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# KNEC KCSE Mathematics Paper 1 Question Paper / 2015 KCSE Tharaka South Joint Examination

## KNEC KCSE Mathematics Paper 1 Question Paper / 2015 KCSE Tharaka South Joint Examination

### SECTION I: (50 Marks)

Answer all the questions in this section

1.

Evaluate:
−16 ÷ 18 𝑥𝑥 6 − 3 𝑥𝑥 8
48 ÷ 6 𝑥𝑥 2
2. Given that 1.05̈ = 1𝑎𝑎
𝑏𝑏
, find the values of a and b

3 marks

2.

Solve for x in the following
3(2x+1) + 32 = 3(x+3) + 3x

3 marks

4.

15 men working 4 hours a day can do a job for 20 days. How long does it take 10 men working 5 hours a day to do the same job.

3 marks

6.

Simplify:
2𝑦𝑦2−3𝑥𝑥𝑥𝑥−2𝑥𝑥2
4𝑦𝑦2− 𝑥𝑥2

4 marks

8.

In the figure below, points A, B, C and C lie on the circumference of a circle. ∠ADC = 780 and line AB = line BC.
Calculate ∠BAC.

2 marks

9.

Given that 1.05̈ = 1𝑎𝑎, find the values of a and b.

3 marks

10.

Solve for x in the following
3(2x+1) + 32 = 3(x+3) + 3x

4 marks

11.

A wire is bent into the shape shown below. BCE is a straight line and CDE is a semicircle radius 1m and centre O. Two ants, starting at the same time moved at equal speeds along the wire from points A and E respectively. How far from C did they meet?

4 marks

12.

15 men working 4 hours a day can do a job for 20 days. How long does it take 10 men working 5 hours a day to do the
same job.

3 marks

13.

All prime numbers between 10 and 20 are arranged in descending order to form a number.
(a) Write down the number. (1 Mark)
(b) State the total value of the third digit in the number formed in (a) above. (1Mark)

2 marks

14.

Simplify
2𝑦𝑦2−3𝑥𝑥𝑥𝑥−2𝑥𝑥2
4𝑦𝑦2− 𝑥𝑥2

2 marks

15.

A Kenyan tourist left America through South Africa. While in South Africa she bought a necklace worth 24 dollars.
Given that 1 rand = 0.15 dollars and 1 rand = 11.24 Kenya shillings, find the value of the necklace in
(a) South Africa rands (1 Mark)
(b) Kenya shillings (2 Marks)

3 marks

16.

In the figure below, points A, B, C and C lie on the circumference of a circle. ∠ADC = 780 and line AB = line BC.
Calculate ∠BAC. (2 Marks)

3 marks

17.

Using tables of reciprocals only to find the value of
5
0.0829 – 14
0.581

3 marks

18.

The volumes of two similar cylinders are 4752cm3 and 1408cm3. If the area of the curved surface of the smaller cylinder is 352cm2, find the area of the curved surface of the larger cylinder.

4 marks

19.

Given that OA�����⃗ = 2i + 3j and �
OB����⃗ 3i – 2j. Find the magnitude of AB to one decimal place.

3 marks

20.

The graph below shows frequency densities for the masses of some 200 students selected from a class. Use it to answer the questions that follow.

(a) Complete the frequency distribution table below. (3 Marks)
Mass in kg
Frequency
(b) State the modal frequency. (1 Mark)

4 marks

21.

Given that tan x0 =3
7
, find Cos (90 – x) 0 giving your answer to 4 significant figures. (2 Marks)

2 marks

22.

An irregular 6 sided polygon has 2 of its interior angles equal to 2x each, 3 angles equal to x each and one side equal to 200. Calculate the value of x.

3 marks

23.

The diagonals of a parallelogram are 20cm and 28.8cm. The angle between the diagonals is 620. Calculate the area of the parallelogram. (3 Marks)

3 marks

### SECTION II: (50 Marks)

Answer only five questions in this section.