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Secondary 1 Mathematics Numbers Ratio Proportion Quiz

Free Sec 1 Maths Numbers Ratio quiz, HY3 Exam version, with questions, answers, and syllabus-aligned practice for Singapore students.

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Questions

Secondary 1 Mathematics Quiz - Numbers Ratio Proportion

Name: ___________________________
Class: ___________
Date: ___________
Score: ___________ / 40

Duration: 50 minutes
Total Marks: 40

Instructions:

Answer all 20 questions.
Show your working clearly where required.
Write your answers in the spaces provided.
Calculators may be used.

Section A: Ratio and Proportion (Questions 1–5)

1. Write the ratio $12 : 18 : 30$ in its simplest form. [2]

2. The ratio of boys to girls in a class is $3 : 5$ . If there are 24 boys, how many girls are there? [2]

3. A recipe uses flour and sugar in the ratio $4 : 1$ . If 600 g of flour is used, how much sugar is needed? [2]

4. Divide $88$ into the ratio $3 : 5$ . [2]

5. The ratio of red to blue marbles is $2 : 7$ . What fraction of the marbles are blue? [2]

Section B: Percentage (Questions 6–10)

6. Find the percentage increase in the number of visitors from 40 to 55. [2]

7. A shirt originally costs $\$ 80$. It is sold at a 15% discount. Find the sale price. [2]

8. In a group of 50 students, 18 prefer cycling the most. Calculate the percentage of the group who prefer cycling the most. [2]

9. The price of a book increased from $\$ 25 $to$ $32$. Find the percentage increase. [2]

10. A bag contains stamps and coins. The number of coins is twice the number of stamps. The number of stamps increases by 75%. If the number of coins remains constant, find the percentage decrease in the number of coins relative to the new required ratio. [3]

Section C: Rate and Speed (Questions 11–15)

11. Bags of rice are filled at a rate of 200 g per second. How many bags weighing 2 kg each can be filled in 1 hour? [2]

12. A car travels 150 km in 3 hours. Find its average speed in km/h. [2]

13. A machine packs 500 g of powder every 2 seconds. How many 1 kg packets can it pack in 10 minutes? [2]

14. Convert 72 km/h to m/s. [2]

15. A cyclist covers 24 km at a speed of 12 km/h. How long does the journey take in hours? [2]

Section D: Inequalities and Mixed Problems (Questions 16–20)

16. Solve $-3q > 9$ and illustrate your solution on the number line below. [3]
Number line:

17. The ratio of apples to oranges is $5 : 2$ . If there are 35 apples, find the total number of fruits. [2]

18. A sum of money is divided between Ali and Bob in the ratio $2 : 3$ . If Ali receives $\$ 40$, how much does Bob receive? [2]

19. The number of stamps is increased by 40% from 120. Find the new number of stamps. [2]

20. Solve $-2x \leq 8$ and state the solution set. [2]

Answers

Secondary 1 Mathematics Quiz - Numbers Ratio Proportion (Answer Key)

Total Marks: 40
Duration: 50 minutes

Section A: Ratio and Proportion

1. [2 marks]
Simplify $12 : 18 : 30$ by dividing each term by the highest common factor 6.
$12 \div 6 = 2$ , $18 \div 6 = 3$ , $30 \div 6 = 5$ .
Answer: $2 : 3 : 5$ .
Teaching note: To simplify a ratio, divide all parts by their HCF. Common mistake: not dividing all three numbers by the same value.

2. [2 marks]
Ratio boys : girls = $3 : 5$ .
$3$ units = 24 boys → $1$ unit = $24 \div 3 = 8$ .
Girls = $5$ units = $5 \times 8 = 40$ .
Answer: 40 girls.
Teaching note: Use the unitary method: find 1 part then multiply.

3. [2 marks]
Flour : sugar = $4 : 1$ .
$4$ units = 600 g → $1$ unit = $600 \div 4 = 150$ g.
Sugar = 150 g.
Answer: 150 g.

4. [2 marks]
Ratio $3 : 5$ , total parts = $3 + 5 = 8$ .
$8$ units = 88 → $1$ unit = $11$ .
Parts: $3 \times 11 = 33$ , $5 \times 11 = 55$ .
Answer: $33$ and $55$ .
Marking: 1 mark for correct unit value, 1 mark for both shares.

5. [2 marks]
Red : blue = $2 : 7$ , total = $2 + 7 = 9$ parts.
Fraction blue = $\frac{7}{9}$ .
Answer: $\frac{7}{9}$ .

Section B: Percentage

6. [2 marks]
Increase = $55 - 40 = 15$ .
Percentage increase = $\frac{15}{40} \times 100\% = 37.5\%$ .
Answer: $37.5\%$ .
Teaching note: Always divide by original value.

7. [2 marks]
Discount = $15\%$ of $80 = 0.15 \times 80 = 12$ .
Sale price = $80 - 12 = 68$ .
Answer: $\$ 68$.

8. [2 marks]
Percentage = $\frac{18}{50} \times 100\% = 36\%$ .
Answer: $36\%$ .

9. [2 marks]
Increase = $32 - 25 = 7$ .
Percentage = $\frac{7}{25} \times 100\% = 28\%$ .
Answer: $28\%$ .

10. [3 marks]
Let stamps = $x$ , coins = $2x$ .
New stamps = $1.75x$ . To keep ratio coins = $2 \times$ stamps, new coins needed = $2 \times 1.75x = 3.5x$ .
But coins remain $2x$ . Decrease from required = $\frac{3.5x - 2x}{3.5x} \times 100\% = \frac{1.5}{3.5} \times 100\% \approx 42.86\%$ .
Answer: $42.86\%$ decrease (to 2 d.p.).
Marking: 1 mark set ratio, 1 mark new required, 1 mark percentage.
Note: Trap is using wrong base; base is new required coins.

Section C: Rate and Speed

11. [2 marks]
1 hour = 3600 s. Total mass = $200 \times 3600 = 720000$ g = 720 kg.
Bags = $720 \div 2 = 360$ .
Answer: 360 bags.

12. [2 marks]
Average speed = $\frac{150}{3} = 50$ km/h.
Answer: 50 km/h.

13. [2 marks]
10 min = 600 s. Every 2 s = 500 g → per s = 250 g. Total = $250 \times 600 = 150000$ g = 150 kg.
Packets = $150 \div 1 = 150$ .
Answer: 150 packets.

14. [2 marks]
$72$ km/h = $72 \times \frac{1000}{3600}$ m/s = $20$ m/s.
Answer: 20 m/s.

15. [2 marks]
Time = $\frac{24}{12} = 2$ hours.
Answer: 2 h.

Section D: Inequalities and Mixed

16. [3 marks]
$-3q > 9$ → divide by $-3$ , reverse sign: $q < -3$ .
Number line: open circle at $-3$ , arrow left.
Marking: 1 mark solve, 2 marks correct illustration.

17. [2 marks]
$5$ units = 35 → 1 unit = 7. Oranges = $2 \times 7 = 14$ . Total = $35 + 14 = 49$ .
Answer: 49.

18. [2 marks]
Ali : Bob = $2 : 3$ . $2$ units = 40 → 1 unit = 20. Bob = $3 \times 20 = 60$ .
Answer: $\$ 60$.

19. [2 marks]
New = $120 \times 1.40 = 168$ .
Answer: 168.

20. [2 marks]
$-2x \leq 8$ → divide by $-2$ , reverse: $x \geq -4$ .
Solution set: $\{x : x \geq -4\}$ .
Answer: $x \geq -4$ .

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