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Form 4 Mathematics Paper 1 Sample Revision Questions and Answers Set 1
Given that x=3, y=-2 and z=-1 find the value of
4
x
y
z
-
2
x
z
2
-
5
y
x
y
3
z
+
3
x
z
3
+
4
y
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1.
Without using mathematical tables or a calculator, evaluate
28.38
×
0.3465
0.645
×
2.175
2.
a).Expand the expression
(
3
x
-
7
)
(
2
x
+
7
)
b)Without using long multiplication or a calculator, use the above expansion with an appropriate substitution of x to find the value of
53
×
47
3.
Janet bought 216 pineapples at sh 50 for every 6 and sold them all at sh 40 for every 3. Calculate the percentage profit she made.
4.
Without using logarithm tables or a calculator, evaluate
log
10
96
+
3
4
log
10
625
-
log
10
12
5.
Given that x=3, y=-2 and z=-1 find the value of
4
x
y
z
-
2
x
z
2
-
5
y
x
y
3
z
+
3
x
z
3
+
4
y
6.
Solve the simultaneous equations 3a+2b=13 5a-3b=9
7.
The figure shows a parallelogram PQRS in which PQ =20cm, QR=11.6cm and angle PQR=
110
0
. Calculate to one decimal place the area of the parallelogram.
8.
A poultry farm has twenty times as many hens as turkeys and three quarters as many ducks as turkeys. (a) If there are t turkeys, write down a simplified expression in t for the total number of birds on the farm. (b) Given that there 75 ducks, calculate as a percentage the sum of turkeys and ducks to the number of hens on the farm
9.
Find the size of each exterior angle of a regular decagon
10.
On a day when the currency exchange rate was 1deutchmark (DM)= ksh 36.75 1 US dollar =ksh 76.50 A German tourist decided to exchange half of his 240 DM into dollars. Calculate to 2 decimal places, the number of dollars he received.
11.
When the sun is at an elevation of
63.5
0
a vertical pole casts a shadow 1.8m long on the ground. Calculate to two decimal places, the height of the pole.
12.
A hollow metal pipe of internal diameter 7cm and external diameter 8cm is 6.16 meters long. Calculate the volume of metal making the pipe in cubic centimeters.
13.
Solve the following inequalities and represent the range of values of x on a single number line. 5-3x>-7 x-6=3x-4
14.
The figure below shows the map of a ranch drawn on a grid of one centimeter squares. (a) Estimate the area of the map in
c
m
2
. (b) Given that the scale of the map is 1:40000, calculate the actual area of the ranch in hectares.
15.
The average mark scored by the first 24 students in a mathematics test is 48.5. The average mark scored by the remaining 16 students is 57.25. Calculate the mean mark for the whole class.
16.
A rectangular water cistern measuring 2.5m long, 1.8m wide and 1.2m high is half full of water. All this water is poured into an empty cylindrical tank of diameter 2.8m. Calculate to one decimal place, the height in centimeters to which the water rises.
17.
The diagram below represents the cross-section of a bridge with a solid part and a tunnel through which the river flows. The tunnel is 8 m long and its cross-section is a semi-circle of radius is 3.5m. The bridge is 5m high and its solid part is filled with concrete. (a) Calculate (i) The cross-sectional area of the solid part. (ii) The volume of concrete used to fill the solid part.
18.
The heights of a number of students were recorded in the table below. Each measurement is given to the nearest cm. (a) Copy and complete the table. (b) State the modal class (c) Use the completed table to calculate the mean height of the students.
19.
The figure shows triangle OAB in which OA=a and OB=b. Points M and N are on OA and AB respectively such that OM=
3
4
OA and AN=
2
3
AB. Lines ON and BM meet at T such that OT=
9
10
ON. (a) Express the following vectors in terms of a and b: (i) AB (ii) BM (iii) ON (b) Given that BT=kBM, express vector BT in two ways and hence find the value of k. (c) Express vector TM in terms of a and b.
20.
The figure below represents a circle centre O and radius 18cm. The minor sector AOB subtends an angle of
140
0
at the centre of the circle. The sector is cut off and folded into a cone. (Take
π
=
2
27
), calculate (a) The radius of the cone so formed. (b) To one decimal place, the height of the cone. (c) To the nearest whole number, the capacity of the cone.
21.
The diagram below represents a frustum ABCD made by removing a small cone from the original right cone. The base radius of the original cone is 35cm and that of the removed cone is 21cm. The frustum is 20cm high as shown. Calculate to the nearest whole number, the total surface area of the frustum.
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