KJSEA 2026 Mathematics Sample Paper with Answers: 10 Timed Grade 9 Questions and Full Marking Scheme

Searching for KJSEA sample papers with answers usually turns up one of two things: a PDF with no marking scheme, or a "leaked paper" that is always fake. This page is neither. It is an original timed practice paper for Grade 9, written by CBC Edu Kenya in the style of KNEC's structured questions, with every answer worked in full and every mark shown, so a parent can mark it properly at the kitchen table.

These are original practice questions, not a KNEC paper and not a leaked paper. They are pitched at the Grade 7 to 9 curriculum and deliberately different from the examples in our earlier post, 10 KJSEA Mathematics worked examples, so a learner who has already worked through that page gets fresh practice here.

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 pen for working and a pencil and ruler for any sketch. A non-programmable calculator is allowed in KJSEA Mathematics, except where a question says "without a calculator".
3. Show all working. In the structured section most of the marks are for method, not for the final number.
4. When the timer ends, stop, then mark using the worked answers. Give the method marks even if the final answer is wrong.

KJSEA 2026 Mathematics sample paper: the questions

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

Worked answers and marking scheme

M marks are for method, A marks for an accurate answer that follows correct method, and B marks for an independent correct statement. If a learner makes a slip early and then works correctly with the wrong number, give the later method marks: that is how KJSEA structured questions are marked, and it is why working matters.

Question 1: indices and standard form (Numbers, Grade 8)

(a) Multiplying powers of the same base: add the indices. Dividing: subtract them.
3⁴ × 3² = 3^{4 + 2} = 3⁶ (M1)
3⁶ ÷ 3³ = 3^{6 − 3} = 3³ = 27 (A1)
Check: 81 × 9 = 729, and 729 ÷ 27 = 27.

(b) Move the decimal point 4 places to the right to get a number between 1 and 10: 0.00058 = 5.8 × 10⁻⁴ (B1)
Common error: writing 58 × 10⁻⁵, which is equal in value but not in standard form, so it earns no mark.

Question 2: hire purchase (Measurement: money, Grade 9)

(a) Deposit = 25/100 × 36,000 = KSH 9,000 (B1)
Instalments = 12 × 2,650 = KSH 31,800 (M1)
Hire purchase price = 9,000 + 31,800 = KSH 40,800 (A1)

(b) Extra paid = 40,800 − 36,000 = KSH 4,800.
4,800 ÷ 36,000 × 100 = 13.33… = 13.3% (B1)
Common error: forgetting the deposit and giving KSH 31,800 as the hire purchase price.

Question 3: quadratic expressions (Algebra, Grades 8 and 9)

(a) Find two numbers whose product is −14 and whose sum is +5: +7 and −2. (M1)
x² + 5x − 14 = (x + 7)(x − 2) (A1)
Check by expanding: x² − 2x + 7x − 14 = x² + 5x − 14.

(b) Difference of two squares: a² − b² = (a − b)(a + b).
103² − 97² = (103 − 97)(103 + 97) = 6 × 200 (M1) = 1,200 (A1)
Check: 103² = 10,609 and 97² = 9,409; 10,609 − 9,409 = 1,200.

Question 4: linear inequalities (Algebra, Grades 7 to 9)

Split the compound inequality into two simple ones and solve each.
3x − 4 < 2x + 5 gives x < 9 (B1)
2x + 5 ≤ 4x + 1 gives 4 ≤ 2x, so x ≥ 2 (B1)
Combined: 2 ≤ x < 9. Integer values: 2, 3, 4, 5, 6, 7, 8 (B1)
Check the ends: x = 2 gives 2 < 9 and 9 ≤ 9, both true. x = 9 gives 23 < 23, false, so 9 is not included.

Question 5: matrices (Algebra, Grade 9)

(a) Each entry of AB is a row of A multiplied term by term by a column of B, then added.
Row 1 of A with column 1 of B: (3 × 2) + (1 × 0) = 6. Row 1 with column 2: (3 × −1) + (1 × 5) = 2.
Row 2 with column 1: (2 × 2) + (4 × 0) = 4. Row 2 with column 2: (2 × −1) + (4 × 5) = 18. (M1)
AB has first row 6, 2 and second row 4, 18. (A1)

(b) Row 1 of B with column 1 of A: (2 × 3) + (−1 × 2) = 4. Row 1 with column 2: (2 × 1) + (−1 × 4) = −2.
Row 2 with column 1: (0 × 3) + (5 × 2) = 10. Row 2 with column 2: (0 × 1) + (5 × 4) = 20.
BA has first row 4, −2 and second row 10, 20. (B1)
AB ≠ BA: matrix multiplication is not commutative, so the order matters. (B1)

Question 6: equation of a straight line (Algebra and Geometry, Grades 8 and 9)

(a) Gradient m = (9 − 3) ÷ (4 − 1) = 6 ÷ 3 = 2 (B1)

(b) Substitute P(1, 3) into y = 2x + c: 3 = 2(1) + c, so c = 1 (M1)
y = 2x + 1 (A1)
Check with Q(4, 9): 2(4) + 1 = 9.

(c) On the x-axis y = 0: 0 = 2x + 1, so x = −½. The point is (−0.5, 0) (B1)

Question 7: volume and capacity of a cone (Measurement, Grade 9)

(a) Volume of a cone = ⅓πr²h
= ⅓ × 22/7 × 7 × 7 × 12 (M1)
= ⅓ × 154 × 12 = 1,848 ÷ 3 = 616 cm³ (A1)

(b) 1 litre = 1,000 cm³, so 616 cm³ = 0.616 litres (B1)
Common error: leaving out the ⅓, which gives the volume of a cylinder, 1,848 cm³.

Question 8: angle of depression (Geometry: trigonometry, Grade 9)

The angle of depression from the top of the tower equals the angle of elevation of the tower top from the pump (alternate angles), so the angle at the pump is 32°. Let d be the horizontal distance.
tan 32° = opposite ÷ adjacent = 18 ÷ d (M1)
d = 18 ÷ 0.6249 (M1) = 28.80… = 28.8 m (A1)
Check: 28.8 × 0.6249 = 17.997, which rounds to 18.
Common error: writing d = 18 × 0.6249 = 11.2 m, which puts the 32° angle at the top of the tower.

Question 9: mode, median and mean (Data Handling, Grades 7 and 9)

(a) The mark with the highest frequency is 6 (6 learners). Mode = 6 (B1)

(b) With 20 learners, the median is the average of the 10th and 11th marks in order. Running totals: mark 4 covers learners 1 to 2, mark 5 covers 3 to 7, mark 6 covers 8 to 13. Both the 10th and 11th are 6, so median = 6 (B1)

(c) Sum of marks = (4 × 2) + (5 × 5) + (6 × 6) + (7 × 4) + (8 × 3) = 8 + 25 + 36 + 28 + 24 = 121 (M1)
Mean = 121 ÷ 20 = 6.05 (A1)
Common error: dividing by 5 (the number of different marks) instead of 20 (the number of learners).

Question 10: probability of combined events (Grade 9)

There are 5 balls, so P(red) = 3/5 and P(green) = 2/5 on every pick, because the first ball is replaced.

(a) P(red and red) = 3/5 × 3/5 = 9/25 (B1)

(b) Red then green, or green then red:
(3/5 × 2/5) + (2/5 × 3/5) = 6/25 + 6/25 (M1) = 12/25 (A1)
Check: P(both green) = 4/25, and 9/25 + 12/25 + 4/25 = 25/25 = 1.
Common error: giving only 6/25 by counting red then green but forgetting green then red.

Answer table (print this for marking)

What the score tells you

Look at where the marks went, not just the total. A learner who lost marks on Questions 5, 6 and 8 has a Grade 9 gap. A learner who lost marks on Question 2(b), 7(b) and 9(c) knows the method but is careless with units and division. Those are different problems with different fixes, and the second one can be fixed in a week. Our guide to method marks in KJSEA Mathematics 903 shows how to lay working out so the marker can award every mark.

Want full KJSEA papers with answers for every subject?

One short sample paper shows the standard. What a Grade 9 candidate needs in the last four weeks is full-length papers in every learning area, in the real KNEC time, with an answer booklet to mark them. That is what the KJSEA Complete Course gives you, for all 9 learning areas:

• Full notes for Grades 7, 8 and 9, every strand and sub-strand, with worked examples and the mistakes that cost marks.
• Predictive papers in the KNEC paper codes and timings, including two full Mathematics 903 papers.
• Separate answer booklets, so the papers can be sat honestly and marked properly.

It is KSH 400 for all nine learning areas 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 KJSEA Complete Course: full notes, predictive papers and separate answer booklets for all 9 learning areas, KSH 400.

Frequently asked questions

When is the KJSEA 2026 Mathematics paper?

Paper 903 Mathematics is on Wednesday 28 October 2026 from 8.30 a.m. to 10.30 a.m. The full week is on our KJSEA and KPSEA 2026 calendar, and what to revise the night before each paper is in the KJSEA timetable, paper by paper.

Is a calculator allowed in KJSEA Mathematics?

Yes, a non-programmable calculator is allowed. Questions that test a skill such as the laws of indices may still ask for an answer without a calculator, as Questions 1 and 3 do here.

Is there a KJSEA 2026 Mathematics PDF with answers?

You can print this page as your PDF: the paper, the worked answers and the answer table are all above. Be wary of anyone selling the "real" 2026 paper before the exam; our note on leaked paper scams explains why they are always fake.

Are these the questions that will come in KJSEA 2026?

No one can honestly say that. These are original questions that practise the sub-strands the curriculum emphasises. Use them to find gaps, not to guess the paper.