##### Mathematics Paper 1 Question Paper

### KCSE CLUSTER TESTS 19

#### Mathematics Paper 1

### SECTION I (50 Marks)

a) Write down in descending order the first, fifth, ninth and tenth prime numbers to form one number. (1mk)

b) State the total value of the third digit of the number formed. (1mk)

c) Determine if the number is divisible by 11. (1mk)

1 marks

Find the equation of a line which passes through the point (1,-3) and is parallel to the line whose equation is** -2x+3y+7=0 ** (3mks)

3 marks

Evaluate without using tables or a calculator

3 marks

. Use squares, square roots and reciprocal tables only to evaluate the following, giving your answer to 3 decimal places. (3mks)

3 marks

The figure below represents the net of a solid, not drawn to scale.

a) Draw and name the solid.

3 marks

The exterior angle of a regular polygon is ΒΌ the interior angle. Find the number of sides of the polygon.

3 marks

Given that. Find without solving for x and y the value of

3 marks

Find all the integral values of x which satisfy the inequalities.

3 marks

Evaluate

3 marks

. Find the value (s) of x if (3 mks)

3 marks

In the figure below O is the centre, angle and angle OMP=160. Find the angles marked x, y and z.

3 marks

. The frequency distribution table below shows the marks obtained by students in a form four class.

On the grid provided below, draw a histogram to represent the information shown above.

3 marks

The marked price of a car in a show room is sh.650000. The car is sold at a discount of 5% through an agent who earns a commission of 8% on the selling price. Find how much the owner earns.

3 marks

. Find the inverse of the matrix

hence solve the simultaneous equations

3 marks

Given that

and that A and B are obtuse angles, Calculate the value of the following without using tables or calculator

3 marks

. A game park lies between three points A,B and C. Point A is 50km from B. Point C is 70km from B and 60km from A respectively. Calculate the area of the ranch to the nearest whole numbers.

3 marks

### SECTION II (45 Marks)

**Attempt ONLY five questions from this section**

Villages A,B,C and D are such that B is 40km due east of A, C is 30km on a bearing of 1450 from B, and D is 40km S 500W of C. a) Using a suitable scale, draw a diagram to show the positions of the villagers. (3mks)

b) Use your diagram to determine i) The bearing of A from D. (1mk)

ii) The distance of A from D (1mk)

iii) The shortest distance between B and the line AD. (2mk)

c) A vertical mast of the height 100m stands at B. Another vertical mast of height 30m stands at a point on the line BC, 200m from B. Find the angle of elevation of the top of the taller mast from the top of the shorter mast.

7 marks

A particle moving at a velocity of 12m/s accelerates to a velocity of 25m/s in the first 10 seconds, it then moves at a constant velocity for the next 30 seconds before coming to rest in another 20 seconds.

a) Draw a velocity- time graph to represent this information.

7 marks

9. In a pentagon ABCDE, AB=4.3cm, BC=4.6cm, CD=7.2cm, DE=5cm, AE=6cm and angle BAE=1100. Diagonal BD is parallel to AE. a)

i) Construct the pentagon accurately. (5mks)

ii) Measure and write down the length of BD. (1mks)

b) i) Drop and measure a perpendicular from C onto AE. (1mk)

ii) Find the area of the pentagon. (2mks)

9 marks

. a) A sum of Ksh.360 was to be divided equally among x homeless boys. An equal amount was to be shared among (x+4) homeless girls. This way, each boy would receive Ksh.3 more than each girl, calculate the amount to be received by each girl. (5mks)

b) But before the actual divisions were done, a well- wisher added Ksh.360 to

the boys kitty and Ksh.y to the girls pool, which made some boys to

dramatically cross-over to the girls side, making the boys group to be a

third of the βgirlsβ group.

i) Find the number of boys that defected to the girlsβ side. (2mks)

ii) If each member in the two groups now received the same amount, find the value of y.

7 marks

The figure below represents a frustrum of a right pyramid. The perpendicular height of the frustrum is 2cm.

Calculate a) The slant height of the frustrum. (1mk)

b) The perpendicular height of the pyramid. (2mks)

c) The surface area of the frustrum. (4mks)

d) The volume of the frustrum. (3mks)

10 marks

Two intersecting circles of radii 12cm and 5cm have their centres 13cm apart. PC is their common chord.

a) Find angle PAB. (2mks)

b) Find the length of PM. (2mks)

c) Calculate the area of quadrilateral APBC. (3mks)

d) Hence find the area of the shaded region. (3mks)

10 marks

. In the figure below OABC is a parallelogram

is a point on AO

such that

3 marks

A particle moves such that t seconds after passing a given point O, its distance s metres from O is given by s=t(3-2t) (4-t)

a) Calculate the time at which it is first at rest. (3mks)

b) Calculate its position when it is next at rest. (2mks)

c) Let P and Q be the positions when it is momentarily at rest in the above two parts. Calculate the distance PQ. (3mks)

d) At what time is its acceleration zero? (2mks)

10 marks