the output?

(b) Output = 14. What is the input?

✅ (a) 5×3=15, 15−7=8   (b) Reverse: 14+7=21, 21÷3=7
Q222 marks

A school timetable: Period 1 starts at 08:30. Each lesson is 55 minutes with 5-minute breaks between.
What time does Period 4 start?

Give your answer in 24-hour format (as HHMM, e.g. 1030 for 10:30)

✅ P1: 08:30. Each period+break = 60 min. P2: 09:30. P3: 10:30. P4: 11:30 → 1130
Q230 marks — Challenge

★ A shopkeeper buys apples at 40p each and sells them at 65p each.
He buys 200 apples. 12 are damaged and cannot be sold.
What is his total profit in pounds? (£)

✅ Cost = 200×40p = £80. Revenue = 188×65p = £122.20. Profit = £42.20

Section A (Number): /14

Section B (Decimals & Data): /10

Section C (Geometry): /10

Section D (Probability): /6