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

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Questions

TuitionGoWhere Practice Paper - Mathematics Secondary 1

TuitionGoWhere Secondary School (AI)

Subject: Mathematics
Level: Secondary 1
Paper: SA2 (Version 5 of 5)
Duration: 1 hour 45 minutes
Total Marks: 75 marks

Name: _________________ Class: _______ Date: _________

Instructions

Answer all questions in the spaces provided.
Show all working clearly. Marks may be awarded for correct methods even if the final answer is wrong.
Calculators are allowed.
Give your answers to 3 significant figures where appropriate, unless otherwise stated.
For questions involving geometry, state your reasons clearly.

Section A [25 marks]

Answer all questions in this section.

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

2. Find the HCF and LCM of 36 and 48 using prime factorisation. [3 marks]

HCF = _____________

LCM = _____________

3. Solve the inequality $-4x > 12$ and illustrate your answer on the number line below. [3 marks]

Solution: x ___________

[Number line from -6 to 2]

4. A recipe for 8 people requires 240g of flour. How much flour is needed for 14 people? [2 marks]

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

6. Calculate $\sqrt{169} - \sqrt[3]{64}$ . [2 marks]

7. Round 0.07849 to 2 significant figures. [1 mark]

8. A bag contains red and blue marbles in the ratio 3:5. If there are 15 red marbles, how many blue marbles are there? [2 marks]

9. Convert 72 km/h to m/s. [2 marks]

10. Find 35% of $480. [2 marks]

11. Increase $250 by 12%. [2 marks]

12. What percentage of 80 is 24? [2 marks]

Section B [30 marks]

Answer all questions in this section.

13. The table shows the number of books sold by a bookstore over 4 months.

Month	January	February	March	April
Books sold	180	225	270	162

(a) Find the percentage increase in books sold from January to March. [2 marks]

(b) Find the percentage decrease in books sold from March to April. [2 marks]

14. A car travels 180 km in 2 hours 30 minutes.

(a) Calculate the average speed of the car in km/h. [2 marks]

(b) How far would the car travel in 45 minutes at this speed? [2 marks]

15. The ratio of boys to girls in a school is 4:5. There are 360 students in total.

(a) How many boys are there in the school? [2 marks]

(b) If 20 more boys join the school, find the new ratio of boys to girls. Give your answer in its simplest form. [3 marks]

16. A water tank can be filled at a rate of 15 litres per minute.

(a) How long will it take to fill a 450-litre tank? Give your answer in hours and minutes. [2 marks]

(b) If the tank is already 40% full, how much more water is needed? [2 marks]

17. In a sale, all prices are reduced by 25%. The sale price of a jacket is $84.

(a) Find the original price of the jacket. [3 marks]

(b) A customer has a further 10% discount voucher to use on the sale price. How much will the customer pay for the jacket? [2 marks]

18. The cost of hiring a plumber is $45 for the first hour plus$ 30 for each additional hour.

(a) Write a formula for the total cost $C in terms of the number of hours$ h (where $h \geq 1$ ). [2 marks]

C = ________________

(b) Calculate the cost of hiring the plumber for 3.5 hours. [2 marks]

(c) If a customer paid $165, for how many hours was the plumber hired? [2 marks]

Section C [20 marks]

Answer all questions in this section.

19. A factory produces widgets at different rates during the day. The table shows the production rate and time periods.

Time Period	Rate (widgets per hour)	Duration (hours)
Morning	120	4
Afternoon	150	3.5
Evening	90	2.5

(a) Calculate the total number of widgets produced during the day. [3 marks]

(b) Find the average production rate for the entire day. [2 marks]

(c) If the factory needs to produce 1500 widgets per day, by what percentage should they increase their average production rate? [3 marks]

20. A mobile phone plan charges a monthly fee of $25 plus$ 0.15 per minute for calls.

(a) Write an expression for the total monthly cost $T in terms of the number of minutes$ m used. [1 mark]

T = ________________

(b) Calculate the total cost if 180 minutes are used in a month. [2 marks]

(c) Sarah's monthly bill was $43. How many minutes did she use? [3 marks]

(d) Another plan offers unlimited calls for $55 per month. For how many minutes would both plans cost the same? [3 marks]

(e) Which plan would be cheaper if Sarah typically uses 250 minutes per month? Show your working. [3 marks]

END OF PAPER

Answers

TuitionGoWhere Practice Paper - Mathematics Secondary 1 SA2 (Version 5) - Answer Key

Total Marks: 75 marks

Section A [25 marks]

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

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

2. Find the HCF and LCM of 36 and 48 using prime factorisation. [3 marks]

Answer: HCF = 12 LCM = 144

Working: $36 = 2^2 \times 3^2$ $48 = 2^4 \times 3$ HCF = $2^2 \times 3 = 12$ (lowest powers) LCM = $2^4 \times 3^2 = 16 \times 9 = 144$ (highest powers)

Marking: 1 mark for prime factorisation, 1 mark for HCF, 1 mark for LCM

3. Solve the inequality $-4x > 12$ and illustrate your answer on the number line. [3 marks]

Answer: $x < -3$

Working: $-4x > 12$ $x < -3$ (dividing by -4 reverses the inequality)

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

Marking: 1 mark for correct inequality solution, 1 mark for reversing inequality sign, 1 mark for correct number line

4. A recipe for 8 people requires 240g of flour. How much flour is needed for 14 people? [2 marks]

Answer: 420g

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 correct answer

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

Answer: $\frac{3}{8}$

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

Marking: 1 mark for converting to fraction, 1 mark for simplifying

6. Calculate $\sqrt{169} - \sqrt[3]{64}$ . [2 marks]

Answer: 9

Working: $\sqrt{169} = 13$ $\sqrt[3]{64} = 4$ $13 - 4 = 9$

Marking: 1 mark for each correct root, 1 mark for final answer

7. Round 0.07849 to 2 significant figures. [1 mark]

Answer: 0.078

Marking: 1 mark for correct answer

8. A bag contains red and blue marbles in the ratio 3:5. If there are 15 red marbles, how many blue marbles are there? [2 marks]

Answer: 25 blue marbles

Working: If red:blue = 3:5 and red = 15 Then 3 parts = 15, so 1 part = 5 Blue marbles = 5 parts = $5 \times 5 = 25$

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

9. Convert 72 km/h to m/s. [2 marks]

Answer: 20 m/s

Working: $72 \text{ km/h} = 72 \times \frac{1000}{3600} = 72 \times \frac{5}{18} = 20$ m/s

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

10. Find 35% of $480. [2 marks]

Answer: $168

Working: $35\% \times 480 = 0.35 \times 480 = 168$

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

11. Increase $250 by 12%. [2 marks]

Answer: $280

Working: Increase = $12\% \times 250 = 0.12 \times 250 = 30$ New amount = $250 + 30 = 280$

Marking: 1 mark for calculating increase, 1 mark for final answer

12. What percentage of 80 is 24? [2 marks]

Answer: 30%

Working: $\frac{24}{80} \times 100\% = 0.3 \times 100\% = 30\%$

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

Section B [30 marks]

13(a) Find the percentage increase in books sold from January to March. [2 marks]

Answer: 50%

Working: January: 180, March: 270 Increase = $270 - 180 = 90$ Percentage increase = $\frac{90}{180} \times 100\% = 50\%$

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

13(b) Find the percentage decrease in books sold from March to April. [2 marks]

Answer: 40%

Working: March: 270, April: 162 Decrease = $270 - 162 = 108$ Percentage decrease = $\frac{108}{270} \times 100\% = 40\%$

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

14(a) Calculate the average speed of the car in km/h. [2 marks]

Answer: 72 km/h

Working: Time = 2 hours 30 minutes = 2.5 hours Speed = $\frac{180}{2.5} = 72$ km/h

Marking: 1 mark for converting time, 1 mark for correct speed

14(b) How far would the car travel in 45 minutes at this speed? [2 marks]

Answer: 54 km

Working: 45 minutes = 0.75 hours Distance = $72 \times 0.75 = 54$ km

Marking: 1 mark for time conversion, 1 mark for correct distance

15(a) How many boys are there in the school? [2 marks]

Answer: 160 boys

Working: Ratio boys:girls = 4:5, total parts = 9 Boys = $\frac{4}{9} \times 360 = 160$

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

15(b) If 20 more boys join the school, find the new ratio of boys to girls. [3 marks]

Answer: 9:10

Working: Original: 160 boys, 200 girls New: 180 boys, 200 girls Ratio = 180:200 = 9:10

Marking: 1 mark for finding original numbers, 1 mark for new numbers, 1 mark for simplified ratio

16(a) How long will it take to fill a 450-litre tank? [2 marks]

Answer: 30 minutes (0 hours 30 minutes)

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

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

16(b) If the tank is already 40% full, how much more water is needed? [2 marks]

Answer: 270 litres

Working: 40% of 450 = $0.4 \times 450 = 180$ litres already in tank Water needed = $450 - 180 = 270$ litres

Marking: 1 mark for calculating current amount, 1 mark for water needed

17(a) Find the original price of the jacket. [3 marks]

Answer: $112

Working: Sale price is 75% of original (100% - 25% = 75%) $84 = 0.75 \times \text{original price}$ Original price = $\frac{84}{0.75} = 112$

Marking: 1 mark for understanding 75%, 1 mark for equation, 1 mark for correct answer

17(b) How much will the customer pay for the jacket? [2 marks]

Answer: $75.60

Working: Further 10% discount on $84 Amount paid =$ 84 \times 0.9 = 75.60$

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

18(a) Write a formula for the total cost. [2 marks]

Answer: $C = 45 + 30(h - 1)$ or $C = 15 + 30h$

Marking: 2 marks for correct formula (accept equivalent forms)

18(b) Calculate the cost for 3.5 hours. [2 marks]

Answer: $120

Working: $C = 45 + 30(3.5 - 1) = 45 + 30(2.5) = 45 + 75 = 120$

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

18(c) If a customer paid $165, for how many hours was the plumber hired? [2 marks]

Answer: 5 hours

Working: $165 = 45 + 30(h - 1)$ $120 = 30(h - 1)$ $4 = h - 1$ $h = 5$

Marking: 1 mark for equation setup, 1 mark for correct answer

Section C [20 marks]

19(a) Calculate the total number of widgets produced. [3 marks]

Answer: 1305 widgets

Working: Morning: $120 \times 4 = 480$ Afternoon: $150 \times 3.5 = 525$ Evening: $90 \times 2.5 = 225$ Total: $480 + 525 + 225 = 1305$

Marking: 1 mark for each period calculation, 1 mark for total

19(b) Find the average production rate for the entire day. [2 marks]

Answer: 130.5 widgets per hour

Working: Total time = $4 + 3.5 + 2.5 = 10$ hours Average rate = $\frac{1305}{10} = 130.5$ widgets per hour

Marking: 1 mark for total time, 1 mark for average rate

19(c) By what percentage should they increase their average production rate? [3 marks]

Answer: 15.0%

Working: Required rate = $\frac{1500}{10} = 150$ widgets per hour Increase needed = $150 - 130.5 = 19.5$ Percentage increase = $\frac{19.5}{130.5} \times 100\% = 15.0\%$

Marking: 1 mark for required rate, 1 mark for increase needed, 1 mark for percentage

20(a) Write an expression for the total monthly cost. [1 mark]

Answer: $T = 25 + 0.15m$

Marking: 1 mark for correct expression

20(b) Calculate the total cost if 180 minutes are used. [2 marks]

Answer: $52

Working: $T = 25 + 0.15(180) = 25 + 27 = 52$

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

20(c) How many minutes did Sarah use? [3 marks]

Answer: 120 minutes

Working: $43 = 25 + 0.15m$ $18 = 0.15m$ $m = \frac{18}{0.15} = 120$

Marking: 1 mark for equation, 1 mark for rearranging, 1 mark for answer

20(d) For how many minutes would both plans cost the same? [3 marks]

Answer: 200 minutes

Working: $25 + 0.15m = 55$ $0.15m = 30$ $m = \frac{30}{0.15} = 200$

Marking: 1 mark for equation, 1 mark for solving, 1 mark for answer

20(e) Which plan would be cheaper for 250 minutes? [3 marks]

Answer: The unlimited plan ($55) is cheaper

Working: Plan 1: $T = 25 + 0.15(250) = 25 + 37.5 = 62.50$ Plan 2: $55 Since$ 55 < $62.50, the unlimited plan is cheaper.

Marking: 1 mark for calculating Plan 1 cost, 1 mark for comparison, 1 mark for conclusion

END OF MARKING SCHEME