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

TuitionGoWhere Practice Paper - Mathematics Secondary 1

TuitionGoWhere Secondary School (AI)

Subject: Mathematics
Level: Secondary 1
Paper: SA2
Duration: 2 hours
Total Marks: 80

Name: _________________ Class: _______ Date: _____________

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Instructions to Candidates

1. This paper consists of TWO sections, A and B.
2. Answer ALL questions.
3. Write your answers in the spaces provided in this question paper.
4. Show all necessary working clearly.
5. Calculators are allowed.
6. Give your final answers to 3 significant figures where appropriate.
7. The use of an approved scientific calculator is expected, where appropriate.

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Section A [40 marks]

Answer all questions in this section.

1. (a) Find the value of $(-3)^2 + 2 \times (-5)$. [2 marks]

Answer: _______________

(b) Express $\frac{2}{3} - \frac{5}{8}$ as a fraction in its simplest form. [3 marks]

Answer: _______________

2. (a) Find the HCF of 72 and 108 by prime factorisation. [3 marks]

Prime factorisation of 72: _______________

Prime factorisation of 108: _______________

HCF = _______________

(b) Hence, write the ratio 72 : 108 in its simplest form. [1 mark]

Answer: _______________

3. Solve the inequality $3x - 7 \leq 2x + 5$ and represent your answer on the number line below. [4 marks]

Working:

Answer: _______________

Number line:

    |-------|-------|-------|-------|-------|-------|-------|-------|
   -2      0       2       4       6       8       10      12

4. A recipe for 8 people uses 600g of sugar and 450g of flour. (a) Find the ratio of sugar to flour in its simplest form. [2 marks]

Answer: _______________

(b) How much sugar is needed if 540g of flour is used? [2 marks]

Answer: _______________

5. The table below shows the number of visitors to a museum over 5 days.

Day	Monday	Tuesday	Wednesday	Thursday	Friday
Visitors	240	180	300	360	420

(a) Find the percentage increase in visitors from Tuesday to Wednesday. [2 marks]

Answer: _______________

(b) Express the number of visitors on Monday as a percentage of the total visitors for the 5 days. [3 marks]

Answer: _______________

6. A water tank is being filled at a constant rate. The graph below shows the volume of water in the tank over time.

[THIS IS FIGURE: A linear graph showing volume (litres) on y-axis from 0 to 500, and time (minutes) on x-axis from 0 to 20. The line passes through points (0, 100) and (20, 500)]

(a) Calculate the gradient of the line. [2 marks]

Answer: _______________

(b) Explain what the gradient represents in this context. [1 mark]

Answer: _______________

(c) How much water was in the tank initially? [1 mark]

Answer: _______________

7. Bags of rice are packed at a rate of 45 kg per minute. Each bag weighs 2.5 kg. (a) How many bags can be packed in 1 hour 20 minutes? [3 marks]

Answer: _______________

(b) If the packing rate increases by 20%, how long will it take to pack 1000 bags? Give your answer in hours and minutes. [4 marks]

Answer: _______________

8. The cost of hiring a car is $25 per day plus$0.40 per kilometre travelled. (a) Write down a formula for the total cost $C$ dollars for hiring the car for $d$ days and travelling $k$ kilometres. [2 marks]

Answer: _______________

(b) Find the total cost for hiring the car for 3 days and travelling 250 km. [2 marks]

Answer: _______________

(c) If the total cost is $195 for a 5-day hire, how many kilometres were travelled? [3 marks]

Answer: _______________

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Section B [40 marks]

Answer all questions in this section.

9. The diagram below shows a rectangular garden with a path around it.

[THIS IS FIGURE: A rectangle within a rectangle. Inner rectangle labeled "Garden" with dimensions (2x + 3) m by (x + 5) m. Outer rectangle shows path width of 2 m on all sides]

(a) Write down, in terms of $x$, expressions for: (i) the length of the outer rectangle [1 mark]

Answer: _______________

(ii) the width of the outer rectangle **[1 mark]**

Answer: _______________

(b) Find, in terms of $x$, an expression for the area of the path only. Give your answer in expanded form. [4 marks]

Answer: _______________

(c) If $x = 8$, calculate the actual area of the path. [2 marks]

Answer: _______________

10. A school conducted a survey about students' favourite subjects. The results are shown in the pie chart below.

[THIS IS FIGURE: A pie chart divided into 5 sectors labeled Mathematics (90°), Science (108°), English (72°), History (54°), and Others (36°)]

The total number of students surveyed was 450.

(a) How many students chose Mathematics as their favourite subject? [2 marks]

Answer: _______________

(b) What percentage of students chose Science? [2 marks]

Answer: _______________

(c) The school wants to increase the number of students who choose History by 50%. If the total number of students remains the same, how many more students need to choose History? [3 marks]

Answer: _______________

11. A shopkeeper buys items at $15 each and sells them with a markup of 40%.

(a) Find the selling price of each item. [2 marks]

Answer: _______________

(b) In one week, the shopkeeper sold 80 items. Calculate: (i) the total revenue [1 mark]

Answer: _______________

(ii) the total profit **[2 marks]**

Answer: _______________

(c) The following week, the shopkeeper reduced the selling price by 15% but sold 25% more items. Did the shopkeeper make more or less profit than the previous week? Show your calculations. [5 marks]

Working:

Conclusion: _______________

12. The table below shows the relationship between the temperature and the number of ice creams sold at a shop.

Temperature (°C)	18	22	26	30	34
Ice creams sold	45	65	85	105	125

(a) Plot the points on the grid below and draw the line of best fit. [3 marks]

[THIS IS FIGURE: A coordinate grid with Temperature (°C) on x-axis (0 to 40) and Ice creams sold on y-axis (0 to 140)]

(b) Use your graph to estimate: (i) the number of ice creams sold when the temperature is 28°C [1 mark]

Answer: _______________

(ii) the temperature when 75 ice creams are sold **[1 mark]**

Answer: _______________

(c) Explain whether it would be reliable to use this graph to predict ice cream sales when the temperature is 5°C. [2 marks]

Answer: _______________

END OF PAPER

TuitionGoWhere Practice Paper - Mathematics Secondary 1 (Answer Key)

Section A [40 marks]

1. (a) $(-3)^2 + 2 \times (-5) = 9 + (-10) = -1$ [2 marks]

(b) $\frac{2}{3} - \frac{5}{8} = \frac{16}{24} - \frac{15}{24} = \frac{1}{24}$ [3 marks] [1 mark for common denominator, 1 mark for subtraction, 1 mark for simplest form]

2. (a) Prime factorisation of 72: $2^3 \times 3^2$ [1 mark] Prime factorisation of 108: $2^2 \times 3^3$ [1 mark] HCF = $2^2 \times 3^2 = 36$ [1 mark]

(b) 72 : 108 = 2 : 3 [1 mark]

3. $3x - 7 \leq 2x + 5$ $3x - 2x \leq 5 + 7$ [1 mark] $x \leq 12$ [2 marks] Number line: Closed circle at 12, arrow pointing left [1 mark]

4. (a) Sugar : Flour = 600 : 450 = 4 : 3 [2 marks]

(b) If flour = 540g, sugar = $\frac{4}{3} \times 540 = 720$g [2 marks]

5. (a) Percentage increase = $\frac{300 - 180}{180} \times 100\% = 66.7\%$ [2 marks]

(b) Total visitors = 240 + 180 + 300 + 360 + 420 = 1500 [1 mark] Monday percentage = $\frac{240}{1500} \times 100\% = 16\%$ [2 marks]

6. (a) Gradient = $\frac{500 - 100}{20 - 0} = \frac{400}{20} = 20$ [2 marks]

(b) The gradient represents the rate of filling in litres per minute [1 mark]

(c) Initially, there were 100 litres in the tank [1 mark]

7. (a) Time = 1 hour 20 minutes = 80 minutes [1 mark] Total mass packed = 45 × 80 = 3600 kg Number of bags = 3600 ÷ 2.5 = 1440 bags [2 marks]

(b) New rate = 45 × 1.2 = 54 kg per minute [1 mark] Total mass for 1000 bags = 1000 × 2.5 = 2500 kg [1 mark] Time = 2500 ÷ 54 = 46.3 minutes = 46 minutes 18 seconds [2 marks]

8. (a) $C = 25d + 0.4k$ [2 marks]

(b) C = 25(3) + 0.4(250) = 75 + 100 = \175$ [2 marks]

(c) $195 = 25(5) + 0.4k$ [1 mark] $195 = 125 + 0.4k$ $70 = 0.4k$ $k = 175$ km [2 marks]

Section B [40 marks]

9. (a) (i) Length of outer rectangle = $(2x + 3) + 4 = 2x + 7$ m [1 mark] (ii) Width of outer rectangle = $(x + 5) + 4 = x + 9$ m [1 mark]

(b) Area of path = Area of outer rectangle - Area of garden [1 mark] = $(2x + 7)(x + 9) - (2x + 3)(x + 5)$ [1 mark] = $2x^2 + 18x + 7x + 63 - (2x^2 + 10x + 3x + 15)$ [1 mark] = $2x^2 + 25x + 63 - 2x^2 - 13x - 15 = 12x + 48$ [1 mark]

(c) When $x = 8$: Area = $12(8) + 48 = 144$ m² [2 marks]

10. (a) Mathematics students = $\frac{90°}{360°} \times 450 = 112.5 \approx 113$ students [2 marks]

(b) Science percentage = $\frac{108°}{360°} \times 100\% = 30\%$ [2 marks]

(c) Current History students = $\frac{54°}{360°} \times 450 = 67.5 \approx 68$ [1 mark] Target = $68 \times 1.5 = 102$ students [1 mark] Additional students needed = $102 - 68 = 34$ students [1 mark]

11. (a) Selling price = 15 \times 1.4 = \21$ [2 marks]

(b) (i) Total revenue = 21 \times 80 = \1680$**[1 mark]** (ii) Total profit =$(21 - 15) \times 80 = $480$ [2 marks]

(c) New selling price = 21 \times 0.85 = \17.85$**[1 mark]** New quantity =$80 \times 1.25 = 100$items **[1 mark]** New profit per item =$17.85 - 15 = $2.85$**[1 mark]** New total profit =$2.85 \times 100 = $285$**[1 mark]** The shopkeeper made less profit ($285 < $480) [1 mark]

12. (a) Points plotted correctly and line of best fit drawn [3 marks] [1 mark for correct plotting, 2 marks for appropriate line]

(b) (i) Approximately 95 ice creams [1 mark] (ii) Approximately 24°C [1 mark]

(c) It would not be reliable because 5°C is far outside the range of data collected (18°C to 34°C). The relationship may not be linear at very low temperatures, and other factors may become significant. [2 marks]

Total: 80 marks

Marking Scheme Notes:

• Award partial marks for correct method even if final answer is wrong
• Accept equivalent forms of answers (e.g., fractions, decimals, percentages)
• For graphical questions, accept reasonable estimates within ±2 units
• Deduct 1 mark for arithmetic errors where method is correct
• Award full marks for alternative correct methods not shown in this scheme