KPSEA 2026 Mathematics Sample Paper with Answers: 15 Timed Grade 6 Questions, Fully Worked

Most "KPSEA Mathematics questions and answers" you will find online are a list of letters with no working, which tells a parent whether a child was right but never why they were wrong. This page is different. It is an original timed practice paper for Grade 6, written by CBC Edu Kenya in the KPSEA multiple-choice format, and every answer is worked step by step, with the mistake behind each wrong option named, so you can mark it at home and know exactly what to reteach.

These are original practice questions, not a KNEC paper and not a leaked paper. If your child has already worked through our KPSEA Mathematics worked examples, these are fresh questions on the same sub-strands.

How to sit this paper

1. Print this page, or copy the questions onto paper. Put the phone away and set a timer for 40 minutes.
2. Use a pencil and a rubber, exactly as on the day. Draw a small grid numbered 1 to 15 with A, B, C and D, and shade one letter per question.
3. Do rough work in the margin. No calculator: KPSEA Mathematics is sat without one.
4. When the timer ends, stop and mark with the answer table. Then read the worked answer for every question that was wrong.

KPSEA 2026 Mathematics sample paper: the questions

Stop here until the 40 minutes are up. The worked answers start below.

Worked answers and marking guide

Each question carries 1 mark, and the mark goes to the correct letter only. The steps below are for learning, so a parent can see exactly where the working went wrong. Every wrong option was built from a real mistake Grade 6 learners make, so the letter your child chose tells you what to fix.

Question 1: total value (Numbers: whole numbers)

Step 1: read the places from the right: 5 ones, 1 ten, 9 hundreds, 2 thousands, 7 ten thousands, 4 hundred thousands, 3 millions.
Step 2: total value = digit × place value = 7 × 10,000 = 70,000. Answer C (1 mark)
Why not the others: A is the face value, not the total value. B and D put the 7 one place too far right or too far left.

Question 2: rounding off (Numbers)

Step 1: the thousands digit is 8 (648,351). Step 2: look at the digit to its right, the hundreds digit, which is 3. Step 3: 3 is less than 5, so the 8 stays and every digit after it becomes zero: 648,000. Answer A (1 mark)
Why not the others: B rounds up when it should not. D rounds to the nearest hundred instead of the nearest thousand. C rounds to the nearest ten thousand.

Question 3: LCM (Numbers: factors and multiples)

Step 1: list multiples of the largest number, 12: 12, 24, 36, 48. Step 2: find the first one that 6 and 8 also divide into exactly. 12 ÷ 8 is not a whole number; 24 ÷ 8 = 3 and 24 ÷ 6 = 4. LCM = 24. Answer B (1 mark)
Why not the others: A is the GCD (the greatest common divisor), which answers a different question. C is a common multiple but not the least. D is 6 × 8 × 12.

Question 4: order of operations (Numbers)

Step 1: division and multiplication first, from left to right: 48 ÷ 6 = 8 and 3 × 4 = 12. Step 2: then addition and subtraction from left to right: 8 + 12 − 5 = 15. Answer B (1 mark)
Why not the others: A comes from working strictly left to right: (8 + 3) × 4 − 5 = 39. D comes from doing 4 − 5 too early. C is a guess.

Question 5: adding fractions (Numbers: fractions)

Step 1: the LCM of 4 and 3 is 12. Step 2: 3/4 = 9/12 and 2/3 = 8/12. Step 3: 9/12 + 8/12 = 17/12. Step 4: 17/12 = 1 5/12. Answer C (1 mark)
Why not the others: A adds the tops and the bottoms (3 + 2 over 4 + 3), the most common fraction error in Grade 6. B forgets the whole number. D is a slip in changing 9/12 and 8/12.

Question 6: multiplying decimals (Numbers: decimals)

Step 1: ignore the points: 24 × 3 = 72. Step 2: count the decimal places in the question: one in 2.4 and one in 0.3, two in total. Step 3: give the answer two decimal places: 0.72. Answer B (1 mark)
Why not the others: A counts only one decimal place. C counts three. D adds instead of multiplying.

Question 7: discount (Measurement: money)

Step 1: discount = 15/100 × 800 = KSH 120. Step 2: price paid = 800 − 120 = KSH 680. Answer D (1 mark)
Why not the others: A is the discount itself, not the price paid. B takes off 15 shillings instead of 15 per cent. C adds the discount.

Question 8: sharing in a ratio (Numbers: ratio)

Step 1: total parts = 3 + 5 = 8. Step 2: one part = 1,200 ÷ 8 = KSH 150. Step 3: Baraka has 5 parts: 5 × 150 = KSH 750. Answer B (1 mark)
Check: Amina gets 3 × 150 = 450, and 450 + 750 = 1,200.
Why not the others: A is Amina's share. C divides by 5 instead of 8. D works out 3/5 of 1,200.

Question 9: shopping and change (Measurement: money)

Step 1: sugar = 3 × 180 = KSH 540. Step 2: flour = 2 × 145 = KSH 290. Step 3: total = 540 + 290 = KSH 830. Step 4: change = 1,000 − 830 = KSH 170. Answer C (1 mark)
Why not the others: B is the bill, not the change. A forgets to multiply (1,000 − 180 − 145). D is a borrowing slip in the subtraction.

Question 10: perimeter (Measurement: length)

The fence goes round the outside, so this is perimeter, not area.
Step 1: perimeter = 2 × (length + width). Step 2: 2 × (12 + 7.5) = 2 × 19.5 = 39 m. Answer C (1 mark)
Why not the others: A adds only two sides. B is the area (12 × 7.5 = 90), which is in square metres and cannot be a length of fence. D is a guess.

Question 11: volume and capacity (Measurement)

Step 1: volume = length × width × height = 2 × 1.5 × 1 = 3 m³. Step 2: 3 × 1,000 = 3,000 litres. Answer A (1 mark)
Why not the others: B and D use the wrong conversion. C multiplies 1.5 by 3,000 by mistake.

Question 12: time (Measurement: time)

Step 1: 10.45 a.m. + 2 hours = 12.45 p.m. Step 2: add 50 minutes: 15 minutes takes it to 1.00 p.m., and 35 more minutes gives 1.35 p.m. Answer B (1 mark)
Check in the 24-hour clock: 10 45 + 2 50 = 13 35, which is 1.35 p.m.
Why not the others: A adds 45 + 50 = 95 and writes it as minutes, but an hour has only 60 minutes. C forgets to carry the extra hour. D adds 20 minutes too many.

Question 13: angles in a triangle (Geometry)

Step 1: the angles of a triangle add up to 180°. Step 2: 48° + 67° = 115°. Step 3: 180° − 115° = 65°. Answer D (1 mark)
Why not the others: A is the sum of the two given angles. B uses 360°, which is for angles at a point. C is a subtraction slip.

Question 14: simple equations (Algebra)

Step 1: take 7 from both sides: 3y = 31 − 7 = 24. Step 2: divide both sides by 3: y = 24 ÷ 3 = 8. Answer A (1 mark)
Check: 3 × 8 + 7 = 24 + 7 = 31.
Why not the others: C stops at 3y = 24. D adds 7 instead of subtracting it. B divides 38 by 3.

Question 15: the mean (Data Handling)

Step 1: add the marks: 12 + 15 + 9 + 18 + 16 = 70. Step 2: divide by the number of learners, 5: 70 ÷ 5 = 14. Answer C (1 mark)
Why not the others: B is the total, not the mean. A is the median (put in order, 9, 12, 15, 16, 18, the middle mark is 15), which is a different average. D is the lowest mark.

Answer table (print this for marking)

What the score tells you

Look at which wrong letters were chosen, not only at the total. A child who chose A in Question 5 and B in Question 10 knows how to calculate but is not reading what the question asks. A child who chose A in Question 12 has a time problem that one evening with a clock face can fix. Our list of common KPSEA Mathematics errors covers more of these patterns, and how to use the 80 minutes covers pacing on the day.

Want full KPSEA papers with answers for every subject?

Fifteen questions show the standard. What a Grade 6 candidate needs in the last weeks is full-length papers for all five KPSEA papers, sat in the real KNEC time, with an answer booklet to mark them. That is what the KPSEA Complete Course gives you:

• Full notes for Grades 4, 5 and 6 in every KPSEA paper, with worked examples.
• Three predictive papers per subject, set in the KNEC time allowed, including three full 30-question Mathematics papers.
• Separate answer booklets with the reason for every answer, so the papers can be marked properly at home.

It is KSH 300 for all five papers and downloads instantly after M-Pesa payment. Like this page, every paper is original practice material, not a KNEC paper and not a leaked one, and we never promise a grade.

Get the KPSEA Complete Course: full notes, predictive papers and answer booklets for all five papers, KSH 300.

Frequently asked questions

When is the KPSEA 2026 Mathematics paper?

Mathematics is the first KPSEA paper, on Monday 26 October 2026 from 8.30 a.m. to 9.50 a.m., followed by English at 10.50 a.m. The full week is in our KPSEA 2026 timetable, paper by paper.

How many questions are in KPSEA Mathematics?

Our predictive papers use 30 multiple-choice questions in 80 minutes, in the published KPSEA style. That is about 2 minutes 40 seconds per question, the same pace as this 15-question sample in 40 minutes.

Is a calculator allowed in KPSEA Mathematics?

No. Grade 6 candidates work without a calculator, which is why every step in the answers above is done by hand.

How should my child shade the answers?

In pencil, firmly, one letter per question, on the personalised answer sheet. Our guide to shading the KPSEA answer sheet shows the mistakes that cost marks.

Are these the questions that will come in KPSEA 2026?

No one can honestly promise that. These are original questions on the sub-strands the Grade 4 to 6 curriculum emphasises. Use them to find gaps, not to guess the paper.