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Secondary 1 Mathematics Numbers Ratio Proportion Quiz
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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 questions in the spaces provided.
- Show all working clearly. Marks are awarded for correct method as well as final answer.
- Do not use a calculator unless a question states otherwise.
- Write your answers in the simplest form where applicable.
- For questions involving ratios, give your answer in the form requested (e.g., in the ratio a : b, as a fraction, or as a percentage).
Section A: Ratio and Simplifying (Questions 1–5)
Each question carries 1 mark. Write your answer in the space provided.
1. Express the ratio 24 : 36 in its simplest form.
Answer: __________________________________
2. Simplify the ratio 1.5 km : 600 m.
Answer: __________________________________
3. Express the fraction as a ratio in the form a : b.
Answer: __________________________________
4. In a class, the ratio of boys to girls is 4 : 5. If there are 20 boys, how many girls are there?
Answer: __________________________________
5. Express 0.75 as a ratio in its simplest form (a : b where a and b are integers).
Answer: __________________________________
Section B: Dividing Quantities and Proportion (Questions 6–10)
Each question carries 2 marks. Show your working clearly.
6. Divide $180 between Alice and Ben in the ratio 2 : 3.
Alice receives: $_________________________________
Ben receives: $_________________________________
7. The ratio of the angles in a triangle is 1 : 2 : 3. Find the size of each angle.
Smallest angle: _____________________________°
Second angle: _______________________________°
Largest angle: ______________________________°
8. A recipe for 4 people requires 300 g of flour. How much flour is needed for 10 people? Assume the quantities are in direct proportion.
Answer: __________________________________ g
9. The ratio of red marbles to blue marbles in a bag is 5 : 3. There are 120 marbles in total. How many red marbles are there?
Answer: __________________________________
10. Three friends share a sum of money in the ratio 3 : 4 : 5. If the smallest share is $45, find the total sum of money.
Answer: $_________________________________
Section C: Percentage and Proportion Applications (Questions 11–15)
Each question carries 3 marks. Show all working.
11. In a school of 840 students, 45% are girls.
(a) How many girls are there?
Answer (a): _________________________________
(b) The rest are boys. Express the number of boys as a percentage of the total number of students.
Answer (b): _________________________________ %
12. A shop sells a dress for $80. During a sale, the price is reduced by 15%.
(a) Find the amount of the discount.
Answer (a): $_________________________________
(b) Find the sale price of the dress.
Answer (b): $_________________________________
13. A laptop costs $1 200 before GST. If GST is 9%, calculate the total price of the laptop including GST.
Answer: $_________________________________
14. The population of a town increased from 15 000 to 16 500 in one year. Express this increase as a percentage of the original population.
Answer: _________________________________ %
15. A bag contains red, blue, and green beads in the ratio 2 : 3 : 5. 30% of the red beads are removed. If there are originally 40 red beads, how many red beads remain?
Answer: __________________________________
Section D: Multi-Step Ratio and Proportion Problems (Questions 16–20)
Each question carries 4 marks. Show all working clearly.
16. The ratio of the number of apples to the number of oranges in a fruit stall is 7 : 4. After 20 apples are sold, the ratio becomes 5 : 4.
(a) How many apples were there at first?
Answer (a): _________________________________
(b) How many oranges are there?
Answer (b): _________________________________
17. A map has a scale of 1 : 25 000.
(a) Two towns are 6 cm apart on the map. Find the actual distance in kilometres.
Answer (a): _________________________________ km
(b) The actual distance between two schools is 3.75 km. Find the distance between them on the map, in centimetres.
Answer (b): _________________________________ cm
18. A sum of $3 600 is shared among three siblings, Xander, Yara, and Zane, in the ratio of their ages. Xander is 12 years old, Yara is 15 years old, and Zane is 18 years old.
(a) Write the ratio of their ages in simplest form.
Answer (a): _________________________________
(b) How much does Yara receive?
Answer (b): $_________________________________
(c) What fraction of the total sum does Zane receive? Give your answer in its simplest form.
Answer (c): _________________________________
19. A fruit seller bought 200 mangoes at $0.60 each. He sold 60% of them at $1.00 each and the rest at $0.40 each.
(a) How much did the fruit seller pay for all the mangoes?
Answer (a): $_________________________________
(b) Find his total selling price.
Answer (b): $_________________________________
(c) Find his overall profit or loss. State clearly whether it is a profit or a loss.
Answer (c): $_________________________________ (profit / loss)
20. The table below shows the number of books read by four students in a reading programme.
| Student | Number of Books |
|---|---|
| Aisha | 12 |
| Ben | 8 |
| Clara | 16 |
| Dan | 4 |
(a) Express the number of books read by Ben as a fraction of the total number of books read by all four students. Give your answer in its simplest form.
Answer (a): _________________________________
(b) Express the ratio of books read by Aisha to Clara to Dan in its simplest form.
Answer (b): _________________________________
(c) A prize is awarded in proportion to the number of books read. If the total prize money is $200, how much does Clara receive?
Answer (c): $_________________________________
End of Quiz
Answers
Secondary 1 Mathematics Quiz - Numbers Ratio Proportion
Answer Key
Section A: Ratio and Simplifying (1 mark each)
1. Express the ratio 24 : 36 in its simplest form.
Answer: 2 : 3
Working: HCF of 24 and 36 = 12. 24 ÷ 12 = 2, 36 ÷ 12 = 3. ∴ 24 : 36 = 2 : 3.
Marking notes: Award 1 mark for correct simplified ratio. Accept equivalent forms such as only if the question format allows, but ratio notation (2 : 3) is expected.
2. Simplify the ratio 1.5 km : 600 m.
Answer: 5 : 2
Working: Convert to the same unit: 1.5 km = 1 500 m. Ratio = 1 500 : 600. Divide both sides by 300: 1 500 ÷ 300 = 5, 600 ÷ 300 = 2. ∴ Ratio = 5 : 2.
Marking notes: Award 1 mark for correct answer. Common mistake: not converting to the same unit before simplifying (e.g., writing 1.5 : 600 = 1 : 400, which is incorrect).
3. Express the fraction as a ratio in the form a : b.
Answer: 3 : 8
Working: means 3 parts out of 8, so the ratio of the part to the whole is 3 : 8 (or the ratio of the part to the remainder is 3 : 5 — but in context of "as a ratio", 3 : 8 is the standard interpretation).
Marking notes: Award 1 mark for 3 : 8. Accept 3 : 5 only if the question explicitly asks for the ratio of the part to the remainder, which it does not here.
4. In a class, the ratio of boys to girls is 4 : 5. If there are 20 boys, how many girls are there?
Answer: 25
Working: Ratio boys : girls = 4 : 5. 4 parts = 20, so 1 part = 20 ÷ 4 = 5. Girls = 5 parts = 5 × 5 = 25.
Marking notes: Award 1 mark for correct answer. Common mistake: writing 20 × 5 = 100 without dividing by 4 first.
5. Express 0.75 as a ratio in its simplest form (a : b where a and b are integers).
Answer: 3 : 4
Working: 0.75 = . ∴ Ratio = 3 : 4.
Marking notes: Award 1 mark for 3 : 4. Common mistake: writing 75 : 100 without simplifying.
Section B: Dividing Quantities and Proportion (2 marks each)
6. Divide $180 between Alice and Ben in the ratio 2 : 3.
Answer: Alice receives $72, Ben receives $108.
Working: Total parts = 2 + 3 = 5. 1 part = $180 ÷ 5 = $36. Alice = 2 × $36 = $72. Ben = 3 × $36 = $108.
Marking notes: Award 2 marks for both correct answers. Award 1 mark for correct method with one arithmetic error, or for finding the value of 1 part correctly. Check that the two amounts add to $180.
7. The ratio of the angles in a triangle is 1 : 2 : 3. Find the size of each angle.
Answer: Smallest angle = 30°, Second angle = 60°, Largest angle = 90°.
Working: Total parts = 1 + 2 + 3 = 6. Sum of angles in a triangle = 180°. 1 part = 180° ÷ 6 = 30°. Smallest angle = 1 × 30° = 30°. Second angle = 2 × 30° = 60°. Largest angle = 3 × 30° = 90°.
Marking notes: Award 2 marks for all three correct angles. Award 1 mark for correct method (finding 1 part = 30°) even if subsequent multiplication is wrong. Common mistake: forgetting that angles in a triangle sum to 180°.
8. A recipe for 4 people requires 300 g of flour. How much flour is needed for 10 people?
Answer: 750 g
Working: Flour per person = 300 g ÷ 4 = 75 g. For 10 people: 75 g × 10 = 750 g.
(Alternative: Direct proportion — , so g.)
Marking notes: Award 2 marks for correct answer with working. Award 1 mark for correct method (e.g., finding amount per person) with arithmetic error. Common mistake: setting up inverse proportion incorrectly.
9. The ratio of red marbles to blue marbles in a bag is 5 : 3. There are 120 marbles in total. How many red marbles are there?
Answer: 75
Working: Total parts = 5 + 3 = 8. 1 part = 120 ÷ 8 = 15. Red marbles = 5 × 15 = 75.
Marking notes: Award 2 marks for correct answer with working. Award 1 mark for correct method with arithmetic error. Common mistake: calculating (finding blue instead of red).
10. Three friends share a sum of money in the ratio 3 : 4 : 5. If the smallest share is $45, find the total sum of money.
Answer: $180
Working: Smallest share = 3 parts = $45. 1 part = $45 ÷ 3 = $15. Total parts = 3 + 4 + 5 = 12. Total sum = 12 × $15 = $180.
Marking notes: Award 2 marks for correct answer with working. Award 1 mark for finding 1 part = $15 correctly. Common mistake: multiplying $45 by 12 directly without first finding 1 part.
Section C: Percentage and Proportion Applications (3 marks each)
11. In a school of 840 students, 45% are girls.
(a) How many girls are there?
Answer (a): 378
Working: Number of girls = 45% of 840 = .
(b) The rest are boys. Express the number of boys as a percentage of the total number of students.
Answer (b): 55%
Working: Percentage of boys = 100% − 45% = 55%. (Alternatively: Number of boys = 840 − 378 = 462. Percentage = .)
Marking notes: Award 1 mark for (a) correct. Award 1 mark for (b) correct. Award 1 mark for clear working in either part. Common mistake in (b): calculating again instead of finding the complement.
12. A shop sells a dress for $80. During a sale, the price is reduced by 15%.
(a) Find the amount of the discount.
Answer (a): $12
Working: Discount = 15% of $80 = \frac{15}{100} \times 80 = 0.15 \times 80 = \12$.
(b) Find the sale price of the dress.
Answer (b): $68
Working: Sale price = $80 − $12 = $68.
Marking notes: Award 1 mark for (a) and 1 mark for (b), plus 1 mark for clear working. If (a) is wrong but (b) correctly uses the student's (a) value, award follow-through mark for (b). Common mistake: writing sale price = 15% of $80 = $12 (confusing discount with sale price).
13. A laptop costs $1 200 before GST. If GST is 9%, calculate the total price of the laptop including GST.
Answer: $1 308
Working: GST amount = 9% of $1 200 = \frac{9}{100} \times 1\,200 = 0.09 \times 1\,200 = \108. Total price = \1 200 + $108 = $1 308.
(Alternative: Total price = 109% of $1 200 = 1.09 × 1 200 = $1 308.)
Marking notes: Award 3 marks for correct answer with complete working. Award 2 marks for correct method with minor arithmetic error. Award 1 mark for finding GST amount ($108) even if final addition is incorrect. Common mistake: giving GST amount ($108) as the final answer instead of total price.
14. The population of a town increased from 15 000 to 16 500 in one year. Express this increase as a percentage of the original population.
Answer: 10%
Working: Increase = 16 500 − 15 000 = 1 500. Percentage increase = .
Marking notes: Award 3 marks for correct answer with working. Award 2 marks for correct method with arithmetic error. Award 1 mark for finding the increase (1 500) correctly. Common mistake: using 16 500 as the denominator instead of 15 000.
15. A bag contains red, blue, and green beads in the ratio 2 : 3 : 5. 30% of the red beads are removed. If there are originally 40 red beads, how many red beads remain?
Answer: 28
Working: Original red beads = 40. 30% removed = . Red beads remaining = 40 − 12 = 28.
Marking notes: Award 3 marks for correct answer with working. Award 2 marks for finding 30% of 40 = 12 but not subtracting. Award 1 mark for attempting to find 30% of 40. Note: The ratio 2 : 3 : 5 is extra information not needed for this calculation — students should identify what is relevant. Common mistake: calculating 70% of 40 directly (= 28) is also acceptable and should be awarded full marks.
Section D: Multi-Step Ratio and Proportion Problems (4 marks each)
16. The ratio of the number of apples to the number of oranges in a fruit stall is 7 : 4. After 20 apples are sold, the ratio becomes 5 : 4.
(a) How many apples were there at first?
Answer (a): 70
(b) How many oranges are there?
Answer (b): 40
Working: Let the original number of apples = 7x and oranges = 4x. After selling 20 apples: apples = 7x − 20. New ratio: . Cross-multiply: . . . . .
(a) Original apples = 7 × 10 = 70. (b) Oranges = 4 × 10 = 40.
Marking notes: Award 4 marks for both correct with complete working. Award 3 marks for correct equation set up and solved with minor error. Award 2 marks for correct algebraic set up () even if not solved correctly. Award 1 mark for attempting to use a variable to represent the parts. Common mistake: subtracting 20 from the ratio directly (7 − 20 is not valid) instead of using algebra.
17. A map has a scale of 1 : 25 000.
(a) Two towns are 6 cm apart on the map. Find the actual distance in kilometres.
Answer (a): 1.5 km
Working: Actual distance = 6 cm × 25 000 = 150 000 cm. Convert to km: 150 000 cm ÷ 100 = 1 500 m; 1 500 m ÷ 1 000 = 1.5 km.
(b) The actual distance between two schools is 3.75 km. Find the distance between them on the map, in centimetres.
Answer (b): 15 cm
Working: 3.75 km = 3.75 × 1 000 = 3 750 m = 3 750 × 100 = 375 000 cm. Map distance = 375 000 ÷ 25 000 = 15 cm.
Marking notes: Award 2 marks for (a) and 2 marks for (b). In (a), award 1 mark for correct multiplication (150 000 cm) even if unit conversion is wrong. In (b), award 1 mark for correct unit conversion to cm even if division is wrong. Common mistakes: forgetting to convert units; dividing instead of multiplying (or vice versa) when converting between map and actual distance.
18. A sum of $3 600 is shared among three siblings, Xander, Yara, and Zane, in the ratio of their ages. Xander is 12 years old, Yara is 15 years old, and Zane is 18 years old.
(a) Write the ratio of their ages in simplest form.
Answer (a): 4 : 5 : 6
Working: Ratio = 12 : 15 : 18. HCF of 12, 15, 18 = 3. 12 ÷ 3 = 4, 15 ÷ 3 = 5, 18 ÷ 3 = 6. ∴ Ratio = 4 : 5 : 6.
(b) How much does Yara receive?
Answer (b): $1 200
Working: Total parts = 4 + 5 + 6 = 15. 1 part = $3 600 ÷ 15 = $240. Yara = 5 × $240 = $1 200.
(c) What fraction of the total sum does Zane receive? Give your answer in its simplest form.
Answer (c):
Working: Zane receives 6 parts out of 15. Fraction = .
Marking notes: Award 1 mark for (a), 2 marks for (b), and 1 mark for (c). In (b), award 1 mark for finding 1 part = $240 even if multiplication is wrong. In (c), accept if not simplified but note that simplest form is required. Common mistake in (a): not simplifying fully (e.g., leaving as 12 : 15 : 18).
19. A fruit seller bought 200 mangoes at $0.60 each. He sold 60% of them at $1.00 each and the rest at $0.40 each.
(a) How much did the fruit seller pay for all the mangoes?
Answer (a): $120
Working: Cost = 200 × $0.60 = $120.
(b) Find his total selling price.
Answer (b): $152
Working: 60% of 200 = 0.6 × 200 = 120 mangoes sold at $1.00 each = $120. Remaining = 200 − 120 = 80 mangoes sold at $0.40 each = $32. Total selling price = $120 + $32 = $152.
(c) Find his overall profit or loss. State clearly whether it is a profit or a loss.
Answer (c): $32 profit
Working: Profit = Selling price − Cost price = $152 − $120 = $32. Since selling price > cost price, it is a profit.
Marking notes: Award 1 mark for (a), 2 marks for (b), and 1 mark for (c). In (b), award 1 mark for finding either group of mangoes correctly. In (c), the word "profit" or "loss" must be stated for the mark. Common mistake: in (b), calculating 60% of 200 = 120 but then multiplying by $0.40 instead of $1.00.
20. The table below shows the number of books read by four students in a reading programme.
| Student | Number of Books |
|---|---|
| Aisha | 12 |
| Ben | 8 |
| Clara | 16 |
| Dan | 4 |
(a) Express the number of books read by Ben as a fraction of the total number of books read by all four students. Give your answer in its simplest form.
Answer (a):
Working: Total books = 12 + 8 + 16 + 4 = 40. Ben read 8 books. Fraction = .
(b) Express the ratio of books read by Aisha to Clara to Dan in its simplest form.
Answer (b): 3 : 4 : 1
Working: Aisha : Clara : Dan = 12 : 16 : 4. HCF of 12, 16, 4 = 4. 12 ÷ 4 = 3, 16 ÷ 4 = 4, 4 ÷ 4 = 1. ∴ Ratio = 3 : 4 : 1.
(c) A prize is awarded in proportion to the number of books read. If the total prize money is $200, how much does Clara receive?
(c) Answer: $80
Working: Total books = 40. Clara's share = \frac{16}{40} \times \200 = 0.4 \times $200 = $80$.
(Alternative using ratio: Total parts = 12 + 8 + 16 + 4 = 40. 1 part = $200 ÷ 40 = $5. Clara = 16 × $5 = $80.)
Marking notes: Award 1 mark for (a), 1 mark for (b), and 2 marks for (c). In (a), accept but note simplest form is required for full marks. In (b), common mistake: including Ben in the ratio (the question asks for Aisha, Clara, and Dan only). In (c), award 1 mark for correct fraction or proportion set up even if multiplication is wrong.
Summary of Marks
| Section | Questions | Marks per Question | Section Total |
|---|---|---|---|
| A | 1–5 | 1 | 5 |
| B | 6–10 | 2 | 10 |
| C | 11–15 | 3 | 15 |
| D | 16–20 | 4 | 20 |
| Total | 20 questions | 40 marks |
Common Mistakes Summary
- Not converting units before working with ratios (e.g., km vs m, cm vs km).
- Forgetting to simplify ratios or fractions to their simplest form.
- Confusing "part to part" with "part to whole" when converting between fractions and ratios.
- Using the wrong denominator in percentage change (must use the original value).
- Not stating "profit" or "loss" in money-related problems where the question asks for it.
- Subtracting from ratio parts directly instead of using algebra when a quantity changes.
- Including irrelevant information from the question (e.g., the ratio of all three colours in Q15 when only red beads are relevant).
- Not showing working — even if the answer is correct, marks may be lost without clear steps.
End of Answer Key