PLE 2025 Mathematics Past Paper & Answers

Write 5,326 in words.

Five thousand, three hundred twenty-six

Use =, < or > to complete: ⁻3 …… ⁺3

⁻3 < ⁺3

Negative numbers are less than positive numbers.

Shade ¼ of the diagram.

The circle has 8 equal parts. ¼ = ²⁄₈, so shade 2 parts.

Convert 1,560 grammes to kilogrammes.

1,000 g = 1 kg → 1,560 ÷ 1,000

= 1.56 kg

Given ξ = {a, b, c, d, e, f, g, h}, M = {a, b, e, f} and K = {b, d}, find n(M ∪ K)′.

M ∪ K = {a, b, d, e, f}

(M ∪ K)′ = {c, g, h}

n(M ∪ K)′ = 3

Find the next number: 128, 64, 32, 16, ……

Each number is divided by 2: 16 ÷ 2

= 8

Using a protractor, draw an angle of 85°.

Draw a straight line and mark the vertex. Place the protractor’s centre on the vertex with the base line on 0°, mark the point at 85° and join it to the vertex. Label the angle 85°.

Round off 37,594 to the nearest thousands.

The hundreds digit is 5 (≥ 5), so round up.

38,000

6,625 people attended; 5,879 were adults. Find the number of children.

6,625 − 5,879

= 746 children

Work out (25 × 26) + (24 × 25).

= 25 × (26 + 24) = 25 × 50

= 1,250

Given a = ½ and b = 12, find 8a + ab.

8 × ½ + ½ × 12 = 4 + 6

= 10

Atim sold every 4 oranges for sh 1,500. Find the money from 200 oranges.

Groups of 4: 200 ÷ 4 = 50

50 × sh 1,500

= sh 75,000

Find the median of 6, 13, 7, 11, 15, 9.

Arrange: 6, 7, 9, 11, 13, 15

Median = (9 + 11) ÷ 2

= 10

Peter is twice as old as Abdul. The sum of their ages is 72 years. Find Abdul’s age.

Let Abdul = x, Peter = 2x → x + 2x = 72 → 3x = 72

x = 24 years

sh 2,000,000 borrowed; interest of sh 720,000 after 2 years. Find the rate per year.

Interest per year = 720,000 ÷ 2 = 360,000

Rate = 360,000 ÷ 2,000,000 × 100

= 18% per year

Annet visited in March 2025 and will visit again after 16 months. When?

12 months → March 2026; 4 more months → July 2026

July 2026

Find the value of k in the diagram.

The interior angle at the left vertex = 40° (vertically opposite angles).

The exterior angle 110° = sum of the two interior opposite angles: k + 40° = 110°

k = 70°

A rectangular chart is 85 cm long and 60 cm wide. Find the length of tape along the edges.

Perimeter = 2 × (85 + 60) = 2 × 145

= 290 cm

Uniform intervals: 7:30 a.m., 9:50 a.m., 12:10 p.m., ……, 4:50 p.m. Find the 4th time.

Interval = 9:50 − 7:30 = 2 hours 20 minutes

12:10 p.m. + 2 h 20 min

= 2:30 p.m.

A die is rolled once. Probability the top face shows a factor of 3.

Factors of 3 on a die: {1, 3} → 2 outcomes out of 6

P = ²⁄₆ = ¹⁄₃

Find n and m in the base five addition 1m2_five + 224_five = 40n_five. (02 marks)

Units: 2 + 4 = 6 = 1 five remainder 1 → n = 1, carry 1.

Fives: m + 2 + 1 = 5 (write 0, carry 1) → m = 2.

Check: 1 + 2 + 1 = 4 ✓

m = 2, n = 1

Write the number expanded as (6 × 10⁴) + (3 × 10²) + (5 × 10¹) + (9 × 10⁰). (02 marks)

60,000 + 300 + 50 + 9

= 60,359

Maths set sh 5,000; a dozen books sh 24,000; a pen costs half the price of a book. Cost of 8 sets, 3 books and 5 pens. (06 marks)

1 book = 24,000 ÷ 12 = sh 2,000; 1 pen = sh 1,000

8 sets = sh 40,000 · 3 books = sh 6,000 · 5 pens = sh 5,000

Total = sh 51,000

Solve 8 − 3t ≥ 23. (03 marks)

−3t ≥ 23 − 8 → −3t ≥ 15

Divide by −3 and reverse the sign:

t ≤ ⁻5

Write the solution set for ⁻2 < x < 2. (01 mark)

{⁻1, 0, 1}

800 guests each used 400 ml of water from 20-litre tanks. Find the number of full tanks used. (04 marks)

Total = 800 × 400 ml = 320,000 ml = 320 litres

Tanks = 320 ÷ 20

= 16 tanks

Represent the information (music 35, debating only 15, music only 17, b neither, 28 do not like music) on a Venn diagram. (04 marks)

Both = 35 − 17 = 18. Not music: 15 + b = 28 → b = 13.

Calculate the total number of pupils in the class. (02 marks)

17 + 18 + 15 + 13

= 63 pupils

State the bearing of the church from the mosque. (01 mark)

The line makes 30° with the west at the church, so the mosque is on 240° from the church. Back bearing: 240° − 180°

= 060°

State the bearing of the church from the hospital. (01 mark)

Hospital from church = 140°. Back bearing: 140° + 180°

= 320°

Find, in metres, the shortest distance from the hospital to the mosque (1 cm : 50 m). (02 marks)

Measure the straight line from the hospital to the mosque on the printed drawing, then multiply by 50.

e.g. 7.1 cm × 50 m

≈ 355 m

Your answer depends on your measurement of the original paper (accept close values).

Ten goats bought for sh 800,000; six sold at sh 110,000 each. Price of each remaining goat for a 25% profit. (06 marks)

Required selling price = 125% × 800,000 = sh 1,000,000

Six goats: 6 × 110,000 = sh 660,000

Remaining 4 goats: 1,000,000 − 660,000 = sh 340,000

Each goat = sh 85,000

M→K at 75 km/h for 2 h, 1 h lunch at K, then 3 h to L. Average speed 55 km/h. Find distance K to L. (05 marks)

Total time = 2 + 1 + 3 = 6 hours

Total distance = 55 × 6 = 330 km

M to K = 75 × 2 = 150 km

K to L = 330 − 150 = 180 km

A(⁻2, ⁻1), B(0, 1), C(4, 1) are vertices of parallelogram ABCD. Plot, find D and join. (05 marks)

B → C moves 4 units right, so A → D also moves 4 units right: D = (⁻2 + 4, ⁻1)

D (2, ⁻1)

Construct triangle LMN: LM = 6.5 cm, ∠NLM = 45°, ∠LMN = 60°; then a perpendicular from N to LM at K. (05 marks)

1. Draw LM = 6.5 cm.
2. At L, construct 90° and bisect it to get 45°.
3. At M, construct 60° (equilateral arc method).
4. Extend both arms to meet at N.
5. (b) With centre N, cut LM at two points; from these points draw arcs below LM to meet; join N to the meeting point — it crosses LM at K (NK ⊥ LM).

Right-angled triangle RST (RS = 16 cm, ST = 12 cm, RT = 20 cm, RT a diameter) cut from a circle. Find the remaining area (π = 3.14). (06 marks)

Radius = 20 ÷ 2 = 10 cm → Circle area = 3.14 × 10 × 10 = 314 cm²

Triangle area = ½ × 16 × 12 = 96 cm²

Remaining area = 314 − 96 = 218 cm²

Janat got ⅜, Adam ⅖ and Moses ⅓ of the land. Who got the largest share? (05 marks)

LCD of 8, 5 and 3 = 120

⅜ = ⁴⁵⁄₁₂₀ · ⅖ = ⁴⁸⁄₁₂₀ · ⅓ = ⁴⁰⁄₁₂₀

Adam got the largest share