KJSEA Grade 9 Mathematics Practice Papers With Answers

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Free Mathematics question paper 1

KJSEA Grade 9 Mathematics Practice Paper 1. Suggested time: 120 minutes. Answer all questions; for calculations, show your working.

Section A: Multiple choice (20 marks)

Question 1 (1 mark)
Work out −8 + 15 − (−6) × 2.

1. 2
2. 26
3. −5
4. 19

Question 2 (1 mark)
What is the cube root of 3,375?

1. 25
2. 45
3. 15
4. 35

Question 3 (1 mark)
Simplify 2³ × 2⁵ ÷ 2⁴.

1. 2²
2. 2¹²
3. 2⁴
4. 2⁶

Question 4 (1 mark)
Write 0.000 482 in standard form.

1. 4.82 × 10⁴
2. 48.2 × 10⁻⁵
3. 4.82 × 10⁻³
4. 4.82 × 10⁻⁴

Question 5 (1 mark)
6 workers take 10 days to build a wall. Working at the same rate, how many days would 4 workers take?

1. 8
2. 12
3. 6⅔
4. 15

Question 6 (1 mark)
Tap A fills a tank in 6 hours and tap B fills it in 3 hours. How long do both taps take together?

1. 2 hours
2. 4.5 hours
3. 9 hours
4. 1.5 hours

Question 7 (1 mark)
Expand and simplify 3(2x − 4) − 2(x − 5).

1. 4x − 2
2. 4x − 22
3. 8x − 2
4. 4x + 2

Question 8 (1 mark)
Solve 5x − 7 = 2x + 11.

1. x = 6
2. x = 4
3. x = 18/7
4. x = 3

Question 9 (1 mark)
Solve the inequality 2x + 3 > 11.

1. x > 7
2. x < 4
3. x > 4
4. x ≥ 4

Question 10 (1 mark)
What is the gradient of the line joining (1, 2) and (4, 11)?

1. 9
2. 3
3. 1/3
4. −3

Question 11 (1 mark)
Which equation has a gradient of −2 and a y-intercept of 5?

1. y = 5x − 2
2. y = −2x + 5
3. y = 2x + 5
4. y = −5x + 2

Question 12 (1 mark)
If A = (2 3) is a 1 × 2 matrix and B is a 2 × 1 matrix with entries 4 and 1 (top to bottom), what is AB?

1. (8 3)
2. (6 4)
3. (14)
4. (11)

Question 13 (1 mark)
What is the area of a circle of radius 7 cm? (Take π = 22/7)

1. 44 cm²
2. 49 cm²
3. 308 cm²
4. 154 cm²

Question 14 (1 mark)
A cylindrical tank has a radius of 0.7 m and a height of 2 m. What is its capacity in litres? (Take π = 22/7)

1. 1,540 litres
2. 3,080 litres
3. 30,800 litres
4. 308 litres

Question 15 (1 mark)
A stone of mass 540 g has a volume of 200 cm³. What is its density?

1. 108 g/cm³
2. 0.37 g/cm³
3. 2.7 g/cm³
4. 27 g/cm³

Question 16 (1 mark)
A bus covers 180 km in 2 hours 30 minutes. What is its average speed?

1. 90 km/h
2. 75 km/h
3. 60 km/h
4. 72 km/h

Question 17 (1 mark)
A saleswoman earns 4% commission on sales. She sells goods worth KES 85,000. What is her commission?

1. KES 34,000
2. KES 340
3. KES 3,400
4. KES 4,250

Question 18 (1 mark)
A triangle with sides 3 cm, 4 cm and 5 cm is enlarged by scale factor 3. What is the perimeter of the image?

1. 12 cm
2. 15 cm
3. 36 cm
4. 108 cm

Question 19 (1 mark)
In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. What is sin θ?

1. 0.8
2. 0.75
3. 1.67
4. 0.6

Question 20 (1 mark)
A bag has 5 red, 3 blue and 2 green beads. One bead is picked at random. What is the probability that it is NOT red?

1. 3/10
2. 1/2
3. 1/5
4. 1/10

Section B: Structured questions (80 marks), type the final answer

Question 21 (8 marks)
Six machines produce 1,200 bottles in 4 hours. Working at the same rate, how many bottles will 9 machines produce in 6 hours?

Answer unit: bottles

Question 22 (8 marks)
Kamau borrowed KES 60,000 from a SACCO at 12% simple interest per year for 3 years. Find the total amount he repaid.

Answer unit: KES

Question 23 (8 marks)
A television costs KES 32,000 cash. On hire purchase, a buyer pays a deposit of KES 8,000 and 12 monthly instalments of KES 2,500. How much more does the buyer pay on hire purchase than in cash?

Answer unit: KES

Question 24 (8 marks)
The sum of two numbers is 47 and their difference is 13. Find the larger number.

Question 25 (8 marks)
A line passes through (2, 7) and has gradient 3. Find the value of its y-intercept c in y = 3x + c.

Question 26 (8 marks)
A rectangular water tank measures 2.5 m by 1.6 m by 1.2 m. How many litres of water does it hold when full?

Answer unit: litres

Question 27 (8 marks)
A ladder 13 m long leans against a vertical wall. Its foot is 5 m from the base of the wall on level ground. How high up the wall does the ladder reach?

Answer unit: m

Question 28 (8 marks)
A boda boda rider leaves Kisumu at 7.15 a.m. and rides 135 km at an average speed of 54 km/h. At what time does he arrive? Give your answer as minutes after 7.15 a.m.

Answer unit: minutes

Question 29 (8 marks)
On a map with scale 1 : 50,000, the distance between two schools is 7.4 cm. What is the actual distance in kilometres?

Answer unit: km

Question 30 (8 marks)
The marks of 8 learners in a test were 56, 72, 64, 48, 80, 68, 60 and 64. Find the mean mark.

Answer unit: marks

Free Mathematics question paper 2

KJSEA Grade 9 Mathematics Practice Paper 2. Suggested time: 120 minutes. Answer all questions; for calculations, show your working.

Section A: Multiple choice (20 marks)

Question 1 (1 mark)
Evaluate 7 − (−3) × 4 + (−20) ÷ 5.

1. 15
2. 36
3. −9
4. 21

Question 2 (1 mark)
What is 2.1³?

1. 92.61
2. 4.41
3. 6.3
4. 9.261

Question 3 (1 mark)
Find ∛0.008.

1. 0.2
2. 0.02
3. 0.4
4. 0.002

Question 4 (1 mark)
Simplify (3²)³ ÷ 3⁴.

1. 3
2. 3⁵
3. 3¹⁰
4. 3²

Question 5 (1 mark)
Write 3.6 × 10⁵ as an ordinary number.

1. 0.000036
2. 36,000
3. 3,600,000
4. 360,000

Question 6 (1 mark)
4 pumps fill a tank in 9 hours. How long would 6 pumps take?

1. 6 hours
2. 13.5 hours
3. 4 hours
4. 12 hours

Question 7 (1 mark)
Kerubo can dig a garden in 6 days and Moraa in 12 days. Working together, how many days do they take?

1. 3
2. 9
3. 4
4. 18

Question 8 (1 mark)
Factorise completely 12xy − 18y.

1. 6y(2x − 3)
2. 6(2xy − 3y)
3. 3y(4x − 6)
4. y(12x − 18)

Question 9 (1 mark)
Solve (2x + 1)/3 = 5.

1. x = 7
2. x = 8
3. x = 2
4. x = 14

Question 10 (1 mark)
Which integers satisfy −1 < x ≤ 2?

1. 0, 1, 2
2. −1, 0, 1, 2
3. 0, 1
4. −1, 0, 1

Question 11 (1 mark)
Find the y-intercept of the line 3y = 6x − 9.

1. 2
2. −9
3. −3
4. 3

Question 12 (1 mark)
Which line is parallel to y = 4x + 1?

1. y = 4x − 7
2. y = −4x + 1
3. y = x/4 + 1
4. y = 1 − 4x

Question 13 (1 mark)
What is the order of a matrix with 2 rows and 3 columns?

1. 3 × 2
2. 2 × 3
3. 6 × 1
4. 5

Question 14 (1 mark)
Find the area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm.

1. 60 cm²
2. 100 cm²
3. 25 cm²
4. 50 cm²

Question 15 (1 mark)
Find the volume of a cylinder of radius 3.5 cm and height 10 cm. (π = 22/7)

1. 110 cm³
2. 385 cm³
3. 770 cm³
4. 220 cm³

Question 16 (1 mark)
A bus leaves at 2245 h and arrives at 0610 h the next day. How long is the journey?

1. 7 h 35 min
2. 8 h 35 min
3. 7 h 25 min
4. 6 h 25 min

Question 17 (1 mark)
KES 1 = 0.0077 US dollars. How many dollars is KES 20,000?

1. 15.4
2. 154
3. 1,540
4. 260

Question 18 (1 mark)
A building 24 m tall is drawn 6 cm tall. The scale is:

1. 1 : 4
2. 1 : 400
3. 1 : 40
4. 1 : 4,000

Question 19 (1 mark)
In a right-angled triangle, adjacent = 12 cm and hypotenuse = 13 cm. Find cos θ.

1. 12/5
2. 5/13
3. 12/13
4. 13/12

Question 20 (1 mark)
A letter is picked at random from the word KENYA. The probability that it is a vowel is:

1. 1/5
2. 3/5
3. 2/5
4. 1/2

Section B: Structured questions (80 marks), type the final answer

Question 21 (8 marks)
Pipe A fills a tank in 4 hours and pipe B empties it in 6 hours. If both are opened when the tank is empty, how many hours does it take to fill?

Answer unit: hours

Question 22 (8 marks)
A salesman earns a basic salary of KES 18,000 plus 5% commission on sales above KES 100,000. In March he sold goods worth KES 340,000. Find his total earnings.

Answer unit: KES

Question 23 (8 marks)
A motorbike costs KES 150,000 cash. On hire purchase, the deposit is 20% of the cash price and there are 18 monthly instalments of KES 8,000. Find the hire purchase price.

Answer unit: KES

Question 24 (8 marks)
3 pens and 2 rulers cost KES 130. 1 pen and 2 rulers cost KES 70. Find the cost of one pen.

Answer unit: KES

Question 25 (8 marks)
A rectangular plot measures 40 m by 25 m. A path 2 m wide runs inside along all four sides. Find the area of the path.

Answer unit: m²

Question 26 (8 marks)
A cylindrical tank of radius 1.4 m and height 2 m is full of water. How many 20-litre jerrycans can it fill? (π = 22/7)

Answer unit: jerrycans

Question 27 (8 marks)
A metal cube of side 4 cm has a density of 7.5 g/cm³. Find its mass in grams.

Answer unit: g

Question 28 (8 marks)
A car travels 120 km at 80 km/h and then 90 km at 60 km/h. Find its average speed for the whole journey.

Answer unit: km/h

Question 29 (8 marks)
A ladder makes an angle of 60° with level ground and its foot is 3 m from the wall. Find the length of the ladder. (cos 60° = 0.5)

Answer unit: m

Question 30 (8 marks)
The mean of 6 numbers is 15. When a seventh number is added, the mean becomes 16. Find the seventh number.

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