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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: 60 minutes
Total Marks: 50

Instructions:

Answer all 20 questions.
Write your answers in the spaces provided.
You are expected to use an approved Graphing Calculator (GC) where appropriate.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
Marks are indicated in brackets [ ] at the end of each question or part question.

Section A: Basic Numerical Skills and Ratios (Questions 1–5)

Focus: Direct application of ratio concepts, percentages, and proportional reasoning.

1. The ratio of the number of boys to the number of girls in a school club is $5:4$ . If there are 135 members in total, how many girls are there?
[1]

2. A sum of $\$ 800 $is divided between Alice, Bob, and Charlie in the ratio$ 3:5:2$. Calculate the amount received by Bob.
[2]

3. The price of a laptop increases from $\$ 1200 $to$ $1380$. Calculate the percentage increase in the price.
[2]

4. In a mixture of concrete, the ratio of cement to sand to gravel is $1:2:4$ by weight. If $150$ kg of sand is used, calculate the total weight of the concrete mixture.
[2]

5. A map has a scale of $1:50,000$ . The distance between two towns on the map is $8.4$ cm. Calculate the actual distance between the towns in kilometres.
[2]

Section B: Proportionality and Variation (Questions 6–10)

Focus: Direct and inverse variation, including square and cube relationships.

6. $y$ is directly proportional to $x$ . When $x = 4$ , $y = 20$ . Find the value of $y$ when $x = 10$ .
[2]

7. $y$ is inversely proportional to the square of $x$ . When $x = 3$ , $y = 5$ . Find the value of $y$ when $x = 5$ .
[3]

8. The time $T$ taken to complete a job is inversely proportional to the number of workers $N$ . If 6 workers take 10 hours to complete the job, how long will it take 15 workers to complete the same job?
[2]

9. The volume $V$ of a sphere is directly proportional to the cube of its radius $r$ . If the radius is doubled, by what factor does the volume increase?
[1]

10. $z$ varies jointly as $x$ and the square root of $y$ . Given that $z = 12$ when $x = 3$ and $y = 16$ , find the value of $z$ when $x = 5$ and $y = 9$ .
[3]

Section C: Financial Mathematics and Growth (Questions 11–15)

Focus: Simple and compound interest, exponential growth/decay models.

11. Calculate the simple interest earned on an investment of $\$ 5000 $at a rate of$ 4%$ per annum for 3 years.
[2]

12. A bank offers an interest rate of $3.5\%$ per annum, compounded annually. Calculate the total amount in the account after 5 years if the initial deposit is $\$ 2000$. Give your answer correct to the nearest cent.
[3]

13. The population of a town is modelled by the equation $P = P_0 e^{kt}$ , where $t$ is the number of years after 2020. In 2020, the population was 50,000. In 2025, the population was 58,000.
(a) Find the value of $k$ correct to 4 decimal places.
(b) Estimate the population in 2030.
[4]

14. A radioactive substance decays such that its mass $M$ grams after $t$ years is given by $M = M_0 e^{-0.05t}$ . Find the time taken for the mass to reduce to half its initial value.
[3]

15. An item loses $10\%$ of its value each year. If its current value is $\$ 800$, what was its value 2 years ago?
[2]

Section D: Applied Contexts and Optimization (Questions 16–20)

Focus: Real-world applications involving ratios, proportions, and basic optimization constraints.

16. A recipe for a cake requires flour and sugar in the ratio $5:2$ . If a baker wants to make a cake using $1.2$ kg of flour, how much sugar is needed?
[2]

17. The cost $C$ of producing $n$ items is given by $C = 100 + 5n$ . The selling price per item is $\$ 8 $. (a) Write an expression for the profit$ P $in terms of$ n$.
(b) Find the minimum number of items that must be sold to make a profit.
[3]

18. A rectangular garden has a perimeter of $40$ m. The ratio of its length to its width is $3:2$ . Calculate the area of the garden.
[3]

19. In a business partnership, Partner A invests $\$ 10,000 $for 6 months, and Partner B invests$ $15,000 $for 4 months. The profit is shared in proportion to the product of investment and time. If the total profit is$ $5,000$, how much does Partner A receive?
[3]

20. The intensity of light $I$ from a source is inversely proportional to the square of the distance $d$ from the source. At a distance of 2 metres, the intensity is 100 units.
(a) Find the intensity at a distance of 5 metres.
(b) Find the distance at which the intensity is 25 units.
[4]

*** End of Quiz ***

Answers

A-Level Maths H1 Quiz - Numbers Ratio Proportion (Answer Key)

1.
Total parts = $5 + 4 = 9$ .
Number of girls = $\frac{4}{9} \times 135 = 60$ .
Answer: 60 girls [1]

2.
Total parts = $3 + 5 + 2 = 10$ .
Value of one part = $\frac{800}{10} = 80$ .
Bob's share = $5 \times 80 = 400$ .
Answer: $\$ 400$ [2]

3.
Increase = $1380 - 1200 = 180$ .
Percentage increase = $\frac{180}{1200} \times 100\% = 15\%$ .
Answer: $15\%$ [2]

4.
Ratio Cement : Sand : Gravel = $1 : 2 : 4$ .
Sand corresponds to 2 parts.
2 parts = $150$ kg $\Rightarrow$ 1 part = $75$ kg.
Total parts = $1 + 2 + 4 = 7$ .
Total weight = $7 \times 75 = 525$ kg.
Answer: $525$ kg [2]

5.
Actual distance in cm = $8.4 \times 50,000 = 420,000$ cm.
Convert to km: $420,000 \div 100,000 = 4.2$ km.
Answer: $4.2$ km [2]

6.
$y = kx$ .
$20 = k(4) \Rightarrow k = 5$ .
Equation: $y = 5x$ .
When $x = 10$ , $y = 5(10) = 50$ .
Answer: $50$ [2]

7.
$y = \frac{k}{x^2}$ .
$5 = \frac{k}{3^2} \Rightarrow 5 = \frac{k}{9} \Rightarrow k = 45$ .
Equation: $y = \frac{45}{x^2}$ .
When $x = 5$ , $y = \frac{45}{5^2} = \frac{45}{25} = 1.8$ .
Answer: $1.8$ [3]

8.
$T = \frac{k}{N}$ .
$10 = \frac{k}{6} \Rightarrow k = 60$ .
Equation: $T = \frac{60}{N}$ .
When $N = 15$ , $T = \frac{60}{15} = 4$ hours.
Answer: $4$ hours [2]

9.
$V \propto r^3 \Rightarrow V = kr^3$ .
If $r$ becomes $2r$ , new volume $V' = k(2r)^3 = 8kr^3 = 8V$ .
Answer: Factor of 8 [1]

10.
$z = k x \sqrt{y}$ .
$12 = k(3)\sqrt{16} \Rightarrow 12 = k(3)(4) \Rightarrow 12 = 12k \Rightarrow k = 1$ .
Equation: $z = x \sqrt{y}$ .
When $x = 5, y = 9$ : $z = 5 \sqrt{9} = 5(3) = 15$ .
Answer: $15$ [3]

11.
Simple Interest $I = P \times r \times t$ .
$I = 5000 \times 0.04 \times 3 = 600$ .
Answer: $\$ 600$ [2]

12.
Compound Amount $A = P(1 + r)^t$ .
$A = 2000(1 + 0.035)^5 = 2000(1.035)^5$ .
$A \approx 2000(1.187686) \approx 2375.37$ .
Answer: $\$ 2375.37$ [3]

13.
(a) $P = P_0 e^{kt}$ .
$58000 = 50000 e^{k(5)}$ .
$1.16 = e^{5k}$ .
$\ln(1.16) = 5k \Rightarrow k = \frac{\ln(1.16)}{5} \approx 0.0297$ .
Answer: $k \approx 0.0297$ [2]

(b) For 2030, $t = 10$ .
$P = 50000 e^{0.0297 \times 10} = 50000 e^{0.297}$ .
$P \approx 50000(1.3458) \approx 67290$ .
(Using exact $k$ : $P = 50000 (1.16)^2 = 67280$ ).
Answer: $67,280$ (or $67,290$ depending on rounding of $k$ ) [2]

14.
Half life means $M = 0.5 M_0$ .
$0.5 M_0 = M_0 e^{-0.05t}$ .
$0.5 = e^{-0.05t}$ .
$\ln(0.5) = -0.05t$ .
$t = \frac{\ln(0.5)}{-0.05} \approx 13.86$ years.
Answer: $13.9$ years [3]

15.
Let value 2 years ago be $V_0$ .
Current Value $V = V_0 (1 - 0.10)^2$ .
$800 = V_0 (0.9)^2 = V_0 (0.81)$ .
$V_0 = \frac{800}{0.81} \approx 987.65$ .
Answer: $\$ 987.65$ [2]

16.
Flour : Sugar = $5 : 2$ .
$\frac{\text{Sugar}}{\text{Flour}} = \frac{2}{5}$ .
Sugar = $\frac{2}{5} \times 1.2 \text{ kg} = 0.48 \text{ kg}$ .
Answer: $0.48$ kg [2]

17.
(a) Revenue $R = 8n$ . Cost $C = 100 + 5n$ .
Profit $P = R - C = 8n - (100 + 5n) = 3n - 100$ .
Answer: $P = 3n - 100$ [1]

(b) For profit, $P > 0$ .
$3n - 100 > 0 \Rightarrow 3n > 100 \Rightarrow n > 33.33$ .
Minimum integer $n = 34$ .
Answer: $34$ items [2]

18.
Perimeter $2(L + W) = 40 \Rightarrow L + W = 20$ .
Ratio $L : W = 3 : 2$ . Let $L = 3x, W = 2x$ .
$3x + 2x = 20 \Rightarrow 5x = 20 \Rightarrow x = 4$ .
$L = 12$ m, $W = 8$ m.
Area $= 12 \times 8 = 96$ m $^2$ .
Answer: $96$ m $^2$ [3]

19.
Partner A: $10,000 \times 6 = 60,000$ units.
Partner B: $15,000 \times 4 = 60,000$ units.
Ratio A : B = $60,000 : 60,000 = 1 : 1$ .
Total profit $\$ 5,000 $split equally. Partner A receives$ $2,500 $. **Answer:**$ $2,500$ [3]

20.
(a) $I = \frac{k}{d^2}$ .
$100 = \frac{k}{2^2} \Rightarrow k = 400$ .
Equation: $I = \frac{400}{d^2}$ .
At $d = 5$ , $I = \frac{400}{5^2} = \frac{400}{25} = 16$ units.
Answer: $16$ units [2]

(b) $25 = \frac{400}{d^2}$ .
$d^2 = \frac{400}{25} = 16$ .
$d = 4$ metres.
Answer: $4$ metres [2]