🏆 Grade 6 Practice Paper 3 — Challenge

✅ Calculator Allowed ⏱ 45 Minutes 📝 40 Marks 25 Questions
Challenge Paper: These questions require more reasoning and multi-step working. You may use a calculator. Always show your working — method marks are awarded. Read each question carefully before answering.
Name:
Date:
Section 1: Number & Powers
1
Calculate 2³ × 5².
[1]
2
What fraction of 2 hours is 45 minutes? Give your answer in its simplest form.
[1]
3
The product of two numbers is 360 and their HCF is 6. Find their LCM.
[2]
4
What is 0.1% of 3000?
[1]
Section 2: Fractions, Decimals & Percentages
5
Write 5/8 as a decimal.
[1]
6
A shop increases all prices by 15%, then reduces them by 10%. An item originally costs £80. What is the final price?
£
[2]
7
Alice scored 68% on a test with 25 questions. How many did she get correct?
[2]
Section 3: Algebra & Sequences
8
Expand: 3(2x − 5)
[1]
9
The nth term of a sequence is 4n − 3.
(a) Find the 10th term:
(b) Which term number gives the value 97? (Show working.)
[2]
10
Solve: x/5 − 3 = 2
x =
[2]
11
Tom and Sarah share pocket money in the ratio 3 : 4. Tom receives £2.10 less than Sarah. How much does Sarah receive?
£
[2]
Section 4: Geometry & Measure
12
All the angles in a quadrilateral add up to ___°.
°
[1]
13
What is the size of each interior angle of a regular octagon?
°
[2]
14
A square has a perimeter of 36 cm. What is its area?
cm²
[2]
15
A cylinder has radius 5 cm and height 10 cm. Using π = 3.14, find its volume. Give your answer to 1 decimal place.
cm³
[2]
16
Three angles in a quadrilateral are 85°, 110° and 95°. Find the fourth angle.
°
[1]
Section 5: Problem Solving
17
A bag has red and blue balls. The probability of picking red is 2/5. There are 8 red balls. How many balls are in the bag altogether?
balls
[2]
18
📦 Josh earns £8.50 per hour and works 35 hours per week. He saves 30% of his earnings every week.
How much does Josh save over 4 weeks?
£
[2]
19
A water tank holds 480 litres when full. It is currently 3/8 full. How many litres are needed to fill it completely?
litres
[2]
20
Write 6.4 × 10³ as an ordinary number.
[1]
21
🚌 A train is 180 m long and travels at 90 km/h. It enters a tunnel that is 720 m long.
How many seconds does it take for the whole train to pass through the tunnel? (Hint: convert speed to m/s.)
seconds
[2]
22
Ben drives 252 km at 70 km/h. He stops for 45 minutes. If he leaves at 9:00 am, at what time does he arrive? (Use 24-hour clock.)
[2]
23
A rectangle has vertices at (1, 1), (5, 1), (5, 4) and (1, 4). Find its perimeter.
units
[2]
24
The sum of interior angles of a hexagon is ___°.
°
[1]
25
🏅 In a school survey, 60% of 150 students prefer maths over English.
How many students prefer maths? Then find how many more students prefer maths than English.
Students preferring maths:
Difference:
[2]
45:00

✅ Mark Scheme — Paper 3 Challenge

1200 2³=8, 5²=25, 8×25=200
23/8 45/120 simplified
360 [2] LCM = Product ÷ HCF = 360 ÷ 6 = 60
43 0.001 × 3000
50.625 5 ÷ 8
6£82.80 [2] 80×1.15=92, 92×0.9=82.8
717 [2] 0.68×25=17
86x − 15
9(a) 37   (b) n=25 4n−3=97 → 4n=100 → n=25
10x = 25 [2] x/5=5, x=25
11Sarah = £8.40 [2] diff=1 part=£2.10, Sarah=4×2.10
12360°
13135° [2] (8−2)×180÷8 = 1080÷8
1481 cm² [2] side=9, 9²=81
15785.0 cm³ [2] 3.14×25×10
1670° 360−85−110−95
1720 balls [2] 8÷(2/5) = 8×5/2 = 20
18£357 [2] 8.50×35=297.50, ×4=1190, ×0.3=357
19300 litres [2] 480×3/8=180 in; 480−180=300
206400
2136 seconds [2] total=900m; 90km/h=25m/s; 900÷25=36
2213:21 [2] drive=3h36min + stop=45min = 4h21min; 9:00+4:21=13:21
2314 units [2] width=4, height=3; P=2(4+3)=14
24720°
2590 prefer maths; difference = 30 0.6×150=90; 90−60=30