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Secondary 1 Mathematics Numbers Ratio Proportion Quiz

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

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Secondary 1 Mathematics AI Generated Generated by Tencent HY3 Free Updated 2026-08-17

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Questions

Secondary 1 Mathematics Quiz - Numbers Ratio Proportion

Name: ___________________________
Class: ______________
Date: ______________
Score: _______ / 40

Duration: 60 minutes
Total Marks: 40
Instructions: Answer all 20 questions. Show your working clearly. Section A and B are short-answer; Section C requires fuller working.

Section A (Questions 1–8, 1 mark each)

Write the ratio $24 : 36$ in its simplest form.
Answer: __________
Express $0.75$ as a percentage.
Answer: __________ %
A recipe uses flour and sugar in the ratio $5 : 2$ . If there are $350\text{ g}$ of flour, how many grams of sugar are needed?
Answer: __________ g
Find $15\%$ of $240$ .
Answer: __________
The ratio of boys to girls in a class is $3 : 4$ . What fraction of the class are boys?
Answer: __________
Increase $80$ by $25\%$ .
Answer: __________
A distance of $3\text{ km}$ is covered in $15$ minutes. Find the speed in $\text{km/h}$ .
Answer: __________ $\text{km/h}$
$12$ workers can build a wall in $5$ days. How many days will $20$ workers take if they work at the same rate?
Answer: __________ days

Section B (Questions 9–14, 2 marks each)

Solve the inequality $-3x > 9$ and illustrate the solution on the number line below.
Answer: $x$ ________

Diagram for Q9 (SEC1 Maths)

Generated diagram for Q9.

A bag contains red and blue marbles in the ratio $4 : 7$ . If there are $44$ red marbles, find the total number of marbles.
Answer: __________
The price of a book is increased from $\$ 12 $to$ $15$. Find the percentage increase.
Answer: __________ %
The number of stamps is twice the number of coins. The number of stamps is increased by $50\%$ . If the number of coins stays the same, find the new ratio of coins to stamps.
Answer: __________
A machine fills packets at $25\text{ g/s}$ . How many $2\text{ kg}$ packets can be filled in $4$ minutes?
Answer: __________
The time taken to paint a fence is inversely proportional to the number of painters. With $3$ painters it takes $10$ hours. How long with $5$ painters?
Answer: __________ hours

Section C (Questions 15–20, 3–4 marks each)

(a) Find the prime factorisation of $60$ and $90$ . [2]
(b) Hence find the HCF and LCM of $60$ and $90$ . [2]
Answer (a): __________
Answer (b): HCF = ________, LCM = ________
A shop increases the price of a shirt by $20\%$ in January, then decreases it by $10\%$ in February. The final price is $\$ 54 $. (a) Find the original price. [2] (b) Find the overall percentage change. [2] Answer (a):$ $______$
Answer (b): __________ %
The ratio of apples to oranges in a basket is $3 : 5$ . After adding $10$ oranges, the ratio becomes $3 : 7$ . Find the original number of apples and oranges. [4]
Answer: apples = ________, oranges = ________
A car travels $240\text{ km}$ at $80\text{ km/h}$ , then $180\text{ km}$ at $60\text{ km/h}$ . Find the average speed for the whole journey. [3]
Answer: __________ $\text{km/h}$
In a survey of $80$ students, $30$ chose badminton, $20$ chose swimming, and the rest chose cycling.
(a) Find the number who chose cycling. [1]
(b) Calculate the percentage who chose badminton. [2]
Answer (a): __________
Answer (b): __________ %
The number of coins is three times the number of notes. The number of coins is decreased by $40\%$ while notes stay the same. Find the new ratio of notes to coins. [4]
Answer: __________

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Answers

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

Total Marks: 40
Topic: Numbers, Ratio & Proportion (Syllabus N1–N4 aligned)

Section A (1 mark each)

Q1. $2 : 3$
Method: Divide both by HCF 12: $24 ÷ 12 = 2$ , $36 ÷ 12 = 3$ . Simplest form uses whole numbers with no common factor.

Q2. $75\%$
Method: $0.75 = \frac{75}{100} = 75\%$ . Multiply decimal by 100 to convert to percentage.

Q3. $140\text{ g}$
Method: Ratio $5 : 2$ → flour $5$ units $= 350\text{ g}$ → $1$ unit $= 70\text{ g}$ . Sugar $= 2 × 70 = 140\text{ g}$ .

Q4. $36$
Method: $15\% × 240 = \frac{15}{100} × 240 = 36$ .

Q5. $\frac{3}{7}$
Method: Boys : girls $= 3 : 4$ → total $7$ parts. Boys fraction $= \frac{3}{7}$ .

Q6. $100$
Method: $25\%$ of $80 = 20$ ; $80 + 20 = 100$ . Or $80 × 1.25 = 100$ .

Q7. $12\text{ km/h}$
Method: $15\text{ min} = \frac{1}{4}\text{ h}$ . Speed $= \frac{3}{1/4} = 12\text{ km/h}$ .

Q8. $3$ days
Method: Inverse proportion: workers × days constant. $12 × 5 = 60$ ; $20 × d = 60$ → $d = 3$ .

Section B (2 marks each)

Q9. $x < -3$
Marking: 1 mark solve, 1 mark number line.
Method: $-3x > 9$ → divide by $-3$ , reverse sign: $x < -3$ . On number line, open circle at $-3$ , arrow left.
Common mistake: Forgetting to reverse inequality when dividing by negative.

Q10. $121$
Method: Ratio $4 : 7$ → red $4$ units $= 44$ → $1$ unit $= 11$ . Total units $= 11$ ; total $= 11 × 11 = 121$ .

Q11. $25\%$
Method: Increase $= 15 - 12 = 3$ . $\frac{3}{12} × 100\% = 25\%$ .

Q12. $2 : 3$
Method: Let coins $= c$ , stamps $= 2c$ . New stamps $= 2c × 1.5 = 3c$ . Ratio coins : stamps $= c : 3c = 1 : 3$ → coins to stamps given as $1:3$ ; but question asks coins to stamps = $1:3$ (written $1:3$ ). Correction: coins stay $c$ , stamps $3c$ → ratio coins : stamps $= 1 : 3$ . (If interpreted as coins to stamps, answer $1:3$ ; if notes say "coins to stamps" then $1:3$ .)
Teaching note: The question asked new ratio of coins to stamps = $c : 3c = 1 : 3$ .

Q13. $3$ packets
Method: Rate $= 25\text{ g/s}$ ; $4\text{ min} = 240\text{ s}$ ; total mass $= 25 × 240 = 6000\text{ g} = 6\text{ kg}$ . Packets $= 6 ÷ 2 = 3$ .

Q14. $6$ hours
Method: $t ∝ 1/p$ → $t = k/p$ . $10 = k/3$ → $k = 30$ . With $5$ painters: $t = 30/5 = 6$ .

Section C

Q15. [4 marks total]
(a) $60 = 2^2 × 3 × 5$ ; $90 = 2 × 3^2 × 5$ [2]
(b) HCF $= 2 × 3 × 5 = 30$ ; LCM $= 2^2 × 3^2 × 5 = 180$ [2]
Teaching: HCF uses lowest powers of common primes; LCM uses highest powers of all primes.

Q16. [4 marks]
(a) Let original $= x$ . After Jan: $1.2x$ . After Feb: $1.2x × 0.9 = 1.08x = 54$ → $x = 50$ . [2]
(b) Change $= (54 - 50)/50 × 100\% = 8\%$ increase. [2]

Q17. [4 marks]
Let apples $= 3u$ , oranges $= 5u$ . After: $3u : (5u+10) = 3 : 7$ → $7×3u = 3×(5u+10)$ → $21u = 15u + 30$ → $6u = 30$ → $u = 5$ . Apples $= 15$ , oranges $= 25$ . [4]

Q18. [3 marks]
Time 1 $= 240/80 = 3\text{ h}$ ; Time 2 $= 180/60 = 3\text{ h}$ . Total dist $= 420\text{ km}$ , total time $= 6\text{ h}$ . Avg speed $= 420/6 = 70\text{ km/h}$ . [3]

Q19. [3 marks]
(a) Cycling $= 80 - 30 - 20 = 30$ . [1]
(b) $\frac{30}{80} × 100\% = 37.5\%$ . [2]

Q20. [4 marks]
Let notes $= n$ , coins $= 3n$ . New coins $= 3n × 0.6 = 1.8n$ . Ratio notes : coins $= n : 1.8n = 1 : 1.8 = 5 : 9$ . [4]