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Form 4 Mathematics Sample Revision Questions and Answers Set 2
Solve for x
log
27
(
x
+
5
)
–
log
27
(
x
–
3
)
=
2
3
(3m 46s)
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1.
The dimensions of a rectangle are measured and given as 6.9 cm by 3.06 cm, calculate to 4 significant figures the percentage error in the area.
2.
Construct rectangle ABCD in which AB = 4cm and BC = 3cm. Inside the rectangle construct the locus of point L1 which is 3 cm from A; Locus of L2 which is equidistant from line AB and AD and locus of point L3 which is 2cm from line AB.
3.
State the amplitude and the phase angle of the curve
y
=
2
sin
{
3
2
x
-
30
}
4.
Express as a surd and simplify
1
+
cos
30
1
-
sin
60
5.
Solve for x
log
27
(
x
+
5
)
–
log
27
(
x
–
3
)
=
2
3
6.
Point P
(
X
0
N
,
30
0
E
)
and Q
(
X
0
N
,
50
0
E
)
are 1935 km apart. Taking R = 6370km and
π
=
22
7
, Find the value of x
7.
The equation of a circle is
x
2
+
4
x
+
y
2
-
5
=
0
. Find the center and the radius of the circle.
8.
Wanyama bought maize flour, sorghum and millet at sh 12, sh 15 and sh 18 per kg respectively. He mixes them in the ratio 1: 2 : x respectively. After selling the mixture at sh 19.20 he made a profit of 20%. Find the value of x.
9.
Chord AB and CD in the figure shown below intersect externally at Q. If AB=5cm, BQ=6 and DQ=4cm. Calculate the length of chord CD.
10.
Find the value of x given that the matrix is a singular matrix.
(
x
+
7
4
-
3
x
)
11.
Given that z varies directly as the square of x and inversely as the square root of y. If x = 2, y= 9 when z = 3, find z when x = 3 and y = 4.
12.
The marks of 80 students in a Mathematics test are shown in the table below.
13.
The image of a point Q(1,2) after a translation is Q1 (-1,2). What is the co-ordinate of the point R whose image is R1(-3, -3) after undergoing the same translation?
14.
Make q the subject of the formula
A
B
=
√
p
+
3
q
q
-
3
p
15.
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.
16.
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 handball 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
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