Secondary 1 Mathematics Semestral Assessment 2 (End of Year) Paper 5

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TuitionGoWhere Practice Paper - Mathematics Secondary 1

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TuitionGoWhere Secondary School (AI)

Subject: Mathematics
Level: Secondary 1 (G3)
Paper: SA2 Practice — Version 5 of 5
Duration: 60 minutes
Total Marks: 60

Name: ___________________________
Class: ___________________________
Date: ___________________________

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Instructions

1. Write your name, class, and date in the spaces provided above.
2. Answer all questions in the spaces provided.
3. Show your working clearly. Marks may be awarded for correct working even if the answer is wrong.
4. Do not use correction fluid or tape.
5. The use of calculators is not allowed unless stated otherwise.
6. The total marks for this paper is 60.

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Section A: Short Answer Questions [20 marks]

Answer all questions. Each question carries 2 marks. Write your answers in the spaces provided.

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1. Express 84 as a product of its prime factors. [2]

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2. Find the highest common factor (HCF) of 48 and 72. [2]

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3. Evaluate: $(-7) + 15 - (-4)$. [2]

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4. Round 3.6478 to 2 decimal places. [2]

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5. Express the ratio $24 : 36$ in its simplest form. [2]

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6. Arrange the following numbers in ascending order:
$\frac{3}{4}$, $0.7$, $65\%$, $\frac{2}{3}$ [2]

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7. Find the lowest common multiple (LCM) of 12 and 18. [2]

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8. Evaluate: $(-3)^2 - 4 \times (-2)$. [2]

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9. Express 0.375 as a fraction in its simplest form. [2]

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10. Simplify the ratio $2.5 \text{ kg} : 750 \text{ g}$. [2]

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Section B: Structured Questions [24 marks]

Answer all questions. Show your working clearly.

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11. A recipe for muffins uses flour and sugar in the ratio $5 : 2$.

(a) If 630 g of flour is used, how much sugar is needed? [2]

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(b) What is the total mass of flour and sugar used? [1]

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12. The price of a laptop is $1,200. During a sale, it is sold at a discount of 15%.

(a) Calculate the discount amount. [2]

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(b) Find the sale price of the laptop. [1]

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13. Three friends, Amir, Bala, and Clara, share a sum of money in the ratio $2 : 5 : 3$.

(a) If Bala receives $45, what is the total sum of money? [3]

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(b) How much does Amir receive? [1]

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14. Evaluate the following, giving your answer as a fraction in its simplest form:
$\frac{3}{4} + \frac{2}{5}$ [2]

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15. A car travels 240 km in 3 hours. At the same speed, how far will it travel in 7 hours? [3]

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16. The temperature at midnight was $-5^\circ\text{C}$. By noon, it had risen by $12^\circ\text{C}$. During the afternoon, it dropped by $8^\circ\text{C}$. What was the temperature at the end of the afternoon? [2]

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Section C: Problem-Solving Questions [16 marks]

Answer all questions. Show your working clearly.

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17. A fruit seller has apples and oranges in the ratio $7 : 4$. After selling 30 apples and buying 30 oranges, the ratio becomes $1 : 1$.

(a) How many apples did the fruit seller have at first? [3]

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(b) How many oranges did the fruit seller have at first? [1]

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18. In a school, the ratio of the number of boys to girls is $5 : 4$. There are 243 students in total.

(a) How many boys are there? [2]

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(b) 20% of the boys and 25% of the girls wear glasses. How many students in total wear glasses? [3]

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19. A sum of money is shared among Pravin, Quinn, and Rita in the ratio $3 : 4 : 8$.

(a) Express Rita's share as a fraction of the total sum. [2]

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(b) If Quinn receives $16 more than Pravin, find the total sum of money. [3]

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20. The table below shows the number of stamps collected by four students.

Student	Number of stamps
Wei Ming	48
Siti	36
Raj	60
Mei Ling	24

(a) Express the ratio of Wei Ming's stamps to Mei Ling's stamps in its simplest form. [1]

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(b) Siti gives $\frac{1}{3}$ of her stamps to Raj. Find the new ratio of Siti's stamps to Raj's stamps in its simplest form. [3]

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— End of Paper —

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SA2 Practice Paper — Answer Key (Version 5 of 5)

Subject: Mathematics | Level: Secondary 1 | Total Marks: 60

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Section A [20 marks]

1. [2]

Working: $84 = 2 \times 42 = 2 \times 2 \times 21 = 2 \times 2 \times 3 \times 7$

$\boxed{84 = 2^2 \times 3 \times 7}$

Marking: 1 mark for correct prime factorisation process, 1 mark for correct final answer.

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2. [2]

Working: $48 = 2^4 \times 3$
$72 = 2^3 \times 3^2$

HCF = $2^3 \times 3 = 8 \times 3 = 24$

$\boxed{24}$

Marking: 1 mark for correct prime factorisations, 1 mark for correct HCF.

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3. [2]

Working: $(-7) + 15 - (-4) = -7 + 15 + 4 = 8 + 4 = 12$

$\boxed{12}$

Marking: 1 mark for correct handling of signs, 1 mark for correct answer.

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4. [2]

Working: 3.6478 → look at the third decimal place: 7 ≥ 5, so round up.

$\boxed{3.65}$

Marking: 2 marks for correct answer. 0 marks for 3.64 or 3.648.

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5. [2]

Working: $24 : 36 = \frac{24}{12} : \frac{36}{12} = 2 : 3$

$\boxed{2 : 3}$

Marking: 1 mark for dividing by common factor, 1 mark for correct simplified ratio.

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6. [2]

Working: $\frac{3}{4} = 0.75$
$0.7 = 0.70$
$65\% = 0.65$
$\frac{2}{3} = 0.666...$

Ascending order: $0.65,\ 0.666...,\ 0.70,\ 0.75$

$\boxed{65\%,\ \frac{2}{3},\ 0.7,\ \frac{3}{4}}$

Marking: 1 mark for correct conversions, 1 mark for correct ordering.

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7. [2]

Working: $12 = 2^2 \times 3$
$18 = 2 \times 3^2$

LCM = $2^2 \times 3^2 = 4 \times 9 = 36$

$\boxed{36}$

Marking: 1 mark for correct prime factorisations, 1 mark for correct LCM.

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8. [2]

Working: $(-3)^2 - 4 \times (-2) = 9 - (-8) = 9 + 8 = 17$

$\boxed{17}$

Marking: 1 mark for correct evaluation of $(-3)^2$ and multiplication, 1 mark for correct final answer.

Common mistake: Writing $(-3)^2 = -9$. This is incorrect; $(-3)^2 = 9$.

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9. [2]

Working: $0.375 = \frac{375}{1000} = \frac{375 \div 125}{1000 \div 125} = \frac{3}{8}$

$\boxed{\frac{3}{8}}$

Marking: 1 mark for writing as fraction over 1000, 1 mark for correct simplification.

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10. [2]

Working: Convert to same units: $2.5 \text{ kg} = 2500 \text{ g}$

$2500 : 750 = \frac{2500}{250} : \frac{750}{250} = 10 : 3$

$\boxed{10 : 3}$

Marking: 1 mark for correct unit conversion, 1 mark for correct simplified ratio.

Common mistake: Not converting units before simplifying.

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Section B [24 marks]

11. [3 total]

(a) [2]

Working: Ratio of flour : sugar = $5 : 2$

If flour = 630 g, then $5 \text{ parts} = 630$

$1 \text{ part} = 630 \div 5 = 126$

Sugar = $2 \times 126 = 252$ g

$\boxed{252 \text{ g}}$

Marking: 1 mark for finding 1 part, 1 mark for correct answer with unit.

(b) [1]

Working: Total mass = $630 + 252 = 882$ g

$\boxed{882 \text{ g}}$

Marking: 1 mark for correct answer. Follow-through from (a) accepted.

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12. [3 total]

(a) [2]

Working: Discount = 15\% \times \1200 = \frac{15}{100} \times 1200 = 0.15 \times 1200 = $180$

$\boxed{\$180}$

Marking: 1 mark for correct method, 1 mark for correct answer.

(b) [1]

Working: Sale price = \1200 - $180 = $1020$

$\boxed{\$1020}$

Marking: 1 mark. Follow-through accepted.

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13. [4 total]

(a) [3]

Working: Ratio Amir : Bala : Clara = $2 : 5 : 3$

Bala's share = 5 parts = $45

1 \text{ part} = 45 \div 5 = \9$

Total = $2 + 5 + 3 = 10$ parts

Total sum = 10 \times 9 = \90$

$\boxed{\$90}$

Marking: 1 mark for finding 1 part, 1 mark for finding total number of parts, 1 mark for correct answer.

(b) [1]

Working: Amir's share = 2 \times 9 = \18$

$\boxed{\$18}$

Marking: 1 mark. Follow-through accepted.

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14. [2]

Working: $\frac{3}{4} + \frac{2}{5} = \frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1\frac{3}{20}$

$\boxed{\frac{23}{20} \text{ or } 1\frac{3}{20}}$

Marking: 1 mark for correct common denominator, 1 mark for correct final answer.

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15. [3]

Working: Speed = $240 \div 3 = 80$ km/h

Distance in 7 hours = $80 \times 7 = 560$ km

$\boxed{560 \text{ km}}$

Marking: 1 mark for finding speed, 1 mark for correct multiplication, 1 mark for answer with unit.

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16. [2]

Working: Midnight: $-5^\circ\text{C}$

After rise: $-5 + 12 = 7^\circ\text{C}$

After drop: $7 - 8 = -1^\circ\text{C}$

$\boxed{-1^\circ\text{C}}$

Marking: 1 mark for correct rise calculation, 1 mark for correct final temperature.

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Section C [16 marks]

17. [4 total]

(a) [3]

Working: Let the number of apples at first = $7x$
Let the number of oranges at first = $4x$

After changes: Apples: $7x - 30$
Oranges: $4x + 30$

New ratio is $1 : 1$, so: $7x - 30 = 4x + 30$ $7x - 4x = 30 + 30$ $3x = 60$ $x = 20$

Apples at first = $7 \times 20 = 140$

$\boxed{140}$

Marking: 1 mark for correct expressions, 1 mark for correct equation, 1 mark for correct answer.

(b) [1]

Working: Oranges at first = $4 \times 20 = 80$

$\boxed{80}$

Marking: 1 mark. Follow-through accepted.

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18. [5 total]

(a) [2]

Working: Ratio boys : girls = $5 : 4$

Total parts = $5 + 4 = 9$

$9 \text{ parts} = 243$

$1 \text{ part} = 243 \div 9 = 27$

Boys = $5 \times 27 = 135$

$\boxed{135}$

Marking: 1 mark for finding 1 part, 1 mark for correct answer.

(b) [3]

Working: Girls = $243 - 135 = 108$ (or $4 \times 27 = 108$)

Boys wearing glasses = $20\% \times 135 = 0.20 \times 135 = 27$

Girls wearing glasses = $25\% \times 108 = 0.25 \times 108 = 27$

Total wearing glasses = $27 + 27 = 54$

$\boxed{54}$

Marking: 1 mark for number of girls, 1 mark for each percentage calculation, 1 mark for total.

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19. [5 total]

(a) [2]

Working: Ratio Pravin : Quinn : Rita = $3 : 4 : 8$

Total parts = $3 + 4 + 8 = 15$

Rita's share = $\frac{8}{15}$ of total

$\boxed{\frac{8}{15}}$

Marking: 1 mark for total parts, 1 mark for correct fraction.

(b) [3]

Working: Quinn − Pravin = $4 - 3 = 1$ part

1 \text{ part} = \16$

Total = 15 \times 16 = \240$

$\boxed{\$240}$

Marking: 1 mark for finding difference in parts, 1 mark for value of 1 part, 1 mark for correct total.

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20. [4 total]

(a) [1]

Working: Wei Ming : Mei Ling = $48 : 24 = 2 : 1$

$\boxed{2 : 1}$

Marking: 1 mark for correct simplified ratio.

(b) [3]

Working: Siti's stamps = 36
Raj's stamps = 60

Siti gives $\frac{1}{3} \times 36 = 12$ stamps to Raj.

Siti now has: $36 - 12 = 24$
Raj now has: $60 + 12 = 72$

New ratio Siti : Raj = $24 : 72 = 1 : 3$

$\boxed{1 : 3}$

Marking: 1 mark for stamps given, 1 mark for new amounts, 1 mark for simplified ratio.

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— End of Answer Key —

Total: 60 marks