S2 Maths Paper: Algebraic Expressions, Linear Inequalities, Ratio And Proportion, Percentage Change, Angles And Statistics

S2 Maths Paper: Algebraic Expressions, Linear Inequalities, Ratio and Proportion, Percentage Change, Angles and Statistics

2026-11-13

S2 Maths – algebra, inequalities and statistics

S2 Maths paper: 6 questions, 24 parts on expansion and factorising, inequalities, ratio and scale, percentage change, angles and statistics.

Download　Question paper PDF　|　Answer key PDF

Paper details　S2 Maths practice paper with 6 questions and 24 parts on expanding and factorising, linear inequalities, ratio and map scale, percentage change, angles with parallel lines, and mean, median, mode and range.

Section A: Algebraic Expressions and Factorisation (18 marks)

Let x = 3 and y = -2, then answer the questions below.

#	Question	Answer and marking notes
1	Expand (2x + 3)(x – 5).	Answer: 2×2 – 10x + 3x – 15 = 2×2 – 7x – 15. (Marking: four products 2, simplification 2)
2	Factorise x2 – 5x – 24.	Answer: the two numbers with product -24 and sum -5 are -8 and 3, so (x – 8)(x + 3). (Marking: numbers 2, factors 2)
3	Find the value of 3(2x – y) + 4y.	Answer: 3(6 + 2) – 8 = 24 – 8 = 16. (Marking: substitution 2, arithmetic 3)
4	Given y = (3x – 7) / 2, make x the subject and find x when y = 4.	Answer: 2y = 3x – 7, so x = (2y + 7) / 3; when y = 4, x = 15 / 3 = 5. (Marking: subject 3, value 2)

Section B: Linear Inequalities in One Unknown (16 marks)

Solve each inequality and then find the required integer.

#	Question	Answer and marking notes
5	Solve 5 – 3x greater than 2x – 10, and find the largest integer solution.	Answer: 15 greater than 5x, so x is less than 3; the largest integer is 2. (Marking: rearranging 2, answer 2)
6	Solve 2(x – 1) at most 7, and find the largest integer solution.	Answer: 2x – 2 at most 7, 2x at most 9, x at most 4.5; largest integer 4. (Marking: expansion 2, answer 2)
7	Solve -4x + 9 less than 1, and find the smallest integer solution.	Answer: -4x less than -8; dividing by -4 reverses the sign, so x is greater than 2 and the smallest integer is 3. (Marking: reversal 2, answer 2)
8	A student needs a mean of 70 over four tests. The first three scores are 62, 75 and 68. What is the minimum score in the fourth test?	Answer: the total needed is 70 x 4 = 280; the first three give 205, so the fourth test needs at least 75. (Marking: total 2, answer 2)

Section C: Ratio and Proportion (16 marks)

Answer the ratio questions; give every answer in simplest form.

#	Question	Answer and marking notes
9	Simplify 84 : 126.	Answer: divide both by 42 to get 2 : 3. (Marking: common factor 2, simplest form 2)
10	Three workers need 5 days to finish a job. How many days do 6 workers need?	Answer: the work is 3 x 5 = 15 worker-days, so 6 workers need 15 / 6 = 2.5 days. (Marking: worker-days 2, answer 2)
11	A map has a scale of 1 : 25 000. Two points are 6.4 cm apart on the map. Find the real distance in km.	Answer: 6.4 x 25 000 = 160000 cm = 1.6 km. (Marking: multiplication 2, unit conversion 2)
12	Share $3600 among three people in the ratio 3 : 4 : 5. Find each share.	Answer: 12 parts in total, each part is 3600 / 12 = 300, so the shares are 900, 1200 and 1500. (Marking: parts 2, three shares 2)

Section D: Percentage Increase and Decrease (16 marks)

Work out the percentage problems; give answers to 1 decimal place where needed.

#	Question	Answer and marking notes
13	An item costs $480 and its price rises by 15%. Find the new price.	Answer: 480 x 1.15 = 552.00 dollars. (Marking: multiplier 2, answer 2)
14	An item marked at $750 is sold at a 20 per cent discount. Find the selling price and the discount percentage.	Answer: selling price 750 x 0.8 = 600.00 dollars, discount 150 dollars, that is 20.0 per cent. (Marking: price 2, percentage 2)
15	An item sells for $612, which is 20 per cent above cost. Find the cost.	Answer: cost = 612 / 1.2 = 510.00 dollars. (Marking: equation 2, answer 2)
16	The population of a district grows from 32000 to 34560. Find the percentage increase.	Answer: the increase is 2560 people, so the percentage is 2560 / 32000 = 8.0 per cent. (Marking: increase 2, percentage 2)

Section E: Angles and Parallel Lines (16 marks)

Answer the geometry questions and state the reason used.

#	Question	Answer and marking notes
17	Two straight lines intersect and one angle is 68 degrees. Find the other three angles.	Answer: the vertically opposite angle is 68 degrees and the two adjacent angles are 112 degrees each, since angles on a straight line add to 180. (Marking: opposite 2, adjacent 2)
18	AB is parallel to CD. A pair of corresponding angles is (3x + 20) degrees and (5x – 10) degrees. Find x and the size of the angle.	Answer: corresponding angles are equal, so 3x + 20 = 5x – 10, giving x = 15 and the angle is 65 degrees. (Marking: equation 2, answer 2)
19	Two angles of a triangle are 52 degrees and 71 degrees. Find the third angle and the exterior angle at that vertex.	Answer: the third angle is 180 – 52 – 71 = 57 degrees and the exterior angle is 180 – 57 = 123 degrees. (Marking: angle sum 2, exterior 2)
20	Each interior angle of a regular polygon is 150 degrees. Find the number of sides.	Answer: the exterior angle is 180 – 150 = 30 degrees, so the number of sides is 360 / 30 = 12. (Marking: exterior 2, sides 2)

Section F: Statistics (18 marks)

The test scores of 12 students are 62, 75, 68, 81, 55, 75, 90, 68, 47, 75, 68 and 100.

#	Question	Answer and marking notes
21	Find the mean score.	Answer: the total is 864, so the mean is 864 / 12 = 72. (Marking: total 2, answer 2)
22	Find the median.	Answer: after sorting, the sixth and seventh values are 68 and 75, so the median is 71.5. (Marking: ordering 2, answer 2)
23	Find the mode and the range.	Answer: 68 and 75 each appear 3 times, so both are modes; the range is 100 – 47 = 53. (Marking: modes 3, range 2)
24	If one more student scoring 76 joins the group, find the new mean to 2 decimal places.	Answer: (864 + 76) / 13 = 72.31. (Marking: new total 3, answer 2)

Find a tutor — free Tutor Registration →

A TutorZone practice paper; original questions and passages, not publisher material.