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A Level H1 Mathematics Numbers Ratio Proportion Quiz
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Questions
A-Level Maths H1 Quiz - Numbers Ratio Proportion
Name: ________________________
Class: ________________________
Date: ________________________
Score: ______ / 50
Duration: 45 minutes
Total Marks: 50
Instructions:
- Answer ALL questions.
- Show all working clearly. Marks are awarded for method.
- Unless otherwise stated, give non-exact answers to 3 significant figures.
- You may use an approved graphing calculator (GC) where appropriate.
- The number of marks for each question or part is shown in brackets [ ].
Section A: Ratio and Proportion (Questions 1–5)
Each question carries 2 marks unless otherwise stated.
1. A recipe for 8 servings requires 300 g of flour. How much flour is needed for 12 servings? [2]
2. The ratio of boys to girls in a school is 3 : 5. There are 480 girls. Find the total number of students in the school. [2]
3. A sum of money is divided between Ali, Ben, and Chen in the ratio 2 : 3 : 5. Ben receives $45. Find the total sum of money. [2]
4. The scale of a map is 1 : 25 000. Two towns are 8.4 cm apart on the map. Find the actual distance between the towns in kilometres. [2]
5. A car travels 240 km on 16 litres of petrol. At the same rate, how far can it travel on 25 litres? [2]
Section B: Percentages and Financial Mathematics (Questions 6–10)
Each question carries 2 marks unless otherwise stated.
6. A shirt originally costs $80. It is discounted by 15% in a sale. Find the sale price. [2]
7. After a 20% increase, the price of a concert ticket is $144. Find the original price. [2]
8. A company's profit increased from 310 000 in 2024. Calculate the percentage increase. [2]
9. A laptop depreciates in value by 12% each year. Its original value is $1800. Find its value after 3 years, giving your answer to the nearest dollar. [3]
10. A bank offers a savings account with interest at 2.5% per annum compounded annually. Mr Tan deposits $5000. Find the amount in the account after 5 years. [3]
Section C: Direct and Inverse Proportion (Questions 11–15)
Each question carries 3 marks unless otherwise stated.
11. The cost, 175. Find the cost of printing 800 brochures. [3]
12. The time, T hours, taken to complete a construction project is inversely proportional to the number of workers, w. With 15 workers, the project takes 24 hours. How long would the project take with 20 workers? [3]
13. The distance, d km, that a car can travel on a full tank is directly proportional to the capacity, c litres, of the tank. A car with a 45-litre tank can travel 540 km. Find the capacity of a tank that allows the car to travel 720 km. [3]
14. The resistance, R ohms, of a wire is directly proportional to its length, L metres, and inversely proportional to the square of its diameter, d mm. A wire of length 50 m and diameter 2 mm has a resistance of 8 ohms. Find the resistance of a wire of length 80 m and diameter 2.5 mm. [4]
15. The volume, V, of a gas at constant temperature is inversely proportional to the pressure, P. When the pressure is 120 kPa, the volume is 2.5 m³. Find the pressure when the volume is 1.8 m³. [3]
Section D: Problem Solving and Applications (Questions 16–20)
Each question carries 3–4 marks.
16. A fruit seller mixes two types of apples. Type A costs 5.00 per kg. He mixes them in the ratio 3 : 2 by weight. Find the cost per kg of the mixture. [3]
17. A rectangular field has length and width in the ratio 5 : 3. The perimeter of the field is 320 m. Find the area of the field. [3]
18. A sum of 420. Find the amount invested in each account. [4]
19. The population of a town is 45 000. The population is expected to grow by 2.5% each year. (a) Find the expected population after 4 years. [2] (b) Find the number of complete years it will take for the population to first exceed 55 000. [2]
20. A cylindrical water tank has a radius of 1.2 m and a height of 3 m. Water flows into the tank at a constant rate of 0.05 m³ per minute. The tank is initially empty. (a) Find the volume of the tank in m³. [1] (b) Find the time, in hours and minutes, to fill the tank completely. [2] (c) After 1 hour, what percentage of the tank is filled? [2]
END OF QUIZ
Answers
A-Level Maths H1 Quiz - Numbers Ratio Proportion
Answer Key and Marking Scheme
Section A: Ratio and Proportion (Questions 1–5)
1. Flour needed = 300 × (12/8) = 300 × 1.5 = 450 g [M1 A1]
2. Boys : Girls = 3 : 5. 5 parts = 480 girls → 1 part = 96. Total parts = 8. Total students = 8 × 96 = 768 [M1 A1]
3. Ben's share = 3 parts = 15. Total parts = 10. Total sum = 10 × 150 [M1 A1]
4. Actual distance = 8.4 × 25 000 = 210 000 cm = 2100 m = 2.1 km [M1 A1]
5. Rate = 240/16 = 15 km per litre. Distance on 25 litres = 15 × 25 = 375 km [M1 A1]
Section B: Percentages and Financial Mathematics (Questions 6–10)
6. Discount = 15% of 12. Sale price = 12 = 80 = $68 [M1 A1]
7. Let original price = 120 [M1 A1]
8. Increase = 250 000 = $60 000. Percentage increase = (60 000/250 000) × 100% = 24% [M1 A1]
9. Value after 3 years = 1800 × (0.88)³ = 1800 × 0.681472 = 1227 (nearest dollar) [M1 M1 A1]
M1 for identifying multiplier 0.88; M1 for correct power; A1 for correct answer.
10. Amount = 5000 × (1.025)⁵ = 5000 × 1.131408... = 5660 (3 s.f.) [M1 M1 A1]
M1 for correct formula; M1 for correct substitution; A1 for correct answer.
Section C: Direct and Inverse Proportion (Questions 11–15)
11. C = kn. 175 = k × 500 → k = 0.35. Cost for 800 = 0.35 × 800 = $280 [M1 M1 A1]
M1 for finding k; M1 for using k to find cost; A1 for correct answer.
12. T = k/w. 24 = k/15 → k = 360. Time with 20 workers = 360/20 = 18 hours [M1 M1 A1]
M1 for finding k; M1 for using k; A1 for correct answer.
13. d = kc. 540 = k × 45 → k = 12. For d = 720: 720 = 12c → c = 60 litres [M1 M1 A1]
M1 for finding k; M1 for solving for c; A1 for correct answer.
14. R = kL/d². 8 = k × 50/2² → 8 = 50k/4 → k = 32/50 = 0.64.
New R = 0.64 × 80/(2.5)² = 51.2/6.25 = 8.192 ≈ 8.19 ohms (3 s.f.) [M1 M1 M1 A1]
M1 for setting up proportionality; M1 for finding k; M1 for substituting new values; A1 for correct answer.
15. V = k/P. 2.5 = k/120 → k = 300. When V = 1.8: 1.8 = 300/P → P = 300/1.8 = 166.666... ≈ 167 kPa (3 s.f.) [M1 M1 A1]
M1 for finding k; M1 for solving for P; A1 for correct answer.
Section D: Problem Solving and Applications (Questions 16–20)
16. Let mixture be 3 kg of A and 2 kg of B (total 5 kg).
Cost = 3 × 5.00 = 10.00 = 20.50/5 = $4.10 [M1 M1 A1]
M1 for choosing convenient masses; M1 for total cost; A1 for correct answer.
17. Let length = 5x, width = 3x. Perimeter = 2(5x + 3x) = 16x = 320 → x = 20.
Length = 100 m, width = 60 m. Area = 100 × 60 = 6000 m² [M1 M1 A1]
M1 for setting up with x; M1 for finding dimensions; A1 for correct area.
18. Let amount at 3% = (12 000 − x).
Interest = 0.03x + 0.04(12 000 − x) = 420.
0.03x + 480 − 0.04x = 420 → −0.01x = −60 → x = 6000.
6000 at 4% [M1 M1 M1 A1]
M1 for setting up variables; M1 for interest equation; M1 for solving; A1 for both amounts.
19. (a) Population after 4 years = 45 000 × (1.025)⁴ = 45 000 × 1.10381... = 49 671.5 → 49 700 (3 s.f.) [M1 A1]
(b) 45 000 × (1.025)ⁿ > 55 000 → (1.025)ⁿ > 55/45 = 1.222...
n log 1.025 > log 1.222... → n > log 1.222... / log 1.025 ≈ 8.12.
Complete years = 9 [M1 A1]
M1 for inequality/logarithm setup; A1 for correct number of years.
20. (a) Volume = πr²h = π × (1.2)² × 3 = π × 1.44 × 3 = 4.32π ≈ 13.57 m³ [B1]
(b) Time = 13.5716... / 0.05 = 271.43 minutes = 4 hours 31 minutes (nearest minute) [M1 A1]
(c) After 1 hour (60 min), volume filled = 0.05 × 60 = 3 m³.
Percentage = (3/13.5716...) × 100% ≈ 22.1% [M1 A1]
M1 for volume after 1 hour; A1 for correct percentage.
Total: 50 marks