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Form 3 Mathematics Revision Questions and Answers Set 2
Express each of the following as a single fraction in its simplest form:
a).
x
+
y
3
-
2
x
-
y
2
b).
1
x
+
1
-
1
x
-
1
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1.
Use logarithms to evaluate
34.33
√
5.25
×
0.04
2.
Solve the equation below.
2
x
+
5
3
-
6
-
2
x
2
=
2
3.
Find all the integers satisfying the inequalities.
3
-
2
x
<
x
-
3
≤
4
4.
Two grades of tea premium and Gold costing Ksh 200 and Ksh 250 per kg respectively are mixed in the ratio 3: 5 by weight. The mixture is then sold at Ksh 260 per kg. Find the percentage profit on the cost price.
5.
Make q the subject of the formula.
P
=
3
√
n
q
-
m
q
6.
Given that;
1
3
-
√
5
-
2
+
2
√
5
3
+
√
5
=
a
+
b
√
c
. Find the values of a, b and c
7.
Find the radius and centre of a circle whose equation is
X
2
+
4
x
+
y
2
–
8
y
+
11
=
0
.
8.
The probability that our school will host soccer and rugby tournament this year is 0.8. If we host the probability of winning soccer is 0.7. If we do not host the probability of winning soccer is 0.4. If we win soccer the probability of winning rugby is 0.8, otherwise if we lose the probability of winning rugby is 0.3. a) Draw a tree diagram to represent this information. b) Use the tree diagram
9.
Given that;
sin
(
3
x
–
50
)
0
–
cos
(
x
+
20
)
0
=
0
and x is an acute angle; find the value of x
10.
The difference between two positive integers is 5 and the sum of their squares is 73. Find the integers.
11.
Find the value of x given that the matrix below is a singular matrix.
[
2
x
-
1
1
x
2
1
]
12.
The diagram below shows a circle centre O. AP is the tangent to the circle. Angle OPA is
23
0
. Find the length of the tangent.
13.
Solve for x in the given equation.
2
+
log
7
(
3
x
–
4
)
=
log
7
98
14.
a) Using a ruler and a compass only, construct triangle ABC in which BC = 8 cm, angle ABC = 30° and angle ACB = 45°. (b) At A drop a perpendicular to meet BC at D and measure AD.
15.
The position vectors of A and B are
(
2
5
)
and
(
8
-
7
)
respectively. Find the magnitude of the vector AB
16.
Two bags A and B contain similar balls. Bag A contains three red and two black balls. Bag B contains four red and three black balls. A ball is picked from each bag. Find the probability that the balls are of the same color.
17.
Solve for x log (x+2) =1+log (4x-3)
18.
Find without using tables or a calculator the value of
1.33
×
0.51
0.19
×
0.0017
19.
The ratio of the size of the exterior angle to the interior angle of a regular polygon is 1:3. Determine the number of sides of the polygon and name it.
20.
Given that 2x²–kx+18 is a perfect square, find k and hence solve the equation 2x²–kx+18=0 by factorization.
21.
Mr. Kanja,Miss Kanene and Mrs Nyaga have to mark a form three math contest for 160 students. They take 5mins, 4mins, and 12mins respectively to mark a script. If they all start to mark at 9.00 am non-stop, what is the shortest time they can take to complete the marking?
22.
Jackie takes 5minutes to run a distance of 1km in a race. Express her speed in a) km/hr b) m/s
23.
A man left
1
5
of his estate in Kerugoya to his wife and
1
3
to each of his two sons .The remainder was to be shared equally among his six brothers. If the estate was worth sh 3 456 000, how much did each of those people get?
24.
A distance of 12km is represented by a length of 4cm on a map. Given that the scale of the map is 1:n, find the a) value of n b) actual area in hectares of a field on the map with an area of 32cm²
25.
Solve the equation
1
3
(
x
+
4
)
–
1
2
(
2
x
–
4
)
=
2
26.
The sides of a right angled triangle measured to the nearest cm are 5cm, 12cm and 13cm Determine the a) limits within which the measured dimensions lie b) percentage error in the area of the triangle.
27.
The coordinates of points A and B are A (2, 3) and B (4,–5). M is the midpoint of vector AB.Determine the coordinates of point M and the magnitude of vector BM.
28.
The equation of line L is y=3x–4 and is perpendicular to line H. They cross each other at the y-intercept of line L. Find the equation of line H.
29.
Solve for a in
3
2
a
+
3
=
2187
30.
The marked price of a car in a dealer’s shop was Ksh.450,000/=. Magari bought the car at 7% discount. The dealer still made a profit of 13%.Calculate the amount of money the dealer had had spent on buying the car.
31.
Solve the following inequality and show your solution on a number line.
4
x
–
3
≤
1
2
(
x
+
8
)
<
x
+
5
32.
Solve for x in the equation Sin (4x-10)-Cos (x+60)=0
33.
A man invests Ksh.24, 000 in an account which pays 16% interest p.a. the interest is compounded quarterly. Find the amount in the account after
1
1
2
years.
34.
Find all the integral values of x which satisfy the inequalities.
x
+
8
>
4
x
-
6
≥
3
(
4
-
x
)
35.
Agnes paid rent which was 1/10 of her net salary. She used ½ of the remaining amount to make a down payment for a plot. She gave her mother Kshs. 2,500 and did shopping worth Kshs. 7,500 for herself. She saved the remainder which was Ksh. 12,500. How much was the down payment that she made.
36.
Truncate 3.2465 to a.3 decimal places b.3 significant figures
37.
An error of 0.5 kg was found when measuring the mass of a bull. If the actual mass of the bull was found to be 200kg.Find the relative error
38.
The thickness of a coin is 0.20 cm. a).Find the percentage error. b).What would be the percentage error if the thickness was stated as 0.2 cm ?
39.
What is the error in the sum of 4.5 cm and 6.1 cm?
40.
What is the error in the difference between the measurements 0.72 g and 0.31 g?
41.
Evaluate
1
2
+
1
6
o
f
(
13
18
-
5
9
)
÷
1
3
42.
Express each of the following as a single fraction in its simplest form: a).
x
+
y
3
-
2
x
-
y
2
b).
1
x
+
1
-
1
x
-
1
43.
The sum of the interior angles of a polygon is
1440
0
. Find the number of the sides of the polygon.
44.
There are a number of unspecified numbers of cows and hens in a den. If there are total of 30 heads and 80 legs in the den, find the number of cows and hens in the den.
45.
The price of a commodity was increased in the ratio 5:4. After one month, the price of the same commodity was reduced in the ratio 7:8 to attract more customers. If the new price was sh. 35, calculate the price of the commodity before the increase.
46.
Take a number n, double it and add five to the result. If this result is doubled again, the new number is 22. Find n.
47.
Solve the following simultaneous equations: 3x+4y=18 2x-y=1
48.
Hussein was allowed a discount of 11% for goods worth sh. 8,000 and a discount of 8.6% for goods worth sh. 17,000. What percentage discount was she allowed altogether?
49.
John and Fred have goats. John has more goats than Fred and if Fred gives john one of his goats, john will have twice as many goats as Fred. If john gives Fred one of his goats, they will have an equal number of goats. How many goats does each have?
50.
Solve for t in the equation
9
t
+
1
+
3
2
t
=
30
.
51.
A line L1 passing through points A(6,4) and B(-1,3) is perpendicular to a line L2 at point B. Find the equation of the line L2 in the form ax + by = c .
52.
Find all the integral values of x which satisfy the inequalities
x
+
11
>
4
x
–
9
≥
2
(
2
–
x
)
53.
The position vectors of X and Y are X= 2i + 4j and Y =3i – 2j respectively. Express XY as a column vector and hence find |XY| ,leaving the answer in 2 significant figures.
54.
The size of each interior angle of a regular polygon is
x
0
and each exterior angle is
x
-
36
3
Calculate the sum of interior angles in the polygon.
55.
The height of cylindrical solid is three times the radius of the circular end. If the total surface area of the solid is
616
c
m
2
, find its radius.
56.
Given that tan x = 2.4, evaluate without use of tables and calculator, sin x – cos x in the form
a
b
where a and b are integers.
57.
Given that
x
x
+
2
y
=
3
8
.Find the ratio x : y
58.
If
√
2
-
√
3
√
2
+
√
3
=
a
+
b
√
c
where a, b and c are rational numbers find the value of b.
59.
In an election for a school captain, a number of students voted for Mandzu, Jamal and Biasha. In a pie chart,the angles representing the total number of votes for Mandzu and Jamal were
81
0
and
216
0
respectively. If Biasha got 84 votes, how many votes did Jamal get?
60.
Given that
(
x
-
1
x
+
1
3
x
x
)
is a singular matrix, find the possible values of x.
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