## KNEC KCSE Mathematics Paper 1 Question Paper / 2015 KCSE Meru South Form 4 Joint Examination

### 2015 KCSE Meru South Form 4 Joint Examination

#### Mathematics Paper 1

### SECTION 1 (50 Marks)

**Answer ALL the questions in this section.**

Evaluate using logarithms:

4 marks

Use the prime factors of 3136 and 2744 to evaluate:

3 marks

A rectangular slab of glass measures 8cm by 3cm by 2cm and has a mass of 5.5kg. Calculate the density of glass in g/cm3.

3 marks

The figure below shows a net of a solid which is not drawn to scale.

(a) Sketch the solid ABCDEF with ABCD as the base. (2 Marks)

(b) Calculate its volume. (2 Marks)

4 marks

A trader at Chuka town sells a school shirt at Sh. 725 and makes 45% profit. During clearance sale he reduced the price of the shirt by 20%. What percentage profit did he make.

3 marks

Fine the value of x in the equation:

27^{x} + 3^{3x-1} = 108

3 marks

The figure below shows a sector of a circle of radius 15cm. Calculate the area of the sector given than angle θ = 2.4 radians.

2 marks

Simplify the expression completely:

3 marks

A ship sails from harbour P on an bearing 0300 for 900km until it reaches harbour Q. It then alters its direction to a bearing of 340+ and sails from 1200km to harbour R. Calculate the distance between harbours P and R.

3 marks

A regular polygon has the sum of its interior angles as 18000.

(i) How many sides are there in the polygon? (2 Marks)

(ii) How many triangles can be made by joining one of its vertices with all other vertices with straight lines.(1 Mark)

3 marks

Without using a calculator evaluate giving your answer as a mixed fraction. (3 Marks)

3 marks

Solve the inequality and state the integral values satisfying the solution.

3 marks

The figure below shows the section of a wedge. AB = 4cm, BC = 13cm, CD = 12Ccm, AD = 3cm and BD = 5cm.

Given that angle ADC = 900, find the volume of the solid and the length of AC.

4 marks

Using reciprocal tables only evaluate

3 marks

The cost per kg of Sony Sugar is KSh. 60 and the cost per kg of Imported Sugar is KSh. 80. The two brands of Sugar are mixed and sold at a profit of 30% above the cost. If 1kg of the mixture was sold at KSh. 84.50, determine the ratio in which the two brands were mixed.

3 marks

The points P1(5,4) and Q1(6,1) are the images of P and Q respectively under translation. Given that the co-ordinates of P and (2,3), find the co-ordinates of Q.

3 marks

### SECTION II (50 Marks)

**Answer only FIVE questions from this section.**

The figure below is a right rectangular based pyramid VABCD where AB = 5cm, BC = 7cm, VC = 13cm and O is a point on the base of the pyramid vertically below V.

Calculate

(a) AC (2 Marks)

(b) VO, the height of the pyramid. (2 Marks)

(c) the angle between the edge VB and the plane ABCD. (3 Marks)

(d) the angle between the planes VBC and ABCD. (3 Marks)

10 marks

The table below shows the distribution of marks of 100 form three students in a mathematics examination.

Marks | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 | 81-90 | 91-100 |

No. of students | 2 | 8 | 15 | 18 | 17 | 14 | 10 | 8 | 6 | 2 |

(a) Using the scale of 1cm represent 10 marks and 1cm to represent 5 students draw a cumulative frequency curve to represent the above information on the provided grid.

(b) Using your graph, estimate the

(i) Median (1 Mark)

(ii) Semi-interquartile range (3 Marks)

(iii) number of students who passed if pass mark was 43% (2 Marks)

10 marks

(a) A lamp shade is in the form of a frustum of a cone of diameter 21cm and 28cm. Its height is 10cm.

Calculate the volume of the lampshade. (5 Marks)

(c) Two circles each of radius 5cm intersects such that the distance between their centres is 6cm. The

length of the common chord joining the two points of intersection is 8cm. Calculate the area of intersection.

(5 Marks)

10 marks

Use a ruler and a pair of compasses only for all construction in this question.

(a) Construct qualilateral PQRS such that PQ = 5cm, PS = 5cm and SR = 4.5cm, angle SPQ = 7500 and angle PSR = 900. (4 Marks)

(b) Drop a perpendicular from S to meet line PQ at N. Measure SN and calculate the area of the triangle SPN.(3 Marks)

(c) Construct a circle passing through vertices P, Q and R of quadrilateral PQRS. Measure the radius of the circle.

(3 Mark)

10 marks

In the figure below, O is the centre of the circle. Angle AEB = 500, angle EBC = 800 and angle ECD = 300.

Giving reasons calculate:

(a) Angle CDE (2 Marks)

(b) Angle DFE (2 Marks)

(c) Obtuse angle COE (2 Marks)

(d) Angle ADE (3 Marks)

10 marks

The length and the width of a rectangular are (6x-1) and (x – 2) respectively. If the length and width are each increased by 4cm the new area is thrice that of the initial rectangle.

(a) Find the dimension of the initial rectangle. (6 Marks)

(b) By what percentage does the area of the rectangle increase after the change. (2 Marks)

(c) What is the difference in size between the length and the width of the initial rectangle. (2Marks)

10 marks

A,B,C and D are four schools where B is 84km north of A an C is on a bearing of N650W from A at a distance of 60km. D

is on a bearing of N200W from C and at a distance of 30km.

Use a scale drawing to show relative positions of A,B,C and D using a scale of 1cm to represent 10km. (5 Marks)

Find;

(a) the distance and bearing of B from C. (2 Marks)

(b) the bearing and distance of D from B. (2 Marks)

(c) the bearing of A and D. (1 Mark)

10 marks

The velocity of a particle after t seconds is given by V = t2 – 4t + 4m/s. Determine the;

(a) initial velocity of the particle. (2 Marks)

(b) time taken the particle is momentarily at rest. (3 Marks)

(c) acceleration of the particle at t = 4. (2 Marks)

(d) displacement of the between t = 1 seconds and t = 13 seconds. (3 Marks)

10 marks

**MATHEMATICS PAPER 1 MARKING SCHEME**

### 2015 KCSE Meru South Form 4 Joint Examination

#### Mathematics Paper 1

### SECTION 1 (50 Marks)

**Answer ALL the questions in this section.**

4 marks

3 marks

3 marks

4 marks

3 marks

3 marks

2 marks

3 marks

3 marks

3 marks

3 marks

3 marks

4 marks

3 marks

3 marks

3 marks

### SECTION II (50 Marks)

**Answer only FIVE questions from this section.**

10 marks

10 marks

10 marks

10 marks

10 marks

10 marks

10 marks

10 marks