##### Mathematics Paper 1 Question Paper

### KCSE CLUSTER TESTS 20

#### Mathematics Paper 1

### SECTION 1 (50 Marks)

**Answer all questions in this section**

Evaluate

2 marks

Otieno bought a radio which he later sold to Kamau at Sh. 7800, making a loss of 20%. At what price would he have sold it in order to make a profit of 15%?

3 marks

The sum of interior angles of a regular polygon is 2160^{0}. Find

a) the number of sides of the polygon. (2mks)

b) the size of each exterior angle of the polygon (2mks)

4 marks

Solve for x:

3 marks

Find the size of the acute angle formed between the lines

4 marks

In Mariwa Primary school, the lessons for lower primary lasts 30min while those of upper primary lasts 40min. The lessons begin at the same time, but the next time they ring together again is break –time. If break-time is at 10.25a.m, at what time do the lessons begin?

3 marks

Express the following recurring decimal as a fraction in the simplest form.

2 marks

The figure below shows trapezium ABCD in which AE=EC and AC=BC. AD=8cm, DC=6cm and angle ACE=48^{0}

a) the size of angle BCE (2mks)

b) the area of trapezium ABCD (2mks)

2 marks

The length of a rectangle is increased by 30% while its width is decreased by 15%. Determine the percentage change in the area of the rectangle.

2 marks

Find the value of x and y in the matrices below:

2 marks

Find all the integral values which satisfy the inequalities.

3 marks

Use tables of squares and reciprocals to evaluate correct to 4 significant figures.

3 marks

Using a ruler and pair of compasses only, draw a parallelogram PQRS in which PQ=8cm, QR=6cm and <QPS=75^{0}. Drop a perpendicular from S to meet PQ at N. Measure the length SN.

4 marks

The cost of running a certain machine varies partly as the number of hours it operates and partly as the amount of fuel it consumes. If the machine runs for 4hrs and consumes 6 litres of fuel, the cost is Sh.3920. If it runs for 3hrs and consumes 5litres the cost is sh.3000. Find the cost of running the machine for 8hrs on 10litres of fuel.

4 marks

The figure below shows a solid made by sticking two equal regular tetrahedra.

a) Sketch the net of the solid

b) If each face is an equilateral triangle of side 5cm, find the surface area of the solid to 4 significant figures.

4 marks

### SECTION 11 (50 Marks)

**Answer only FIVE questions in this section**

A water bucket is in the shape of a frustrum of a cone as shown below. The diameter of the bucket at the top and bottom are 30cm and 20cm respectively and 60cm deep.

a) If the bucket is filled with water, find the area of its surface in contact with water. (4mks)

b) Find the capacity of the bucket in litres (4mks)

c) The bucket is used to draw water from a well to fill a cylindrical water tank of radius 1.5m and height 4.5m. How many buckets full of water must be drawn in order to fill the tank? (2mks)

10 marks

The angle of elevation of the top of a flag post from a point A on the level ground is 130. The angle of elevation of the top of the flag post from another point B nearer the flag post and 120m from A is 30^{0}. B is between A and the bottom of the flag post and the three points are collinear.

a) Find the height of the flag post FT (5mks)

b) Find the distance from the point B to the top of the flag post (2mks)

c) Find the distance from A to T. (3mks)

10 marks

i) AC (1mk)

ii) AN (1mk)

iii) DM (1mk)

c) State the ratio in which

i) X divides line DM (1mk)

ii) N divides line AX (1mk)

10 marks

A farmer keeps dairy and beef cattle in his farm. There are a total of 430 animals. One market day he took a third of the beef cattle and a fifth of the dairy cattle to the market to sell. A total of 320 animals remained in the farm.

a) Find the number of beef cattle and the number of dairy cattle originally in the farm. (5mks)

b) If the price of each dairy cow was Sh.38,000 while beef cow was Sh.16,400, how much money did the farmer realize from the sale? (3mks)

c) The following year, the number of dairy animals changed in the ratio 5:4 while that of beef cattle changed in the ratio 2:3. How many animals did the farmer have together? (2mks)

10 marks

A bus starts from Migori at 6.30 am travelling to Kisumu at 60km/h and arrives at 2.30pm.

a) Find the distance between Kisumu and Migori (2mks)

b) At 8.15am, a van leaves Kisumu travelling at 75km/h towards Migori along the same route as the bus . At what time did the two vehicles meet? (4mks)

c) Find the distance of the meeting point from Migori. (2mks)

d) If the van took a total of 20 minutes to refuel on the way, at what time did it arrive in Migori? (2mks)

10 marks

c) Use your graph to solve the equations

d) State the co-ordinates of the maximum point of the curve. (1mk)

10 marks

Rates of tax in operation in 2012 are given in the table below.

a) Mr. Ochola pays Ksh. 12,075 as P.A.Y.E. He is entitled to house allowance of Ksh. 12,000 p.m and getting a monthly tax relief of sh.1162.

Calculate his monthly pay. (7mks)

b) Mr. Ochola’s other deductions per month were: co-operative society contribution Ksh.5000 Loan repayment Ksh.12,500

Calculate his net salary per month. (3mks)

10 marks

A frequency distribution of marks obtained by 180 candidates is to be represented in a histogram. The table below shows the grouped marks. Frequencies for all the groups and also the area and height of the rectangle for the group 70-100 marks are given.

a) i) Complete the table (4mks)

ii) On the grid provided, draw the histogram. (2mks)

b) i) State the group in which the median mark lies (1mk)

ii) A vertical line drawn through the median mark divides the total area of the histogram into two equal parts.

Using this information or otherwise estimate the median mark. (3mks)

10 marks