S1 Mathematics Practice Paper (Set 2) | Algebra And Equations, Percentages, Rates, Volume, Statistics, Coordinates (with Answers)

S1 Mathematics Practice Paper (Set 2) | Algebra and Equations, Percentages, Rates, Volume, Statistics, Coordinates (with answers)

2026-11-15

Mathematics · S1

S1 Mathematics paper: 6 questions, 24 parts, 100 marks, 60 minutes, covering algebra, percentages, rates, volume, statistics and coordinates, with answers.

Paper details　S1 Mathematics Practice Paper (Set 2) | Algebra and Equations, Percentages, Rates, Volume, Statistics, Coordinates (with answers)

Algebra and Equations

Simplify the expressions or solve the equations below.

#	Question	Answer and marking notes
1	Simplify 3(2x − 5) + 4x.	Answer: 10x − 15. (6x − 15 + 4x = 10x − 15)
2	Solve the equation 5x − 7 = 23.	Answer: x = 6. (5x = 30, so x = 6)
3	Solve the equation 2(x + 3) = x + 11.	Answer: x = 5. (2x + 6 = x + 11, so x = 5)
4	Find the value of x² − 3x + 1 when x = −2.	Answer: 11. (4 + 6 + 1 = 11)

Percentages

The following parts are percentage calculations.

#	Question	Answer and marking notes
5	Find 35% of 240.	Answer: 84. (240 × 35% = 84)
6	A number becomes 96 after increasing by 20%. Find the number.	Answer: 80. (96 ÷ 1.2 = 80)
7	An item with a marked price of 250 dollars is sold at a 20% discount. Find the selling price.	Answer: 200 dollars. (250 × 80% = 200 dollars)
8	A quantity rises from 50 to 62. Find the percentage increase.	Answer: 24%. ((62 − 50) ÷ 50 × 100% = 24%)

Rates

The following parts are about speed, time and distance.

#	Question	Answer and marking notes
9	A car travels 180 km in 2.5 hours. Find its average speed.	Answer: 72 km/h. (180 ÷ 2.5 = 72)
10	At a speed of 60 km/h, how long does a journey of 150 km take?	Answer: 2.5 hours. (150 ÷ 60 = 2.5)
11	A person covers 90 km in the first 2 hours and 60 km in the next hour. Find the average speed for the whole journey.	Answer: 50 km/h. ((90 + 60) ÷ (2 + 1) = 50)
12	Convert 72 km/h into m/s.	Answer: 20 m/s. (72 ÷ 3.6 = 20)

Area and Volume

Use 22/7 for pi in the following parts.

#	Question	Answer and marking notes
13	A cylinder has radius 7 cm and height 10 cm. Find its volume.	Answer: 1540 cm³. (22/7 × 7 × 7 × 10 = 1540)
14	A triangle has base 12 cm and height 9 cm. Find its area.	Answer: 54 cm². (12 × 9 ÷ 2 = 54)
15	A cuboid measures 5 cm by 4 cm by 3 cm. Find its total surface area.	Answer: 94 cm². (2 × (5×4 + 5×3 + 4×3) = 2 × 47 = 94)
16	A circle has diameter 14 cm. Find its circumference.	Answer: 44 cm. (22/7 × 14 = 44)

Statistics

The following parts are about mean, median and mode.

#	Question	Answer and marking notes
17	Find the mean of 12, 15, 18, 20 and 25.	Answer: 18. ((12 + 15 + 18 + 20 + 25) ÷ 5 = 90 ÷ 5 = 18)
18	Find the median of 3, 5, 7, 9, 11, 13, 15 and 17.	Answer: 10. (there are 8 values, so the median is the mean of the two middle values 9 and 11, which gives 10)
19	Find the mode of 4, 6, 6, 7, 9 and 6.	Answer: 6. (the value 6 appears three times, more often than any other)
20	A bar chart shows the daily sales of a shop over five days: 8, 12, 10, 15 and 5 items. Find the total sales.	Answer: 50 items. (8 + 12 + 10 + 15 + 5 = 50)

Coordinates and Graphs

The following parts use a rectangular coordinate plane.

#	Question	Answer and marking notes
21	Which quadrant contains the point A(3, −4)?	Answer: the fourth quadrant. (the first coordinate is positive and the second is negative)
22	Find the distance between A(1, 2) and B(5, 2).	Answer: 4 units. (5 − 1 = 4, as the two points lie on the same horizontal line)
23	Find the reflection of the point (−3, 5) in the x-axis.	Answer: (−3, −5). (reflection in the x-axis keeps the first coordinate and reverses the sign of the second)
24	A triangle has vertices O(0, 0), P(6, 0) and Q(0, 4). Find its area.	Answer: 12 square units. (base 6 and height 4, so 6 × 4 ÷ 2 = 12)

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