Secondary 1 Mathematics Semestral Assessment 2 (End of Year) Paper 1

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TuitionGoWhere Exam Practice (AI) — SA2 Practice Paper

Mathematics Secondary 1 — Numbers, Ratio & Proportion (Version 1 of 5)

School: TuitionGoWhere Secondary School (AI)
Subject: Mathematics
Level: Secondary 1
Paper: SA2 Practice Paper (Topic: Numbers, Ratio & Proportion)
Version: 1 of 5
Duration: 60 minutes
Total Marks: 60
Name: ______________________
Class: _________
Date: ____________

Instructions:

1. Answer all questions in the spaces provided.
2. Show all working clearly. No calculator required unless stated.
3. Write your answers in the units given.
4. Section A: 10 short questions (2 marks each). Section B: 6 structured questions (3 marks each). Section C: 4 extended questions (5 marks each).

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Section A (20 marks)

Answer all questions. 2 marks each.

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

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2. Express $45$ cm as a percentage of $1.2$ m.

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3. Solve $-4x > 12$ and state the solution.

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4. A recipe uses flour and sugar in the ratio $5 : 2$. If $250$ g of flour is used, how much sugar is needed?

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5. A machine packs rice at $500$ g per second. How many $2$ kg bags can be filled in $10$ minutes?

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6. The price of a book increased from \8$to$$10$. Find the percentage increase.

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7. The ratio of boys to girls in a class is $3 : 4$. If there are $21$ boys, how many girls are there?

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8. Decrease $80$ by $15\%$.

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9. A car travels $240$ km in $3$ hours. Find its average speed in km/h.

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10. The number of red marbles is twice the number of blue marbles. If there are $18$ blue marbles, how many red marbles are there?

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Section B (18 marks)

Answer all questions. 3 marks each.

11. The number of coins in a bag is twice that of stamps. There is an increase of $75\%$ in the number of stamps. If the number of coins remains constant, find the percentage decrease in the number of coins relative to the new total number of items.

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12. Solve $-3q > 9$ and illustrate the solution on the number line below.

Image pending generation: diagram for Q12.

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13. Bags of baking powder are filled at a rate of $40$ g per second. How many bags weighing $1.2$ kg each can be filled in $2$ hours?

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14. In a survey of $50$ students, $20$ chose badminton, $15$ chose swimming, and the rest chose cycling. Calculate the percentage of students who chose cycling.

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15. 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.

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16. A shirt originally cost \40$. It is sold at a$30%$ discount. Find the sale price and the percentage of the original price paid.

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Section C (22 marks)

Answer all questions. 5 marks each.

17. A shop sold $200$ items in January and $260$ items in February.
(a) Find the percentage increase in sales. [2]
(b) If sales in March decreased by $10\%$ from February, find the number of items sold in March. [3]

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18. The ratio of money saved by Ali, Bob and Cai is $2 : 3 : 5$. If Cai saved \120$ more than Ali, find the total amount saved by all three.

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19. A water tank is filled at a rate of $3$ litres per minute. At the same time, water flows out at $0.5$ litres per minute.
(a) Find the net filling rate in litres per minute. [1]
(b) How long will it take to fill a $50$ litre tank from empty? [2]
(c) If the outflow is stopped after half the time in (b), find the total time to fill the tank. [2]

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20. The number of stamps is $x$. The number of coins is $3x$. Stamps increase by $50\%$, and coins decrease by $20\%$.
(a) Write expressions for the new numbers. [2]
(b) Find the overall percentage change in the total number of items. [3]

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End of Paper

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TuitionGoWhere Exam Practice (AI) — SA2 Practice Paper Answer Key

Mathematics Secondary 1 — Numbers, Ratio & Proportion (Version 1 of 5)

Total Marks: 60

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Section A (20 marks)

1. [2 marks]
$24 : 36 = \frac{24}{12} : \frac{36}{12} = 2 : 3$
Answer: $2 : 3$
Teaching note: Divide both terms by HCF 12. Simplest form means no common factor other than 1.

2. [2 marks]
$1.2$ m $= 120$ cm. $\frac{45}{120} \times 100\% = 37.5\%$
Answer: $37.5\%$
Teaching note: Convert to same unit before percentage. Common mistake: using 1.2 directly without converting.

3. [2 marks]
$-4x > 12 \Rightarrow x < -3$ (divide by -4, reverse sign)
Answer: $x < -3$
Teaching note: Dividing by negative reverses inequality.

4. [2 marks]
Flour : Sugar $= 5 : 2$. $250$ g flour $\rightarrow 250 \div 5 = 50$ g per unit. Sugar $= 2 \times 50 = 100$ g.
Answer: $100$ g
Teaching note: Use unitary method.

5. [2 marks]
$10$ min $= 600$ s. Total mass $= 500 \times 600 = 300\,000$ g $= 300$ kg. Bags $= 300 \div 2 = 150$.
Answer: $150$ bags
Teaching note: Convert time to seconds; bag mass to grams or total to kg consistently.

6. [2 marks]
Increase $= 10 - 8 = 2$. $\frac{2}{8} \times 100\% = 25\%$.
Answer: $25\%$
Teaching note: Percentage increase = change/original × 100.

7. [2 marks]
$3$ units $= 21 \Rightarrow 1$ unit $= 7$. Girls $= 4 \times 7 = 28$.
Answer: $28$
Teaching note: Ratio parts method.

8. [2 marks]
$15\%$ of $80 = 12$. $80 - 12 = 68$.
Answer: $68$
Teaching note: Decrease = original × (1 - %).

9. [2 marks]
Speed $= 240 \div 3 = 80$ km/h.
Answer: $80$ km/h
Teaching note: Average speed = distance/time.

10. [2 marks]
Red $= 2 \times 18 = 36$.
Answer: $36$
Teaching note: Direct ratio application.

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Section B (18 marks)

11. [3 marks]
Let stamps $= x$, coins $= 2x$. New stamps $= 1.75x$. Coins constant $= 2x$.
New total $= 1.75x + 2x = 3.75x$. Original total $= 3x$.
Percentage decrease in coins relative to new total: coins are $2x$ out of $3.75x$, so "decrease" interpreted as coins' share drop: original share $= 2x/3x = 66.7\%$, new share $= 2x/3.75x = 53.3\%$, drop in share $= 13.3$ pts. But if asked decrease in number of coins (constant) vs new total items, coins did not decrease in count. Mark scheme: state coins constant (1), new total (1), explain no decrease in coin count but share reduced (1).
Answer: Coins unchanged; percentage of total fell from $66\frac{2}{3}\%$ to $53\frac{1}{3}\%$.
Teaching note: Careful reading; ratio constraint removed.

12. [3 marks]
$-3q > 9 \Rightarrow q < -3$. Number line: open circle at $-3$, arrow left.
Answer: $q < -3$, diagram as placeholder.
Teaching note: Open circle for strict inequality.

13. [3 marks]
$2$ h $= 7200$ s. Mass $= 40 \times 7200 = 288\,000$ g $= 288$ kg. Bags $= 288 \div 1.2 = 240$.
Answer: $240$ bags
Teaching note: Unit consistency.

14. [3 marks]
Cycling $= 50 - 20 - 15 = 15$. Percentage $= \frac{15}{50} \times 100\% = 30\%$.
Answer: $30\%$
Teaching note: Find remainder first.

15. [3 marks]
Apples $= 3u$, oranges $= 5u$. After: $5u + 10 = 7u \Rightarrow 2u = 10 \Rightarrow u = 5$. Apples $= 15$.
Answer: $15$
Teaching note: Same apple count, solve for u.

16. [3 marks]
Discount $= 40 \times 0.30 = 12$. Sale price $= 28$. Percent paid $= 70\%$.
Answer: \28$,$70%$
Teaching note: Discount then subtract.

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Section C (22 marks)

17. [5 marks]
(a) [2] Increase $= 60$, $\frac{60}{200} \times 100 = 30\%$.
(b) [3] March $= 260 \times 0.9 = 234$.
Answer: (a) $30\%$ (b) $234$ items

18. [5 marks]
Ali : Bob : Cai $= 2 : 3 : 5$. Cai - Ali $= 3$ units $= 120 \Rightarrow 1$ unit $= 40$. Total $= 10$ units $= 400$.
Answer: \400$

19. [5 marks]
(a) [1] Net $= 3 - 0.5 = 2.5$ L/min.
(b) [2] Time $= 50 \div 2.5 = 20$ min.
(c) [2] First half (10 min) fills 25 L, remaining 25 L at 3 L/min $= 8\frac{1}{3}$ min, total $= 18\frac{1}{3}$ min.
Answer: (a) $2.5$ (b) $20$ min (c) $18\frac{1}{3}$ min

20. [5 marks]
(a) [2] Stamps new $= 1.5x$, coins new $= 2.4x$.
(b) [3] Total orig $= 4x$, new $= 3.9x$, change $= -0.1x$, $\frac{-0.1x}{4x} \times 100 = -2.5\%$.
Answer: (a) $1.5x, 2.4x$ (b) decrease $2.5\%$