KJSEA Grade 9 Mathematics Trial Exam Questions with Answers

KJSEA Grade 9 Mathematics Trial Exam Questions with Answers

Instructions: Answer all questions in the spaces provided. Section A consists of 20 multiple-choice questions. Section B consists of 20 structured questions. Total marks: 100.

SECTION A: (20 MARKS)

Answer ALL questions in this section. Each question carries 1 mark.

1. A shopkeeper increased the price of sugar from Ksh 120 to Ksh 144. What was the percentage increase?
A. 20%
B. 24%
C. 25%
D. 15%

Answer: A

2. A grade 9 teacher wrote the expression 5⁻² on the board. What is the value of 5⁻²?
A. 25
B. -25
C. 1/25
D. -1/25

Answer: C

3. A trader bought a phone for Ksh 8000 and sold it at a loss of 15%. What was the selling price of the phone?
A. Ksh 6800
B. Ksh 6200
C. Ksh 6400
D. Ksh 5800

Answer: A

5. Three containers of capacity 15, 20 and 24 litres are used to fill other containers. What is the smallest container that they can fill?
A. 180 litres
B. 240 litres
C. 60 litres
D. 120 litres

Answer: D (LCM of 15, 20, and 24 = 120)

6. Express 0.00036 in standard form.
A. 3.6 × 10⁻⁴
B. 3.6 × 10⁻⁵
C. 3.6 × 10⁻⁶
D. 3.6 × 10⁻³

Answer: A

7. Five machines working 8 hours a day take 5 days to complete a task. How many days will four machines working 8 hours a day take?
A. 6
B. 10
C. 6 ¼
D. 8

Answer: C (5×5 = 25 machine-days; 25÷4 = 6.25 = 6¼ days)

8. Solve for x: 5 – 3x ≥ 11
A. x ≥ 2
B. x ≤ 2
C. x ≥ -2
D. x ≤ -2

Answer: D (5 – 3x ≥ 11 → -3x ≥ 6 → x ≤ -2)

9. A straight line has its equation as 3x + 4y – 2 = 0. What is the gradient of the line?
A. -3
B. -3/4
C. 2
D. -1.5

Answer: B (3x + 4y – 2 = 0 → 4y = -3x + 2 → y = -3/4 x + 1/2; gradient = -3/4)

10. A straight line passing through the origin also passes through point (2,2). Which of the following is an equation of the line?
A. x + y = 0
B. x – y = 0
C. x = -y
D. -x = y

Answer: B (Points (0,0) and (2,2) give gradient 1, equation y = x or x – y = 0)

11. A parcel of land has an area of 3.5 hectares. What is the area in square metres?
A. 35000
B. 3500
C. 350000
D. 30500

Answer: A (1 hectare = 10,000 m²; 3.5 × 10,000 = 35,000 m²)

13. A cylindrical water tank has a diameter of 2 m and height 3 m. What is its volume in m³? (Use π = 3.14)
A. 9.42
B. 12.56
C. 18.84
D. 3.14

Answer: A (Volume = πr²h = 3.14 × 1² × 3 = 9.42 m³)

14. A road sign is in the shape of an equilateral triangle of side 48 cm. Find the area of the triangle.
A. 997.68 cm²
B. 1995.36 cm²
C. 1152 cm²
D. 576 cm²

Answer: A (Area = (√3/4) × s² = (1.732/4) × 2304 = 0.433 × 2304 = 997.63 cm²)

15. A motorist covered a distance of 45 km in 50 minutes. What was his speed in km/h?
A. 90
B. 0.9
C. 37.5
D. 54

Answer: D (Speed = distance/time = 45 km ÷ (50/60) h = 45 × 60/50 = 54 km/h)

16. A sphere has a diameter of 21 cm. Determine the surface area of the sphere. (Use π = 22/7)
A. 4851 cm²
B. 38808 cm²
C. 5544 cm²
D. 1386 cm²

Answer: D (Surface area = 4πr² = 4 × 22/7 × (10.5)² = 4 × 22/7 × 110.25 = 4 × 22 × 15.75 = 4 × 346.5 = 1386 cm²)

17. A sales agent is paid a basic salary of sh. 5000. She is also paid a commission of 5% on all the goods sold. In one month, she sold goods worth sh. 50000. How much did she earn that month?
A. Sh. 2500
B. Sh. 7500
C. Sh. 5250
D. Sh. 250

Answer: B (Commission = 5% × 50000 = 2500; Total = 5000 + 2500 = 7500)

18. A line L₁ is perpendicular to L₂ of equation x = 2y + 3. Which of the following is the gradient of L₁?
A. -2
B. 2
C. -1/2
D. 1/2

Answer: A (x = 2y + 3 → 2y = x – 3 → y = ½x – 3/2; gradient L₂ = ½; perpendicular gradient = -2)

19. Town A is on a bearing of 120° from town B. Which of the following correctly represents the compass bearing of A from B?
A. S30°E
B. N30°W
C. N60°W
D. S60°E

Answer: D (120° from North = 60° from South towards East = S60°E)

20. When a die is rolled once, what is the probability of getting an even number?
A. 1/2
B. 1/3
C. 2/3
D. 1/6

Answer: A (Even numbers: 2,4,6 → 3 outcomes out of 6 = 3/6 = 1/2)

SECTION B: (80 MARKS)

Answer ALL questions in the spaces provided.

21. A farmer harvested 1.25 tonnes of maize. He packed the maize into 50 kg bags.

a) How many bags did he obtain? (2 marks)

Answer:

• 1.25 tonnes = 1.25 × 1000 = 1250 kg

• Number of bags = 1250 ÷ 50 = 25 bags

(Award 1 mark for correct conversion, 1 mark for correct division)

b) If he sold the bags at Ksh 3250 per bag, how much did he earn from the sale of the maize? (2 marks)

Answer:

• Total earnings = 25 × 3250 = Ksh 81,250

(Award 2 marks for correct multiplication)

22. A learner wrote the expression 9^(y-2) ÷ 3 = 81. Use the laws of indices to determine the value of y. (3 marks)

Answer:

• 9^(y-2) ÷ 3 = 81

• 3^(2(y-2)) ÷ 3¹ = 3⁴

• 3^(2y-4-1) = 3⁴

• 3^(2y-5) = 3⁴

• 2y – 5 = 4

• 2y = 9

• y = 4.5

(Award 1 mark for expressing in base 3, 1 mark for equating indices, 1 mark for solving)

23. In a farm, there are goats, sheep, donkeys and cows. The goats are 1/3 of the total while the sheep are 1/6. A quarter of the remainder are donkeys while the rest are cows.

a) What fraction of the animals are cows? (3 marks)

Answer:

• Goats = 1/3, Sheep = 1/6

• Total so far = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2

• Remainder = 1 – 1/2 = 1/2

• Donkeys = 1/4 of remainder = 1/4 × 1/2 = 1/8

• Cows = Remainder – Donkeys = 1/2 – 1/8 = 4/8 – 1/8 = 3/8

(Award 1 mark for finding total of goats and sheep, 1 mark for finding donkeys, 1 mark for cows)

b) If the cows are 36 animals, find the number of goats. (2 marks)

Answer:

• Cows = 3/8 of total = 36

• Total animals = 36 × 8/3 = 96 animals

• Goats = 1/3 of total = 1/3 × 96 = 32 goats

(Award 1 mark for finding total, 1 mark for finding goats)

24. The volume of a cube is 3454.78 cm³.

a) Write the volume correct to four significant figures. (1 mark)

Answer: 3455 cm³

(Award 1 mark for correct rounding)

b) Use mathematical tables to determine the length of the cube. (3 marks)

Answer:

• Volume of cube = s³

• s = ∛3454.78

• From cube root tables: ∛3454.78 ≈ 15.12 cm (or as obtained from tables)

(Award 1 mark for formula, 2 marks for correct cube root reading)

25. A company recorded a loss of Ksh 5,600,000.

a) Express this loss in standard form. (2 marks)

Answer: 5.6 × 10⁶

(Award 2 marks for correct standard form)

b) The loss was shared among four stakeholders A, B, C and D in the ratio 2:3:4:1 respectively. How much more than A and D did C receive? (4 marks)

Answer:

• Total parts = 2 + 3 + 4 + 1 = 10 parts

• Value of one part = 5,600,000 ÷ 10 = 560,000

• C receives = 4 × 560,000 = 2,240,000

• A receives = 2 × 560,000 = 1,120,000

• D receives = 1 × 560,000 = 560,000

• A + D = 1,120,000 + 560,000 = 1,680,000

• C – (A + D) = 2,240,000 – 1,680,000 = 560,000

(Award 1 mark for total parts, 1 mark for value of one part, 1 mark for individual amounts, 1 mark for difference)

26. Work out the value of 54 ÷ 9 + (-40 × 5) – (-9). (3 marks)

Answer:

• 54 ÷ 9 = 6

• (-40 × 5) = -200

• -(-9) = +9

• 6 + (-200) + 9 = 6 – 200 + 9 = -185

(Award 1 mark for each correct operation)

27. A tank has an inlet tap and a discharge tap. The inlet tap takes 30 minutes to fill the tank while the discharge tap takes 45 minutes to empty the tank. The tank was empty and the two taps were opened at the same time.

a) What fraction of the tank had water after 15 minutes? (2 marks)

Answer:

• Inlet rate per minute = 1/30

• Discharge rate per minute = 1/45

• Net rate = 1/30 – 1/45 = (3 – 2)/90 = 1/90

• After 15 minutes = 15 × 1/90 = 15/90 = 1/6 full

(Award 1 mark for net rate, 1 mark for fraction after 15 minutes)

b) How long will it take to fill half of the tank? (3 marks)

Answer:

• Let time = t minutes

• (1/90)t = 1/2

• t = 1/2 × 90 = 45 minutes

(Award 1 mark for equation, 2 marks for solving)

28. A teacher estimated the length of a football pitch to be 100 metres. When the length was measured, it was established to be 94 metres. Determine the percentage error. (3 marks)

Answer:

• Error = 100 – 94 = 6 m

• Percentage error = (error/actual value) × 100%

• = (6/94) × 100%

• = 0.06383 × 100% = 6.38%

(Award 1 mark for error, 1 mark for formula, 1 mark for correct percentage)

29. A straight line passes through points (4, -2) and (-2, 4).

a) Determine the gradient of the line. (2 marks)

Answer:

• Gradient = (y₂ – y₁)/(x₂ – x₁)

• = (4 – (-2))/(-2 – 4)

• = (4 + 2)/(-6)

• = 6/(-6) = -1

(Award 2 marks for correct gradient)

b) Work out the equation of the line in the form y = mx + c. (3 marks)

Answer:

• Using point (4, -2) and m = -1

• y – y₁ = m(x – x₁)

• y – (-2) = -1(x – 4)

• y + 2 = -x + 4

• y = -x + 4 – 2

• y = -x + 2

*(Award 1 mark for using point-gradient formula, 1 mark for correct substitution, 1 mark for final equation)*

30. A rectangular plot has a length (x + 5) m and width (x – 3) m. If the perimeter of the plot is 36 m, determine the area of the plot. (4 marks)

Answer:

• Perimeter = 2(length + width) = 2[(x + 5) + (x – 3)] = 2(2x + 2) = 4x + 4

• Given perimeter = 36 m

• 4x + 4 = 36

• 4x = 32

• x = 8

• Length = x + 5 = 13 m

• Width = x – 3 = 5 m

• Area = length × width = 13 × 5 = 65 m²

(Award 1 mark for perimeter expression, 1 mark for solving x, 1 mark for finding length and width, 1 mark for area)

31. Solve the compound inequality below and represent on a number line. -3 ≤ 2x – 1 < 5 (4 marks)

Answer:

• Left inequality: -3 ≤ 2x – 1

• -3 + 1 ≤ 2x

• -2 ≤ 2x

• -1 ≤ x

• Right inequality: 2x – 1 < 5

• 2x < 6

• x < 3

• Combined: -1 ≤ x < 3

(Award 1 mark for left inequality, 1 mark for right inequality, 1 mark for combined, 1 mark for number line representation)

33. During his birthday party, Kevin bought birthday caps in the shape of cones. If one cap had a radius of 7 cm and a slant height of 10 cm, calculate its surface area. (Use π = 22/7) (3 marks)

Answer:

• Surface area of cone (excluding base) = πrl

• = 22/7 × 7 × 10

• = 22 × 10 = 220 cm²

(Award 1 mark for formula, 2 marks for correct calculation)

35. A motorist travelled from town P to town Q at an average speed of 72 km/h. He took 20 minutes to drive from town P to town Q. He drove back from town Q to town P at an average speed of 24 km/h. Calculate the motorist’s average speed for the whole journey. (4 marks)

Answer:

• Distance P to Q = speed × time = 72 × (20/60) = 72 × 1/3 = 24 km

• Time from Q to P = distance/speed = 24/24 = 1 hour

• Total distance = 24 + 24 = 48 km

• Total time = 20/60 + 1 = 1/3 + 1 = 4/3 hours

• Average speed = total distance/total time = 48 ÷ (4/3) = 48 × 3/4 = 36 km/h

(Award 1 mark for distance, 1 mark for return time, 1 mark for total distance and time, 1 mark for average speed)

37. Use scale drawing to answer this question. Two posts P and Q are 80 km apart. Post R is on a bearing of 140° from P and 250° from Q. Using a scale of 1 cm to represent 10 km, find the distance from P to R. (4 marks)

Answer:

• Scale: 1 cm = 10 km, so 80 km = 8 cm

• Draw PQ = 8 cm

• At P, draw bearing 140° (40° from South towards East)

• At Q, draw bearing 250° (20° from West towards South)

• Let the lines intersect at R

• Measure PR on scale drawing

• PR ≈ 4 cm = 40 km (actual measurement may vary slightly)

(Award 1 mark for correct scale and PQ, 1 mark for correct bearings, 1 mark for correct intersection, 1 mark for measured distance)

38. A plane leaves Cairo (30°E, 30°N) for Beijing (120°E, 40°N). It takes off at 8.00 am. Calculate the time at Beijing when the plane lands if the flight took 14 hours. (4 marks)

Answer:

• Longitude difference = 120°E – 30°E = 90°

• 1° = 4 minutes, so time difference = 90 × 4 = 360 minutes = 6 hours

• Beijing is East of Cairo, so Beijing time is ahead

• Time in Beijing at takeoff = 8:00 am + 6 hours = 2:00 pm

• Flight duration = 14 hours

• Landing time in Beijing = 2:00 pm + 14 hours = 4:00 am next day

(Award 1 mark for longitude difference, 1 mark for time difference, 1 mark for Beijing time at takeoff, 1 mark for landing time)

39. Construct a pentagon of side 3 cm.

40. A class of 40 students recorded the following number of siblings:

a) Draw a bar graph.

b) Find the mean number of siblings. (1 mark)

Answer:

• Sum = (0×2) + (1×5) + (2×10) + (3×12) + (4×8) + (5×3)

• = 0 + 5 + 20 + 36 + 32 + 15 = 108

• Mean = 108 ÷ 40 = 2.7 siblings

(Award 1 mark for correct mean)

Master Your KJSEA Mathematics Exam with Authentic Trial Questions

Preparing for the Kenya Junior School Education Assessment (KJSEA) Grade 9 Mathematics can be challenging without the right practice materials. This comprehensive collection of mathematics KJSEA trial examination questions has been carefully designed to mirror the actual KJSEA Mathematics format, helping students build confidence and master exam techniques before the big day. The questions cover all key areas, including numbers, algebra, geometry, measurement, statistics, and probability, ensuring thorough preparation across the entire Mathematics syllabus.

According to the official KJSEA examination structure, the Grade 9 KJSEA Mathematics exam consists of two sections: Section A with 20 multiple-choice questions (20 marks) and Section B with 20 structured questions (80 marks). The total time allocated is 2 hours, and the paper carries 100 marks.

Why Use These KJSEA Grade 9 Mathematics Trial Questions?

1. Authentic KJSEA Exam Experience
These KJSEA trial questions follow the exact structure and style of the official KJSEA Mathematics examination as outlined by KNEC. Students get a realistic feel of what to expect on exam day with questions covering all strands of the Grade 9 Mathematics curriculum.

2. Comprehensive Coverage
With 40 questions covering all key areas: percentages, indices, profit and loss, square roots, LCM, standard form, rates and ratios, inequalities, gradients, equations, area, volume, speed, surface area, commission, bearings, probability, fractions, algebra, perimeter, compound inequalities, Pythagoras theorem, surface area of cones, volume of frustums, average speed, area of segments, scale drawing, longitude and time, and statistics. This KJSEA revision resource ensures thorough preparation across the entire Mathematics syllabus.

3. Marking Scheme Included
Understanding how marks are allocated is crucial for exam success. Each question comes with the correct answer, and section B questions include detailed marking guidance, allowing students, teachers, and parents to assess performance accurately and identify areas needing improvement.

4. Time Management Practice
Working through these 40 mathematics KJSEA trial questions under timed conditions helps students develop the speed and efficiency needed to complete the actual exam within the allocated time of 2 hours.

5. Ideal for Teachers and Tutors
This KJSEA revision resource serves as an excellent teaching aid for classroom revision, homework assignments, and mock examinations. Teachers can use the marking scheme to provide consistent feedback.

KJSEA Grade 9 Mathematics Trial Exam Questions with Answers Frequently Asked Questions (FAQ)

1. What is KJSEA?

KJSEA stands for Kenya Junior School Education Assessment. It is the national examination administered to Grade 9 students under the Competency-Based Curriculum (CBC) in Kenya, marking the end of Junior School education. The assessment determines students’ progression to Senior School pathways (STEM, Social Sciences, or Arts & Sports) based on their performance. KJSEA combines Grade 9 exam scores (60%), Grades 7 and 8 assessments (20%), and Grade 6 KPSEA results (20%).

2. How is KJSEA Mathematics exam structured?

According to the official KNEC structure, KJSEA Grade 9 Mathematics paper consists of :

• Section A: 20 multiple-choice questions (20 marks)

• Section B: 20 structured questions requiring working and explanations (80 marks)
  Total time: 2 hours | Total marks: 100

3. What topics are covered in KJSEA Mathematics Exam?

Key KJSEA maths revision topics include :

• Numbers: Percentages, indices, standard form, LCM, rates, and ratios

• Algebra: Solving equations and inequalities, gradient, linear equations

• Geometry: Area, volume, surface area, Pythagoras theorem, bearings

• Measurement: Perimeter, area of sectors, volume of cylinders and spheres

• Statistics: Mean, bar graphs, frequency tables

• Probability: Basic probability

• Commercial Arithmetic: Profit and loss, commission, percentage error

4. Are these trial questions similar to the actual KJSEA exam?

Yes, these KJSEA trial questions have been compiled based on the official Grade 9 KJSEA past papers and marking schemes. They follow the KJSEA examination format, question styles, and difficulty level as outlined by the Kenya National Examinations Council.

5. How should I use these mathematics KJSEA trial questions for effective revision?

• Attempt Section A under timed conditions (about 20-30 minutes) – each question carries 1 mark

• For Section B, practice showing all working clearly, as marks are awarded for steps

• Review incorrect answers using the marking scheme

• Focus on weak areas identified through self-assessment

• Practice mental maths for Section A to save time

• Attempt the full paper in one sitting to build exam stamina

• Use the questions for group discussions and peer learning

6. How can teachers use this KJSEA revision resource?

Teachers can use these KJSEA trial questions for :

• Classroom KJSEA revision exercises

• KJSEA Mock examinations and continuous assessment tests

• Homework assignments

• Identifying student strengths and weaknesses

• Group discussion activities

• Teaching exam technique and time management

• Developing lesson plans and teaching materials

7. Is the marking scheme accurate?

Yes, all answers have been verified against KJSEA Grade 9 Mathematics marking schemes from official trial examinations. Section B answers include key steps that examiners look for when awarding marks, following the principle of awarding marks for correct working, even if the final answer is wrong.

8. How can I track my progress?

Keep a record of your scores after each attempt. Aim for at least 70% (70/100) before sitting for the actual examination. Focus on understanding mathematical concepts rather than memorizing answers, especially for Section B questions that require the application of multiple concepts.

9. What are the career pathways for Mathematics?

Mathematics lays the foundation for careers in :

• STEM Fields: Engineering, computer science, architecture, surveying

• Finance and Business: Accounting, banking, economics, actuarial science

• Education: Mathematics teacher, lecturer, tutor

• Research and Data Science: Statistician, data analyst, researcher

• Physical Sciences: Physics, chemistry, astronomy

• Technology: Software development, IT, artificial intelligence

10. How important is showing mathematical working in Section B?

Showing working is extremely important in KJSEA Mathematics. Marks are awarded for correct steps even if the final answer is wrong. Students should always show all calculations, formulas used, and logical steps taken to arrive at the answer.

11. What common mistakes should I avoid in KJSEA maths paper?

• Misreading questions – read carefully before answering

• Not showing working in Section B

• Making careless arithmetic errors

• Forgetting units in final answers

• Rushing through Section A – each question carries equal marks

• Not attempting all questions in Section B

• Poor time management – spending too much time on one question

• Ignoring negative signs in algebra

KJSEA Grade 9 Mathematics Prediction Questions and Trial Paper

These are KJSEA trial examination questions designed for KJSEA revision purposes based on the official KJSEA examination structure.

Success in KJSEA Mathematics comes from consistent practice, understanding fundamental concepts, and applying problem-solving strategies. Use these trial questions to build confidence and identify areas for improvement. Remember that mathematics is about logical thinking and a systematic approach to problem-solving. Keep practicing, show all your working, and always check your answers for reasonableness.