Secondary 1 Mathematics Numbers Ratio Proportion Quiz

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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.

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

1. Write the ratio $24 : 36$ in its simplest form.
   Answer: __________

2. Express $0.75$ as a percentage.
   Answer: __________ %

3. 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

4. Find $15\%$ of $240$.
   Answer: __________

5. The ratio of boys to girls in a class is $3 : 4$. What fraction of the class are boys?
   Answer: __________

6. Increase $80$ by $25\%$.
   Answer: __________

7. A distance of $3\text{ km}$ is covered in $15$ minutes. Find the speed in $\text{km/h}$.
   Answer: __________ $\text{km/h}$

8. $12$ workers can build a wall in $5$ days. How many days will $20$ workers take if they work at the same rate?
   Answer: __________ days

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

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

Image pending generation: diagram for Q9.

10. 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: __________

11. The price of a book is increased from \12$to$$15$. Find the percentage increase.
    Answer: __________ %

12. 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: __________

13. A machine fills packets at $25\text{ g/s}$. How many $2\text{ kg}$ packets can be filled in $4$ minutes?
    Answer: __________

14. 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

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

15. (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 = ________

16. 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): __________ %

17. 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 = ________

18. 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: __________ $\text{km/h}$

19. 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): __________ %

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

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

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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. $12 × 5 = 60$; $20 × d = 60$ → $d = 3$.

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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: $t = 30/5 = 6$.

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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]