中文（繁體）
中文（简体）
English
P6 Maths Practice Paper: Percentages, Speed, Circles and Statistics (100 marks)
P6 Maths paper: 6 questions, 25 parts, 100 marks, 50 minutes. Discounts, simple interest, speed, circle area, fractions, cuboid volume, mean and range. Full answers.
Part 1: Percentages and Discounts (16 marks)
A shop holds an anniversary sale. A jacket marked at 480 dollars is sold at 60 per cent of the marked price. A pair of sports shoes is sold at 357 dollars, which is 15 per cent below the marked price. Chi Ming also deposits 2500 dollars in a bank at 4 per cent simple interest per year for 3 years.
| # | Question | Answer and marking notes |
|---|---|---|
| 1 | (a) Find the selling price of the jacket. | Answer: 480 x 0.6 = 288 dollars. The selling price is 288 dollars. |
| 2 | (b) By what percentage is the selling price of the jacket below the marked price? | Answer: 1 – 0.6 = 0.4, so it is 40 per cent cheaper. Equivalently (480 – 288) / 480 x 100% = 40%. |
| 3 | (c) Find the marked price of the sports shoes. | Answer: 357 / 0.85 = 420 dollars. The selling price is 85 per cent of the marked price. |
| 4 | (d) Find the simple interest and the total amount after 3 years. | Answer: Interest = 2500 x 4% x 3 = 300 dollars; total amount = 2500 + 300 = 2800 dollars. |
Part 2: Speed (16 marks)
A truck travels 180 km in 2.5 hours. Chi Ming walks at 1.2 m per second. An athlete runs 400 m in 50 seconds.
| # | Question | Answer and marking notes |
|---|---|---|
| 5 | (a) Find the average speed of the truck in km per hour. | Answer: 180 / 2.5 = 72, so the average speed is 72 km per hour. |
| 6 | (b) At the same speed, how long does the truck take to travel 270 km? Give the answer in hours and minutes. | Answer: 270 / 72 = 3.75 hours, that is 3 hours 45 minutes, since 0.75 hour = 45 minutes. |
| 7 | (c) How far does Chi Ming walk in 10 minutes? | Answer: 10 minutes = 600 seconds; 1.2 x 600 = 720 m. |
| 8 | (d) Find the speed of the athlete in m per second and in km per hour. | Answer: 400 / 50 = 8 m per second; 8 x 3.6 = 28.8 km per hour. |
Part 3: Circles and Rings (18 marks)
Take pi as 3.14. A circle has radius 7 cm. A semicircle has diameter 14 cm. A ring has outer radius 10 cm and inner radius 7 cm.
| # | Question | Answer and marking notes |
|---|---|---|
| 9 | (a) Find the circumference of the circle. | Answer: 2 x 3.14 x 7 = 43.96 cm. |
| 10 | (b) Find the area of the circle. | Answer: 3.14 x 7 x 7 = 153.86 square cm. |
| 11 | (c) Find the perimeter of the semicircle. | Answer: arc = 3.14 x 7 = 21.98 cm; adding the diameter 14 cm gives 35.98 cm. |
| 12 | (d) Find the area of the ring. | Answer: 3.14 x (100 – 49) = 3.14 x 51 = 160.14 square cm. |
Part 4: Fractions and Decimals (16 marks)
Work out the following. Give fractions in simplest form. A box contains 48 sweets.
| # | Question | Answer and marking notes |
|---|---|---|
| 13 | (a) Work out 3/4 + 5/6. | Answer: 9/12 + 10/12 = 19/12, that is 1 and 7/12. |
| 14 | (b) Work out 2 and 1/3 x 3/7. | Answer: 7/3 x 3/7 = 1. |
| 15 | (c) Change 0.625 into a fraction in simplest form. | Answer: 0.625 = 625/1000 = 5/8. |
| 16 | (d) After 5/8 of the sweets are eaten, how many sweets are left? | Answer: 3/8 remains; 48 x 3/8 = 18 sweets. |
Part 5: Area, Volume and Capacity (17 marks)
A cuboid measures 12 cm by 8 cm by 5 cm. A cube has edge 6 cm.
| # | Question | Answer and marking notes |
|---|---|---|
| 17 | (a) Find the total surface area of the cuboid. | Answer: 2 x (96 + 60 + 40) = 392 square cm. |
| 18 | (b) Find the volume of the cuboid. | Answer: 12 x 8 x 5 = 480 cubic cm. |
| 19 | (c) Find the volume of the cube. | Answer: 6 x 6 x 6 = 216 cubic cm. |
| 20 | (d) Express the volume of the cuboid in litres. | Answer: 1000 cubic cm = 1 litre, so 480 cubic cm = 0.48 litre. |
Part 6: Statistical Measures (17 marks)
The numbers of books read by five students are 12, 15, 15, 18 and 20.
| # | Question | Answer and marking notes |
|---|---|---|
| 21 | (a) Find the mean. | Answer: 80 / 5 = 16 books. |
| 22 | (b) Find the median. | Answer: With 5 ordered values the median is the third one, 15 books. |
| 23 | (c) Find the mode. | Answer: 15 appears twice, so the mode is 15 books. |
| 24 | (d) Find the range. | Answer: 20 – 12 = 8 books. |
| 25 | (e) A sixth student joins and the mean of the six students becomes 17 books. Find the number of books read by the sixth student. | Answer: The total must be 17 x 6 = 102; 102 – 80 = 22 books. |
Find a tutor — freeTutor Registration →
A TutorZone practice paper; original questions and passages, not publisher material.