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

TuitionGoWhere Practice Paper - Mathematics Secondary 1

SA2 Version 2 - Answer Key

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Section A [30 marks]

Question 1 [2 marks]

Express 84 as a product of its prime factors.

Answer: $84 = 2^2 \times 3 \times 7$

Working: $84 = 4 \times 21 = 4 \times 3 \times 7 = 2^2 \times 3 \times 7$

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

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Question 2 [3 marks]

Solve the inequality $-4x > 12$ and illustrate your solution on the number line.

Solution: $x < -3$

Working: $-4x > 12$ $x < -3$ (dividing by -4 and reversing inequality sign)

Number line: Open circle at -3, arrow pointing left

Marking: 1 mark for correct inequality manipulation, 1 mark for correct solution, 1 mark for correct number line

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Question 3 [2 marks]

Find the HCF and LCM of 36 and 48 using prime factorisation.

HCF = 12 LCM = 144

Working: $36 = 2^2 \times 3^2$ $48 = 2^4 \times 3$ HCF = $2^2 \times 3 = 12$ LCM = $2^4 \times 3^2 = 144$

Marking: 1 mark for each correct answer

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Question 4 [3 marks]

A recipe for 8 people requires 240g of flour. How much flour is needed for 14 people?

Answer: 420 g

Working: Flour per person = $240 \div 8 = 30$ g For 14 people = $30 \times 14 = 420$ g

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

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Question 5 [2 marks]

Express $\frac{3}{8}$ as a percentage.

Answer: 37.5%

Working: $\frac{3}{8} = 0.375 = 37.5\%$

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

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Question 6 [3 marks]

The ratio of boys to girls in a class is 3:4. If there are 21 students in total, find the number of boys and girls.

Number of boys: 9
Number of girls: 12

Working: Total ratio parts = $3 + 4 = 7$ Boys = $\frac{3}{7} \times 21 = 9$ Girls = $\frac{4}{7} \times 21 = 12$

Marking: 1 mark for method, 1 mark for boys, 1 mark for girls

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Question 7 [2 marks]

A car travels 180 km in 2.5 hours. Calculate its average speed in km/h.

Answer: 72 km/h

Working: Average speed = $\frac{180}{2.5} = 72$ km/h

Marking: 1 mark for formula, 1 mark for correct answer

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Question 8 [3 marks]

The price of a shirt increased from $24 to$30. Calculate the percentage increase.

Answer: 25%

Working: Increase = $30 - 24 = 6$ Percentage increase = $\frac{6}{24} \times 100\% = 25\%$

Marking: 1 mark for finding increase, 1 mark for method, 1 mark for correct answer

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Question 9 [2 marks]

Convert 72 km/h to m/s.

Answer: 20 m/s

Working: $72 \text{ km/h} = 72 \times \frac{1000}{3600} = 20$ m/s

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

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Question 10 [3 marks]

In a survey of 120 students, 45 preferred Mathematics, 36 preferred Science, and the rest preferred English. What percentage of students preferred English?

Answer: 32.5%

Working: English = $120 - 45 - 36 = 39$ Percentage = $\frac{39}{120} \times 100\% = 32.5\%$

Marking: 1 mark for finding number preferring English, 1 mark for method, 1 mark for correct answer

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Question 11 [2 marks]

If $\frac{2x}{3} = 8$, find the value of $x$.

Answer: $x = 12$

Working: $\frac{2x}{3} = 8$ $2x = 24$ $x = 12$

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

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Question 12 [3 marks]

A water tank can be filled at a rate of 15 litres per minute. How long will it take to fill a 450-litre tank?

Answer: 30 minutes

Working: Time = $\frac{450}{15} = 30$ minutes

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

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Section B [30 marks]

Question 13 [4 marks]

The number of stamps in a collection is three times the number of coins. There is an increase of 60% in the number of stamps. If the total number of items becomes 208, find the original number of coins.

Answer: 40 coins

Working: Let original coins = $c$ Original stamps = $3c$ New stamps = $3c \times 1.6 = 4.8c$ New total = $c + 4.8c = 208$ $5.8c = 208$ $c = \frac{208}{5.8} = \frac{2080}{58} = \frac{1040}{29} = 40$

Marking: 1 mark for setting up variables, 1 mark for forming equation, 1 mark for solving, 1 mark for correct answer

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Question 14 [5 marks]

(a) The total number of bags sold. [2 marks]

Answer: 207 bags

Working: Morning: $25 \times 3 = 75$ bags Afternoon: $18 \times 4 = 72$ bags
Evening: $30 \times 2 = 60$ bags Total = $75 + 72 + 60 = 207$ bags

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

(b) The average rate of bags sold per hour for the entire day. [3 marks]

Answer: 23 bags per hour

Working: Total time = $3 + 4 + 2 = 9$ hours Average rate = $\frac{207}{9} = 23$ bags per hour

Marking: 1 mark for total time, 1 mark for method, 1 mark for correct answer

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Question 15 [6 marks]

(a) Find the fixed charge and the hourly rate. [3 marks]

Fixed charge: $20 **Hourly rate:**$25 per hour

Working: From 1 hour to 2 hours: increase = $70 - 45 = 25$ Hourly rate = $25 per hour Fixed charge =$45 - 25 = 20$

Marking: 1 mark for finding hourly rate, 1 mark for finding fixed charge, 1 mark for correct values

(b) Calculate the total cost for hiring the plumber for 6.5 hours. [2 marks]

Answer: $182.50

Working: Cost = $20 + 25 \times 6.5 = 20 + 162.50 = 182.50$

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

(c) If a customer paid $145, how long did the plumber work? [1 mark]

Answer: 5 hours 0 minutes

Working: $145 = 20 + 25t$ $125 = 25t$ $t = 5$ hours

Marking: 1 mark for correct answer

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Question 16 [4 marks]

(a) If two towns are 8 cm apart on the map, what is the actual distance between them in km? [2 marks]

Answer: 2 km

Working: Actual distance = $8 \times 25000 = 200000$ cm = 2 km

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

(b) A lake has an actual area of 6.25 km². What is its area on the map in cm²? [2 marks]

Answer: 10 cm²

Working: Area scale = $(25000)^2 = 625000000$ Map area = $\frac{6.25 \times 10^{10}}{625000000} = 10$ cm²

Marking: 1 mark for understanding area scale, 1 mark for correct answer

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Question 17 [5 marks]

(a) If there are 45 workers in Department A, find the total number of workers in the factory. [2 marks]

Answer: 135 workers

Working: Ratio A:B:C = 5:3:7 If A has 45 workers, then 1 part = $45 \div 5 = 9$ Total = $(5 + 3 + 7) \times 9 = 15 \times 9 = 135$ workers

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

(b) Due to expansion, Department B increases its workforce by 40%. Find the new ratio. [3 marks]

Answer: 5:4.2:7 or 25:21:35

Working: Original: A = 45, B = 27, C = 63 New B = $27 \times 1.4 = 37.8$ New ratio = 45:37.8:63 = 5:4.2:7 In simplest form = 25:21:35

Marking: 1 mark for calculating new B, 1 mark for forming ratio, 1 mark for simplest form

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Question 18 [6 marks]

(a) Calculate the amount of water in the tank after each phase. [3 marks]

After Phase 1: 60 litres
After Phase 2: 6 litres
After Phase 3: 42 litres

Working: Phase 1: $30 \times 2 = 60$ litres Phase 2: $60 - 18 \times 3 = 60 - 54 = 6$ litres
Phase 3: $6 + 24 \times 1.5 = 6 + 36 = 42$ litres

Marking: 1 mark for each phase

(b) What is the overall rate of change of water in the tank? [2 marks]

Answer: 6.46 litres per hour

Working: Net change = $42 - 0 = 42$ litres Total time = $2 + 3 + 1.5 = 6.5$ hours Rate = $\frac{42}{6.5} = 6.46$ litres per hour

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

(c) What percentage of the tank is filled at the end? [1 mark]

Answer: 28%

Working: Percentage = $\frac{42}{150} \times 100\% = 28\%$

Marking: 1 mark for correct answer