KPSEA Mathematics: 8 Grade 6 Worked Examples Every Learner Should Master

Mathematics can lift a Grade 6 learner's KPSEA result more than almost any other subject, because it rewards method you can practise. A child who shows clear working earns marks even when the final answer slips. This guide walks through eight worked examples across the topics KPSEA returns to, taken from our KPSEA Grade 4-6 Complete Revision Course (see a free sample first). Work each one on paper, then check the steps.

Numbers

1. Place value

Write the place value of 7 in 4,703,158. Counting from the right, the 7 sits in the hundred thousands place, so its value is 700,000.

2. Fractions

Work out  3⁄4 + 1⁄8. Use a common denominator of 8:  6⁄8 + 1⁄8 = 7⁄8.

3. Percentages

Find 25% of 240.  25% means 25 out of 100, so (25 ÷ 100) × 240 = 60.

4. Money

A book costs KSH 120. Find the change from KSH 200.  200 − 120 = KSH 80. Always line up the shillings before subtracting.

Measurement

5. Perimeter and area

A rectangle is 8 cm long and 5 cm wide.  Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm.  Area = 8 × 5 = 40 cm². Note the units: length in cm, area in cm².

6. Length conversion

Convert 3.5 km to metres.  1 km = 1,000 m, so 3.5 × 1,000 = 3,500 m.

Everyday problems

7. Percentage profit

A trader buys goods for KSH 3,200 and sells for KSH 3,600.  Profit = 3,600 − 3,200 = 400.  Percentage profit = (400 ÷ 3,200) × 100 = 12.5%.

8. Average (mean)

Find the mean of 4, 7, 9 and 10.  Add them: 4 + 7 + 9 + 10 = 30.  Divide by how many: 30 ÷ 4 = 7.5.

How marks are earned in KPSEA Maths

• Show every step. Working earns method marks even if the final answer is wrong.
• Write units (cm, cm², KSH). A missing unit can cost a mark.
• Check the answer makes sense before moving on.
• Underline the final answer so the marker sees it clearly.

Practise, then mark against the scheme

These eight are a start; a strong result comes from practising every topic and marking honestly. Every subject in our KPSEA course now includes a detachable answer booklet, so you can print the questions for your child and keep the answers to mark later. Fit it into a routine with our holiday revision timetable, and see how the marks are awarded in our marking-scheme guide.

Revise the whole subject

The KPSEA Grade 4-6 Complete Revision Course covers Mathematics and all five core subjects, notes, topical questions with marking schemes, and mock papers, for KSH 300 (or KSH 150 per subject). See the free sample, and join our free Facebook community.

Frequently asked questions

My child gets answers right but loses marks. Why?

Usually because the working or units the scheme rewards are missing. Teach them to show every step and write units every time.

How often should we practise Maths?

A short daily session beats a long weekly one. Twenty minutes of practice, then mark it together, builds real confidence.