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

### 2015 KCSE Tharaka South Joint Examination

#### Mathematics Paper 1

### SECTION I: (50 Marks)

**Answer all the questions in this section**

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

Solve for x in the following

3(2x+1) + 32 = 3(x+3) + 3x

3 marks

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

Simplify:

2𝑦𝑦2−3𝑥𝑥𝑥𝑥−2𝑥𝑥2

4𝑦𝑦2− 𝑥𝑥2

4 marks

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

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

3 marks

Solve for x in the following

3(2x+1) + 32 = 3(x+3) + 3x

4 marks

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

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

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

Simplify

2𝑦𝑦2−3𝑥𝑥𝑥𝑥−2𝑥𝑥2

4𝑦𝑦2− 𝑥𝑥2

2 marks

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

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

Using tables of reciprocals only to find the value of

5

0.0829 – 14

0.581

3 marks

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

Given that OA�����⃗ = 2i + 3j and �

OB����⃗ 3i – 2j. Find the magnitude of AB to one decimal place.

3 marks

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

Given that tan x0 =3

7

, find Cos (90 – x) 0 giving your answer to 4 significant figures. (2 Marks)

2 marks

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

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.**