🏆 Grade 5 Practice Paper 3 — Challenge

Extended Problem Solving  |  Cambridge Primary Stage 5 Style

⏱ 60 Minutes
✏️ 50 Marks
🖩 Calculator OK
📋 20 Questions
60:00
Click timer to start · Questions are worth 2–4 marks each

Section A — Number & Calculation (16 marks)

Q12 marks

A factory produces 1,248 items per day. How many items does it produce in 5 weeks?
(5 working days per week)

✅ 1248 × 5 × 5 = 1248 × 25 = 31,200
Q23 marks

A number rounded to the nearest 100 gives 700. When rounded to the nearest 10 it gives 650.
What could the number be? Write the largest possible value.

✅ Rounded to 10 = 650: range 645–654. Rounded to 100 = 700: range 650–749. Intersection = 650–654. Largest = 654
Q33 marks

I am thinking of a number. When I multiply it by 8 and add 15, I get 127. What is my number?

✅ 127 − 15 = 112. 112 ÷ 8 = 14
Q42 marks

Tickets for a concert cost £12 for adults and £8 for children.
A family buys 2 adult and 3 child tickets. How much do they pay in total?

✅ 2×12 + 3×8 = 24 + 24 = £48
Q53 marks

The prime factorisation of 360 is 2³ × 3² × 5.
(a) How many factors does 360 have?
(Hint: (3+1)(2+1)(1+1) = ?)

(b) Find the HCF of 360 and 252, given 252 = 2² × 3² × 7

✅ (a) (3+1)(2+1)(1+1) = 4×3×2 = 24   (b) 2²×3² = 4×9 = 36
Q63 marks

A mobile phone costs £480. A shop offers two payment options:
Option A: Pay full price and get 20% off.
Option B: Pay a £50 deposit + 12 monthly payments of £35.
How much cheaper is the better option?

✅ Option A: 480×0.8 = £384. Option B: 50+12×35 = 50+420 = £470. Option A is £86 cheaper.

Section B — Fractions, Decimals & Percentages (12 marks)

Q73 marks

A school has 600 students. 2/5 are in Years 7-9, 1/3 are in Years 4-6, and the rest are in Years 1-3.
How many students are in Years 1-3?

✅ 2/5 of 600=240, 1/3 of 600=200. Remaining=600−240−200=160
Q83 marks

A coat costs £120. In a sale it is reduced by 25%, then there is an extra 10% off the reduced price.
What is the final price?

✅ 25% off 120 = 90. 10% off 90 = 9. Final = 90−9 = £81
Q93 marks

Calculate: 3½ − 1¾
Give your answer as a mixed number. Write the whole number part.

And the fraction part — write the numerator (denominator = 4):

✅ 3½ = 3 2/4. 3 2/4 − 1 3/4 = 2 6/4 − 1 3/4 = 1 3/4. Whole = 1, Numerator = 3
Q103 marks

A survey asked 240 people their favourite colour. 30% said blue, 1/4 said red, and the rest said other.
How many people said "other"?

✅ Blue: 30%×240=72. Red: 1/4×240=60. Other: 240−72−60=108

Section C — Geometry & Measurement (14 marks)

Q113 marks

A room is L-shaped. It is made from two rectangles:
• Large rectangle: 10 m × 6 m
• Small rectangle (cut out of the corner): 4 m × 3 m
Find: (a) The area of the room.

(b) The perimeter of the room (count all outside edges carefully).

✅ (a) 10×6 − 4×3 = 60 − 12 = 48 m²   (b) Edges: 10+6+6+3+4+3 = 32 m
Q123 marks

A triangle has a base of 9 cm and a height of h cm. Its area is 54 cm².
Find h.

✅ ½ × 9 × h = 54 → 4.5h = 54 → h = 12 cm
Q132 marks

A cuboid storage box: length 40 cm, width 30 cm, height 25 cm.
(a) Volume in cm³?

(b) Volume in litres? (1000 cm³ = 1 litre)

✅ (a) 40×30×25 = 30,000 cm³   (b) 30 litres
Q143 marks

A path surrounds a rectangular garden. The garden is 8 m × 5 m. The path is 1.5 m wide all the way around.
Find the total area (garden + path).

✅ Outer: (8+3)×(5+3) = 11×8 = 88 m²
Q153 marks

A cyclist leaves town at 09:00 and arrives 2 hours 45 minutes later. He cycles at 16 km/h.
How far did he travel? (Distance = Speed × Time)

✅ Time = 2.75 h. Distance = 16 × 2.75 = 44 km

Section D — Data, Probability & Patterns (8 marks)

Q163 marks

Five friends' test scores: 72, 85, 68, 91, x.
The mean is 80. Find x.
Then find the median of all five scores.

✅ Sum = 80×5 = 400. x = 400 − (72+85+68+91) = 400−316 = 84. Sorted: 68,72,84,85,91. Median = 84
Q172 marks

A bag has 4 red, 3 blue and x green counters. P(green) = 3/10.
Find x, then find the total number of counters.

✅ P(green) = x/(7+x) = 3/10 → 10x = 3(7+x) → 10x = 21+3x → 7x = 21 → x = 3. Total = 10
Q183 marks

A sequence has the rule: Multiply by 2, then subtract 1.
First term is 3.
(a) Write the first 5 terms.

What is the 5th term?

(b) If the rule changes to: add 3 starting from 5, what is the 8th term?

✅ (a) 3, 5, 9, 17, 33. 5th = 33   (b) 5, 8, 11, 14, 17, 20, 23, 26. 8th = 26
Q192 marks

A pie chart shows how 180 students travel to school.
Walk: 60°, Bus: 120°, Car: 90°, Cycle: 90°.
How many students walk?

✅ 60/360 × 180 = 1/6 × 180 = 30
Q200 marks — Super Challenge ⭐⭐

★★ A square has area 196 cm². A rectangle has the same perimeter as the square.
The rectangle's length is twice its width.
Find the area of the rectangle.

✅ Square side = 14cm, perimeter = 56cm. Rect: 2l+2w=56, l=2w → 2(2w)+2w=56 → 6w=56 → w=28/3... Wait: 2(2w+w)=56 → 6w=56 → w=28/3. Use nice numbers: l=2w, 2(2w+w)=56 → 6w=56 → w≈9.33. Area = l×w = 2w² = 2×(28/3)² ≈ 174.2 cm².
★ Actually: w=56/6=28/3, l=56/3. Area=(56/3)×(28/3)=1568/9≈174.2 cm²

Section A (Number): /16

Section B (Fractions): /12

Section C (Geometry): /14

Section D (Data): /8