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Form 4 Mathematics Sample Revision Questions and Answers Set 3
Without using logarithms table, solve the equation
log
(
5
x
-
4
)
=
log
(
x
-
2
)
+
1
3
log
27
(1m 44s)
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1.
The gradient of curve at any point is given by 2x – 1. Given that the curve passes through point (1, 5), find the equation of the curve.
2.
Agotho has a rectangular plot that was measured to the nearest meter and found to be 80m in length and 60m in width. Determine the percentage error in its perimeter.
3.
(a) Expand
(
x
-
0.2
)
5
in descending powers of x. (b) Use your expansion up to the fourth term to evaluate
9.8
5
4.
Solve for n in the following equation
7
2
n
-
4
=
2401
5.
Find the values of x between
0
0
and
180
0
such that 2 cos 3x = 3 sin 3x
6.
Given that the numbers 4, 6, 2,4,1,3,2,4,1 are the ages of pupils in a baby school. Find a) The mode b) The mean c) The median
7.
The position vectors of A and B are given as a=2i-3j+4k and b=-2i-j+2k respectively Find to 2 decimal places, the length of vector AB
8.
Find the equation of a straight line which is perpendicular to the line 8x + 2y - 3 = 0 given that they intersect at y = 0.
9.
In the figure below, AD is a tangent to the circle at D. AB=11cm and BC=8cm. Find the length of AD.
10.
A trader mixed grades A, B and C of coffee in the ratio 2:3:5 respectively. Grade A cost sh. 650 per kg, grade B cost sh. 500 per kg and grade c cost sh. 420 per kg. (a) Find the cost of 1kg of the mixture (b) If the trader sold the mixture at a profit of 20%, calculate the selling price of 3kg of the mixture
11.
Find the center and radius of a circle whose equation is
3
x
2
+
3
y
2
-
24
x
+
6
y
+
3
=
0
12.
The effort (E) applied on a lever to lift a load (L) is partly constant and partly varies as L. When L=3, E=4 and when L=15, E=10. Find the equation connecting E and L.
13.
Make n the subject of the equation.
p
q
=
m
2
3
√
1
-
n
2
14.
Find the value of x for which the matrix below is a singular matrix.
(
4
+
x
2
10
x
-
4
)
15.
Simplify leaving your answer in form of
a
+
b
√
c
. State the value of a, b and c.
√
7
√
3
-
√
2
-
√
7
√
3
+
√
2
16.
Without using mathematical tables, evaluate the expression below.
3
log
5
–
1
2
log
64
+
6
log
2
17.
Find the integral of
x
2
+
1
18.
A translation maps the point Q (5, -3) onto Q1 (2, -5) (a) Determine the translation vector. (b) A point R1 is the image of R (-2, -3) under the same translation. Find the length of Q1R1.
19.
The masses of 40 children being interviewed to join Std 1 by a certain school were as recorded in the table below. Calculate the mean mass of the students giving your answer to 4 significant figures
20.
The first term of an arithmetic sequence is (2x+1) and the common difference is (x+1) if the product of the first and the second terms is zero, find the first three terms of the two possible sequences.
21.
Solve for x and y
3
2
x
-
y
=
27
4
x
÷
16
y
=
1
22.
A line L1 passes through point B and is parallel to the line 2y = 5x – 16. M is the mid-point of line AB. Given the coordinates of A and M are (2, 3) and (4, 2) respectively, find the equation of line L1 in the form y = mx + c.
23.
From the information below, calculate the standard deviation of the data given. 8, 12, 4, 1, 6, 5
24.
The cash price of a fridge is ksh 30,000. Anne bought the fridge on hire purchase by paying a deposit of ksh. 7,500 and 14 monthly installments of ksh.1875 each. Calculate the monthly rate of interest she was charged. Give your answer to 2 decimal places.
25.
Express the following in surd form and simplify by rationalizing the denominator
1
1
-
sin
45
26.
Two similar containers have masses 256kg and 108 kg respectively. If the surface of the smaller container has an area of
810
c
m
2
, what is the area of the corresponding surface of the larger container?
27.
A man spent
1
9
of his salary on food and
1
4
of the remainder on electricity and water bills. He paid fees with 20% of his salary and invested 16% of what was left on business. After taking a game drive on which he spent ksh 2000, he saved ksh 5350. Calculate his total monthly earnings.
28.
Mr. Omondi bought peas at ksh. 40 per kg and beans at ksh. 20 per kg. In what ratio must he mix the two so that a profit of 20% is realized by selling the mixture at ksh.36 per kg?
29.
Find the value of x in; Cos (3x – 30) = Sin (7x + 50)
30.
Solve the simultaneous inequalities and state the integral values.
4
x
-
3
≤
6
+
x
-
8
-
3
x
<
x
+
4
31.
The distance s meters of an object varies partly with time t seconds and partly with square root of time. Given that s = 16 when t = 4 and s = 48 when t = 16. Write an equation connecting s and t.
32.
Show that for the sum of the values of x in the diagrams below is:
10
±
2
√
5
33.
The figure below shows a circle center O, radius 10 cm. The chord PQ = 16cm. Calculate the area of the unshaded region.
34.
The velocity of a particle after t seconds is given by
V
=
20
t
–
2
t
2
. If the particle starts from rest at point O and moves along a straight line; it comes momentarily to rest at point P and starts moving again back towards O. Determine: (a) The time when the particle reaches O while on its way back from P. (b) The expression for its acceleration a.
35.
A business lady bought 180 mangoes at Shs.60 for every five mangoes. She sold some of them at Shs.30 for every three and the rest at Sh.30 for every four. If she made a
33
1
3
%
loss, calculate the number of mangoes sold at Shs.30 for every four.
36.
Write an equation of a circle that has a diameter whose end points are at (2,7) and (-6, 15) in the form
x
2
+
y
2
+
a
x
+
b
y
+
c
=
0
where a,b and c are integers
37.
Express y in terms of d, given that
d
=
3
√
y
-
1
y
+
1
38.
The size of an interior angle of a regular polygon is
x
2
while its exterior angle is 3x. Find the number of sides of the polygon
39.
Without using logarithms table, solve the equation
log
(
5
x
-
4
)
=
log
(
x
-
2
)
+
1
3
log
27
40.
By completing the square, solve for x in the equation
2
x
2
-
6
=
x
.
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