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Form 4 Mathematics paper 1 and paper 2 sample revision questions with answers
Without using a mathematical table or a calculator, simplify
3
√
7
+
√
2
-
2
√
2
+
√
7
(2m 59s)
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1.
Given that a = -2, b=-1 and c = -3, evaluate
2
(
a
+
c
)
2
-
(
a
-
b
)
(
b
-
c
)
-
2
c
3
(
a
+
b
)
-
2
(
b
-
c
)
2.
Annette has some money in two denominations only. Fifty shilling notes and twenty shilling coins. She has three times as many fifty shilling notes as twenty shilling coins. If altogether she has sh. 3400, find the number of fifty shilling notes and 20 shilling coins.
3.
In the figure below PQ is parallel to RS. Calculate the value of x and y
4.
Solve the following simultaneous equations using substitution Method. 4a+3b=120 2a+5b=130
5.
The angles of a quadrilateral are 3x, 2x, x +14 and 2(x – 7) degrees. Find the smallest angle.
6.
A rectangle measures 3.6 cm by 2.8 cm. Find the percentage error in calculating its perimeter.
7.
Make x the subject of the formula if
y
=
a
x
+
b
8.
Give the combined solution for the range of x values satisfying the inequality
2
x
+
1
<
10
–
x
<
6
x
–
1
9.
Expand
(
x
+
y
)
6
hence evaluate
(
1.02
)
6
to 3 decimal places.
10.
Rationalize the denominator in
√
3
1
-
√
3
11.
If log x = a and log y = b, express in terms of a and b Log
x
3
y
12.
Find the equation of the locus of points equidistant from point L (6, 0) and N (-8, 4).
13.
The value of a machine is shs. 415,000. The machine depreciates at a rate of 15% p.a. Find how many years it will take for the value of the machine to be half of the original value.
14.
Given that the matrix below has no inverse, find the value of k
[
k
3
3
k
]
15.
Find the standard deviation of the data below: 3, 5,2,1,2,4,6,5
16.
The co-ordinate of point A is (2, 8) vector AB =
(
5
-
2
)
and vector BC =
(
4
3
)
Find the co-ordinate of point C.
17.
The nth term of a G.P is given by
5
×
2
2
n
-
2
(i) Write down the first 3 terms of the G.P (ii) Calculate the sum of the first 5 terms
18.
It costs Maina shs. 13 to buy 3 pencils and 2 rubbers, while Mutiso spent shs.9 to buy one pencil and 2 rubbers. Calculate the cost of a pencil and one rubber.
19.
3 bells ring at intervals of 12min, 18min and 30min respectively. If they rang together at 11.55am, when will they ring together again?
20.
A piece of wood of volume
90
c
m
3
weighs 54g. Calculate the mass in kilograms of
1.2
m
3
of the wood.
21.
Make L the subject of the formula H =
√
3
d
(
L
-
d
)
10
L
22.
A quantity P varies partly as n and partly as the square of n. When P =-3,n=-1 and when P = 18,n=2.Find P when n=1.
23.
The seventh term of an arithmetic sequence is 17,three times the third term is 3.Calculate the first term and the common difference of the sequence.
24.
Fid the inverse of the matrix below
(
5
-
2
2
-
1
)
Hence find the point of intersection of the lines whose equations are 5x- 2y =5 y=2x-3
25.
The dimensions of a rectangle are given as 4.1cm by 2.8cm. Calculate the relative error in the area.
26.
The volume of cuboid A is
64
c
m
3
while that of a similar cuboid B is
8
c
m
3
. If the width of cuboid A is 2cm, find the width of cuboid B.
27.
Without using a mathematical table or a calculator, simplify
3
√
7
+
√
2
-
2
√
2
+
√
7
28.
Kipkemboi running at 10m/s starts 5m ahead of Mutola who is running at 12m/s.How far from Kipkemboi’s starting point does Mutola overtake him?
29.
Show that
4
y
2
+
4
x
2
=
12
x
-
12
y
+
7
is the equation of a circle, hence find the co-ordinates of the centre and the radius.
30.
A line passes through A(1,1) and B(x, y).The mid-point of AB is (3,5).If line BC is perpendicular to AB,find the equation of line BC.
31.
Evaluate
28
+
18
-
2
-
-
15
-
(
12
)
3
32.
Each interior angle of a regular polygon is
100
o
larger than the exterior angle. Determine the number of sides of the polygon.
33.
Find the integral values that satisfy the inequalities
4
x
-
6
≥
x
-
12
8
-
3
x
≥
2
x
-
7
34.
Find the least number of biscuits that can be packed into carton boxes which contain either 9 or 15 or 20 or 24 with none left over.
35.
Evaluate without using mathematical tables or calculators, the square root of
0.0273
x
1.152
1.3
x
1.68
36.
Kamau bought five exercise books and three geometrical sets for sh.725. If he had bought four similar exercise books and five geometrical sets, he would have paid sh.375 more. How much would he pay for two exercise books and six geometrical sets.
37.
A cold water tap can fill a bath in 10 minutes while a hot water tap can fill it in 8 minutes. The drainage pipe can empty it in 5 minutes. The cold water and hot water taps are left running for 4 minutes. After which all the three taps are left running. Find how long it takes to fill the bath.
38.
The hire purchase term of a cupboard is a deposit of Ksh. 4,400 and six monthly instalments of ksh. 900 each. The hire purchase price is 175% of the cost price while the cash price is 25% more than the cost price. What is the cash price of the cupboard?
39.
The circle below whose area is
18.05
c
m
2
circumscribes a triangle ABC where AB = 6.3 cm, BC = 5.7 and AC = 4.8cm. Find the area of the shaded part.
40.
Determine the quartile deviation for the following set of numbers. 7,5,10,6,5,8,7,3,2,7,8,9
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