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Form 3 Mathematics Revision Questions and Answers Set 1
Solve the logarithmic equation below for the value of x
log
10
(
3
x
+
1
)
-
log
10
(
x
–
2
)
=
log
10
10
(1m 39s)
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1.
A straight line, L, passes through the point with coordinates (4, 7) and is perpendicular to the line with equation y = 2x + 3. Find an equation of the straight line L.
2.
Simplify completely
3
x
2
+
9
x
x
2
-
9
3.
Find the value of c in the equation
7
-
5
c
9
=
32
4.
Make t the subject of the formula.
S
=
3
√
3
Q
-
4
t
R
+
t
5.
Three businessmen Njoroge, Mwaura and Kimani contributed a total of sh. 82, 250 to start a business. The ratio of the contribution of Njoroge to Mwaura was 2:3 and that of Mwaura to Kimani was 4:5. How much did Kimani contribute?
6.
Coordinates of points A and B are (2, -3) and (6, 5) respectively. Given that N is a point on AB such that the ratio AN: NB = 1:3, find the coordinates of point N.
7.
Find the integral values of x which satisfy the compound inequality
2
(
2
-
x
)
<
4
x
–
9
<
x
+
11
8.
A volume of 0.05 litres of water is poured into an empty measuring cylinder. A piece of metal with mass 135g is put into the cylinder. If the density of the metal is 9600 kg/
m
3
find the new reading of the cylinder.
9.
A newspaper vendor has 30 bank notes with a total value of Sh. 900, if the notes are either in Sh. 20 or Sh. 50 denominations, how many of each does he have?
10.
A trouser whose marked price is Kshs 800 is sold to a customer after allowing him a discount of 13%. If the trader makes a profit of 20%, find how much the trader paid for the trouser.
11.
(a) Find the inverse of the matrix.
[
1
2
2
2
]
(b)Hence solve the simultaneous equations. x + 2y = 21 2x = 34 – 2y
12.
The length of a rectangle was increased by 30% while its width decreased by 15%. Determine the percentage change in the area of the rectangle.
13.
Without using tables, solve the equation.
log
10
(
10
x
+
50
)
–
log
10
(
x
-
4
)
=
2
14.
The sum of interior angles of a triangle is given by
(
10
x
-
2
y
)
0
while that of a hexagon is given by
(
30
x
+
24
y
)
0
.Calculate the values of x and y
15.
The third term and the sixth term of a geometric series are
3
1
3
and
11
1
4
respectively. Calculate the (a) Common ratio (b) First term
16.
The hire purchase price of a machine is sh 36750. If 10% is paid as deposit and the rest of the money is spread over 15 equal monthly instalments, find the amount payable every month.
17.
Solve for ?? in the equation
125
-
x
×
5
2
(
x
-
2
)
=
25
x
+
2
18.
A rhombus ABCD with its side 15cm and diagonal AC = 24cm. Find the other diagonal BD
19.
The length of three wires are 36m, 48m and 72m. Pieces of wire of equal lengths were cut from the three wires, calculate the least number of pieces obtained.
20.
A two-digit number is such that the sum of the digits is 14. When the digits are reversed its value is 36 more than the original number. Find the original number.
21.
A rectangular card measures 5.3 cm by 2.5 cm. find a) The absolute error in the area of the card b).The relative error in the area of the card
22.
Given
8.6
c
m
÷
3.4
c
m
Find: a).The absolute error in the quotient. b).The relative error in the quotient.
23.
Find AC in the figure below, if AB= 4 cm, BC = 6 cm and
A
B
C
=
60
0
24.
Simplify the following. i).
3
√
2
+
5
√
2
ii).
8
√
5
-
2
√
5
25.
Simplify
log
6
9
+
log
6
8
-
log
6
2
26.
Simplify 2log 5 + 2log 2
27.
Solve for x
4
x
=
12
28.
Solve for x:
log
5
(
x
+
1
)
+
log
5
(
x
-
3
)
=
1
29.
Franny invests ksh 16,000 in a savings account. She earns a simple interest rate of 14%, paid annually on her investment. She intends to hold the investment for 1 year. Determine the future value of the investment at maturity.
30.
Calculate the rate of interest if sh 4500 earns sh 500 simple interest after 1 year.
31.
Esha invested a certain amount of money in a bank which paid 12% p.a. simple interest. After 5 years, his total savings were sh 5600.Determine the amount of money he invested initially.
32.
Find the amount accrued if ksh. 1000 is invested for 2 years at 10% per annum compound interest.
33.
Find the amount accrued when ksh. 6250 is invested for 2 years at 4% per annum compound interest.
34.
An iron box cost ksh 500 and every year it depreciates by 10% of its value at the beginning of that that year. What will its value be after 4 years?
35.
A minibus cost sh 400000.Due to wear and tear, it depreciates in value by 2 % every month. Find its value after one year
36.
Aching wants to buy a sewing machine on hire purchase. It has a cash price of ksh 7500.She can pay a cash price or make a down payment of sh 2250 and 15 monthly instalments of sh.550 each. How much interest does she pay under the instalment plan?
37.
The initial cost of a ranch is sh.5000, 000.At the end of each year, the land value increases by 2%.What will be the value of the ranch at the end of 3 years?
38.
Find the time in which ksh. 15625 will amount to ksh. 17576 at 4% compound interest.
39.
Find the compound interest on ksh.5000 at 20% per annum for 1.5 years compound half yearly.
40.
Find compound interest on ksh. 47145 at 12% per annum for 6 months, compounded quarterly.
41.
Evaluate without using calculator
(
1
3
7
-
5
8
)
×
2
3
3
4
+
1
5
7
÷
4
7
o
f
2
1
3
42.
Find all integral values of x which satisfy the inequalities.
2
(
2
–
x
)
<
4
x
–
9
<
x
+
11
43.
Simplify the expression
p
2
-
4
m
2
2
m
2
-
7
m
p
+
3
p
2
44.
Solve the logarithmic equation below for the value of x
log
10
(
3
x
+
1
)
-
log
10
(
x
–
2
)
=
log
10
10
45.
Solve using completing square method
4
x
2
–
12
x
+
9
=
0
46.
Calculate the compound interest on sh.9,000 for 2 years at 12.5% p.a compounded half yearly.
47.
Simplify
125
2
3
÷
3
4
243
-
2
3
48.
Determine the equation of the line through the point A(5,3) and parallel to the line y=2x+3
49.
Without using a calculator, evaluate:
2
1
2
-
1
1
5
o
f
2
1
4
-
(
-
1
4
)
3
50.
Without using mathematical tables or calculators, evaluate:
0.38
×
0.23
×
2.7
0.114
×
0.0575
51.
Make M the subject of the formulae
K
=
(
M
V
2
X
+
M
)
52.
A quantity R varies partly as X and partly inversely as y. Find the equation connecting R, X and y, when X = 1, y = 2and R = 4, when X = 3, y = 2 and R = 10.
53.
Solve for x in 2 log x + log 6 = 2 + log 9
54.
There are three athletes A, B and C in a 100m race. A is twice as likely to win as B, while B is twice as likely to win as C. Find the probability that:- (a)A does not win the 100m race. (b)Either B or C wins the 100m race.
55.
Given that (5m – 2n): (2m – n) = 7:5. Find the ratio m: n
56.
Indian type A of rice costs ksh. 70 per kilogram while Egyptian type B of rice costs ksh 84 per kilogram. A shopkeeper mixes the two types of rice in the ratio 4:3 respectively. At what price must he sell the mixture to make a profit of 26% per kilogram?
57.
A bus and a matatu starts from Nairobi to Kisii via Narok at the same time making a distance of 280km. The matatu averages 20km/h faster than the bus and reaches there 1 hour 36minutes earlier. Determine the speed of the bus.
58.
Evaluate without using a calculator.
5
6
o
f
(
4
1
3
-
3
5
6
)
5
12
×
3
25
+
1
5
9
÷
2
1
3
59.
The interior angle of a regular polygon is
108
0
. How many sides has the polygon?
60.
A salesman is paid a salary of Sh. 10,000 per month. He is also paid a commission on sales above Sh. 100,000. In one month he sold goods worth Sh. 500,000. If his total earnings that month was Sh. 56,000. Calculate the rate of commission.
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