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Form 4 Mathematics Sample Revision Questions and Answers Set 1
A sphere has a surface area of
18.0
c
m
2
. Find its density if the sphere has a mass of 100 grams.
(2m 46s)
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1.
Find the value of x given that: Log (15 – 5x)-1=log (3x-4)
2.
M
(
30
0
N
,
75
0
W
)
and N
(
30
0
N
,
105
0
E
)
are two points on the earth’s surface. Find the shortest distance between them in Km (take R= 6370km and
π
=
22
7
)
3.
Given that the dimensions of a rectangle are 20.0cm and 25.0cm. Find the percentage error in calculating the area.
4.
Make d the subject of the formula.
a
=
b
√
d
+
s
5
f
5.
Two variables X and Y are such that X varies partly as Y and partly as the square root of Y. Given that X=30 when Y=9 and X=14 when Y=16. Find the relationship between X and Y.
6.
The second, fourth and seventh terms of an AP are the first three consecutive terms of GP. Find the common ratio if the first term of the AP is 2.
7.
The cost of maize flour and millet flour is kshs.40 and kshs.52 respectively. Calculate the ratio in which they are mixed if a profit of 15% was made by selling the mixture at Kshs.52.90 per kilogram.
8.
Simplify
1
2
o
f
16
-
10
+
2
(
1
2
÷
1
4
)
1
3
×
3
3
4
÷
1
4
9.
A straight line
L
1
whose equation is 3x + 2y = 5 is perpendicular to another line
L
2
passing through the origin. Find the co-ordinates of both the X and Y- intercepts of line
L
2
.
10.
Two similar spheres have surface areas of
64
c
m
2
and
144
c
m
2
respectively. If the volume of the larger sphere is
250
c
m
3
calculate the volume of the smaller sphere.
11.
A triangle measures 7cm by 13cm by 18cm. Calculate the area of the triangle.
12.
Find all the integral values satisfying the inequalities
3
-
2
n
<
n
-
3
≤
4
and also represent the solution on a number line.
13.
Simplify
x
+
3
3
-
2
x
-
1
4
14.
Evaluate without using mathematical tables or calculators.
3
√
3375
5
√
3125
15.
Solve for x given
5
x
+
1
+
6
(
5
x
)
-
70
=
205
16.
Given that Cos (90 -B) =
√
3
2
determine without using trigonometric tables the value of Cos B
17.
Find the Centre and radius of a circle whose equation is
3
x
2
+
3
y
2
–
18
x
+
12
y
–
9
=
0
18.
Chord AB and CD intersect externally at Q. If AB=5cm BQ = 6cm and DQ=4cm. Calculate the length of CQ.
19.
Two boys and a girl shared some money. The younger boy got
5
18
of it; the elder boy got
7
12
of the remainder and the girl got the rest. Find the percentage share of the younger boy to the girl’s share.
20.
Calculate the interest on sh 10,000 invested for 1
1
2
years at 12 % p.a. Compounded semi-annually.
21.
Make q the subject of the formula
A
B
=
√
p
+
3
q
q
-
3
p
22.
If a certain unfair coin is tossed, the chance of obtaining a tail is 25%. Find:- a) The probability of getting two heads when the coin is tossed twice. b) The probability of obtaining at least one tail when the coin is tossed twice.
23.
During inter-school competitions, rugby and football teams from Ranje sec school took part. The probability that the rugby would win their first match was
1
8
while that the football team could lose was
4
7
. Find the probability that; (a) Both teams won their first matches. (b) At least one team won the first match
24.
A squared brass plate is 2mm thick and has a mass of 1.05kg. The density of brass is 8.4g/
c
m
3
. Calculate the length of the plate in centimeters.
25.
A sphere has a surface area of
18.0
c
m
2
. Find its density if the sphere has a mass of 100 grams.
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