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Form 2 Mathematics Revision Questions and Answers Set 3
Find the integral values of X which satisfy the inequalities
3
x
–
2
<
10
x
≤
2
+
5
x
(2m 19s)
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1.
The marked price of a modern camera is Ksh. 24,000. A trader sold it to a customer at a 10% discount. If the trader still made a profit of 20% on the cost price, what was its cost price?.
2.
The gradient of a line L through A (2x, 4) and B(-1, x) is
1
7
. Find the equation of line perpendicular to L through B.
3.
Two similar container hold
2000
c
m
3
and 6.75 litres respectively. If the smaller container has a diameter of 15.50cm. What is the radius of the larger container correct to 1 decimal place.
4.
A truck left Nairobi at 7.00am for Nakuru at an average speed of 60km/h. At 8.00am a bus left Nakuru for Nairobi at an average speed of 120km/h. How far from Nairobi did the vehicles meet if Nairobi is 180km from Nakuru
5.
Given that
3
5
x
-
2
y
=
243
and that
3
2
x
-
y
=
3
, calculate the value of x and y.
6.
2
3
of the animals on a farm are cows and
3
4
of the remainder are goats and the rest are Sheep. If there are 100 sheep what would be the angle in a pie chart that would represents sheep and cows respectively.
7.
Solve for y
3
2
-
5
3
y
>
8
+
y
2
8.
How much will Pauline get correct to the nearest fifty cents when she changes Tsh 200 000 into Kenya shillings, if she is charged 2% commission on a day when the exchange rate between Kenya and Tanzanian is Ksh 1 = Tsh 17.3.
9.
Simplify
5
(
x
-
2
y
)
-
2
(
x
-
8
y
)
x
2
-
4
y
2
10.
Given that the column vectors P =
(
-
3
4
)
q=
(
16
-
4
)
r =
(
9
6
)
and that a = 2p -
3
4
q +
2
3
r Express a as a column vector and hence calculate its magnitude
11.
A two digit number is such that 4 times the units digit exceeds the tens digit by 1. If the digits are reversed, the number formed is decreased by 45. Find the number.
12.
A boy walk directly from point Q towards the foot of a vertical flag post 200m away. After covering a distance of 140m, he observes the angle of elevation of the top of the flag post as 75°. Calculate the angle of depression of point Q from the top of the flag post.
13.
Solve for x and y in the simultaneous equations below. xy + 6 = 0 x – 2y = 7
14.
Evaluate
2
1
2
o
f
1
3
4
-
5
1
4
1
2
5
+
2
(
1
1
4
-
2
3
4
)
15.
Find the area of triangle ABC in which AB = 13.6cm, BC = 4.2cm and AC = 10.2cm
16.
Makau, Wanjiru and Kemboi start a race at 9.03 a.m. in the same direction to run around a circular course. Makau makes the circuit in 252 seconds. Wanjiru in 308 seconds and Kemboi in 198 seconds. If they start from the same point, at what time will they next be all at the starting point together?
17.
Momanyi spent one eighth of his February salary on farming, half on school fees and two thirds of the remainder on food. Calculate his February salary and the amount he spent on school fees if he spent sh. 3200 on food.
18.
Evaluate without using tables or calculators
√
45
×
(
2.04
)
2
2.89
×
√
0.05
19.
Three pens and four exercise books cost Sh. 87. Two pens and five exercise books cost Sh. 93. Find the cost of one pen and one exercise book.
20.
Find the integral values of X which satisfy the inequalities
3
x
–
2
<
10
x
≤
2
+
5
x
21.
ABCD is a rhombus. A is the point (2, 1) and C is the point (4, 7). Find the equation of the diagonal BD in the form ax + by = c.
22.
A man walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes that the angle of elevation of the top of the building is 450.Determine the angle of elevation of the top of the building from A.
23.
A straight line L1 is perpendicular to another line L2 whose equation is 3y+4x=12. If the two lines meet at point P which lies on the x-axis,find: i) The co-ordinate of point P. ii) The equation of line L1 in the form y=mx+c
24.
Mr. Ochuodho who deals in electronics sells a radio to a customer at Kshs. 1,440 after giving him a discount of 10% but finds that he still makes a 20% profit. Find the profit Mr. Ochuodho would make if he does not give a discount.
25.
A solid block in the shape of a cylinder has a height of 14cm and weighs 22kg. If it is made of material of density 5g/
c
m
3
find the radius of the cylinder. Take
π
=
22
7
26.
Simplify completely by factorization
20
-
45
x
2
6
x
2
-
x
-
2
27.
Solve the simultaneous inequalities given below and list all the integral values of x
3
-
x
2
≥
x
+
1
3
≥
2
x
+
1
-
3
28.
Patricia a student at Ongeti mixed Secondary bought 5 pens and 3 exercise books from solving supermarket at Kshs. 135, at the same time Jane her class mate also bought 4 pens and 5 exercise books and spent Ksh. 25 more than Patricia. Find the cost of each pen and exercise book
29.
Given that
sin
(
3
x
-
35
)
0
–
cos
(
x
+
20
)
0
=
0
and x is an acute angle, find its value.
30.
A train of length 80m crosses a bridge 20 m long in 5 seconds. Calculate the average speed of the train in km/h
31.
Mr. Ombogo the principal of Chiga secondary would wish to cover the floor of the new administration block using the square tiles. The floor is a rectangle of sides 12.8m by 8.4m. Find the area of each of the largest tiles which can be used to fit exactly without breaking
32.
The exterior angle of a regular polygon is an eighth of interior angle. How many sides does the regular polygon have?
33.
Solve
2
8
x
=
512
34.
The ratio of the area of two similar rooms is
4
25
(a) Find the ratio of their length. (b) Find the area of the bigger room if the area of the smaller room is
8
m
2
35.
A ladder leans against a wall so that its foot is 2.5m away from the foot of the wall and its top is 4m up the way. Calculate the angle it makes with the ground.
36.
Solve the following inequalities and represent the solution on a number line hence state the integral values
7
x
–
4
≤
9
x
+
2
<
3
x
+
14
37.
A minibus covered a distance of 210km at an average speed of 90km/h. If it travelled
2
3
of the distance at a speed of 105 km/h, at what speed did it travel the rest of the distance?
38.
Find the value of x given that:
2
x
=
0.0625
39.
When a piece of cloth was washed, it shrank. Its length decreased from 150 cm to 120 cm.In what ratio did it decrease?
40.
Find these statistics of the following data 4, 2, 2, 6, 1, 3, 4, 1, 4 a) Mode b) Median c) Mean
41.
Solve for x in the equation
32
x
-
1
÷
8
x
-
4
=
64
÷
2
x
42.
Solve for y in the equation:
5
2
y
+
1
=
4
(
5
)
y
+
1
-
15
43.
If X is a positive integer, find all possible values of x given that
1
<
2
5
x
2
<
7
44.
Given that:- r = 5i – 2j and m = -2i + 6j – k are the position vectors for R and M respectively.
45.
Given that: a =2i +j -2k and b = -3i +4j –k find:- /a + b/
46.
Equal squares as large as possible are ruled off on a rectangular board 54cm by 78cm.Find the size of each square. How many squares are there?
47.
Find the integral values of x which satisfy the simultaneous inequalities
4
x
-
3
<
12
+
2
x
<
2
+
5
x
48.
Simplify and give your answer in the simplest form:
1
2
o
f
3
1
2
+
1
1
2
(
2
1
2
-
2
3
)
3
4
o
f
2
1
2
÷
1
2
49.
Solve for x in the equation:
2
3
x
+
2
+
8
x
=
160
50.
Find the equation of a line passing through (2,-3) and is perpendicular to the line 4y -6x +5= 0.Give your answer in the form ax +by +c = 0.
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