# KCSE Mathematics Paper 1 Revision Exercise Set 3

KCSE Mathematics Paper 1 Revision Exercise Set 3

Lessons (**17**) * SHARE*

- 1.
Factorise completely the expression
#45a^2 – 20b^2#
and hence or otherwise find its value when a= 5 and b= 3.

4m 20s - 2.
Given the ratio x:y = 2:3, find the ratio (5x – 2y) : (x + y)

2m 59s - 3.
Kasila’s office is 18 km from where she works. She uses her car to travel to and from her office everyday for 6 days a week. Her car consumes petrol at the rate of 1 litre for every 12 km and petrol costs sh 56.20 per litre. Allowing 2 weeks of holiday in a year, calculate the amount of money Kasila’s spends on petrol
going to and from her office in one year.

4m 35s - 4.
A rectangle whose length is 7cm longer than its width has an area of 120#cm^2.#
a) Taking x to represent the length of the rectangle, from a quadratic equation in x for the area of the triangle.
b) By factorising solve the quadratic equation and hence state the dimensions of the rectangle.

8m 19s - 5.
Simplify the expression
3(2a + b – 2c ) –2( a + 2b -3c)

2m 44s - 6.
An article which is marked for sh 450 is sold to customer for sh 393.75. What percentage discount is the customer allowed?

2m 15s - 7.
A rectangle which measures 18 cm by 8 cm has the same area as a square. Find which figure has the greater perimeter and by how much.

4m 10s - 8.
Given that p=3, q= -2 and r=-1 evaluate
#(2(p+r)^2-(p-q)(q-r)-2r)/(3(p+q)-2(q-r))#

6m 11s - 9.
Given the column vectors
a=#((-3),(2))#, b=#((4),(-6))#,c=#((5),(-10))# and that p=2a-#1/2 b +2/5 c#
express p as a column vector and hence calculate its magnitude |p| correct to 2 decimal places.

5m 0s - 10.
In the figure ABCD is a rhombus in which angle ADC = 140°.AB is produced to F such that AB = BF.
Giving reasons for your answer find the size of;
a) angle BAC
b) angle BCF

9m 10s - 11.
Evaluate
#(8/27)^2 times(16)^(1/2)div(81)^(1/4)#

7m 23s - 12.
The table below shows the masses of 50 students in Form One class. These measurements are recorded to the nearest kilogram.
a) State the modal class.
b) Calculate the median mass.

7m 42s - 13.
You are given that Cos#theta=8/10#. Without using mathematical tables express in fraction form the value of
a) Sin #theta#
b) Tan ( 90 - #theta#)

5m 11s - 14.
Giving your answer in the simplest terms possible, express
#(2x – y)^2-(x - y) (x + y)#
In terms of x only given that
y= 2x - 1

7m 27s - 15.
A sales lady is paid commission at the rate of 3 cents in every shilling on all goods she sells. During one month she sold 12 television sets at sh 15 500 each, 8cassets players at sh 5650 each and 4 refrigerators at sh 21 700 each. Calculate the
total commission she earned in that month.

4m 34s - 16.
A newly built classroom measuring 6.3m long, 4.5m wide and 3.2m high is to be cemented on the floor and all inside walls. The classroom has one door measuring 1.85m by 80 cm and four windows measuring 1.5 m by 70 cm each. Cementing materials costs sh 500 per square metre while labour costs
20% of the cost of cementation materials. Calculate
a) to one decimal place, the total surface area to be

9m 55s - 17.
The diagram shows the frustum of a right pyramid made by cutting off small pyramid halfway up the vertical height of the original pyramid. The frustum stands on a rectangular base measuring 24cm by 10cm while the removed pyramid stands on a rectangular base measuring 12cm by 5 cm.
Given that the slant height of the original pyramid is 28cm, calculate
a) To one decimal place the vertical height of

14m 16s

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