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Form 2 Mathematics Mixed Revision Questions With Answers Set 2
Solve the equation am + bn = r, given that m =
(
-
3
-
2
)
n =
(
0
4
)
r =
(
-
6
0
)
and a and b are scalars.
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1.
Find the equation of a line which is parallel and midway between the lines
y
x
-
3
=
1
and
y
-
2
x
-
1
= 1
2.
Find the area of a triangular piece of land whose sides are 7m, 9 m and 14 m.
3.
ABCDEFGH is a cube of side 8 cm. If N is the midpoint of AB, find the area of triangle HNG.
4.
Three spacecrafts in different orbits go around the earth at intervals of 3,6 and 7 hours respectively. An engineer at an observatory on earth first observes the three crafts cruising above one another at 6.35 am. At what time will they be text observed in a similar configuration if they all revolve around the earth from east to west?
5.
Find a if
a
4
-
15
a
2
-
34
=
0
.
6.
Find the area of a parallelogram ABCD in which AB = 12 cm, BC = 16 cm and
∠
ABC = 25°
7.
The mean mass of x objects is x kg and the mean mass of y is y kg. Show that the mean mass of the remainder is x + y.
8.
By substituting x + 2y =p in the equation
(
x
+
2
y
)
2
+
3
(
x
+
2
y
)
-
4
=
0
, solve the quadratic equation in p. Hence, find possible values of x + 2y. If x - 2y = 4, find all the possible values of x and y.
9.
The logarithms of the squares of a and b are 1.204 and 0.954 respectively. Find the logarithm of their product.
10.
Find the number of cubes, each of side 19 cm, that can be made from a rectangular sheet of metal measuring 2.28 m by 1.52 m.
11.
The length L of a pendulum whose complete swing takes a total time T is given by the formula
L
=
T
2
g
4
p
2
. Calculate L when T = 2.31, g = 9.81 and
π
=3.142.
12.
Find all the points having integral co-ordinates which satisfy the three inequalities:
y
≥
6
-
x
,
y
≤
x
+
4
and x < 4.
13.
Find the region satisfied by the inequalities;
y
≥
0
,
y
+
x
<
5
and
2
x
+
y
≥
4
. (a) State the points of intersection of the boundary lines. (b) Find the area of the region.
14.
A triangle whose vertices are A (4, 6), B(3, 4) and C (5, 4) is enlarged with scale factor -1 and centre of enlargement (4, 0). The image is then reflected in the line y= - x followed by an enlargement with linear scale factor - 1 and centre (0, 0). Find the co-ordinates of the vertices of the final image.
15.
Calculate the radius of a sphere whose volume is 259
c
m
3
. (take
π
= 3.142)
16.
Find the area of the region bounded by the inequalities
y
≤
1
2
(
2
x
+
4
)
, y < 3 (2 - x) and y > 0. If the region is reflected in the line x = 0 followed by a reflection in y =0, write down the inequalities satisfying the final image.
17.
Two spheres have surface areas of 36
c
m
2
and 49
c
m
2
respectively. If the volume of the smaller sphere is 20.2
c
m
3
, calculate the volume of the larger one.
18.
Simplify:
(
a
-
c
)
2
-
(
a
+
c
)
2
(
a
2
+
c
2
)
2
-
(
a
2
-
c
2
)
2
. Find the value of the expression when a =
1
3
and c =
1
17
.
19.
A pond holds 27 000 litres of water. Find the number of litres of water a similar pond would hold if its dimensions were double the first one.
20.
(a) A shopkeeper makes a profit of Sh 200 by selling 20 blankets and 50 towels. He makes a loss of Sh 7 if he sells 35 blankets and 28 towels of the same kind. Determine the profit (or loss) on each of the two items sold. (b) If he sold 12 blankets, find the number of towels he should sell to realize an overall profit of Sh 3012.
21.
Find the area of the quadrilateral below.
22.
The length of an arc of a circle is
1
10
of its circumference. If the area of the circle is 13.86
c
m
2
, find: (a) the angle subtended by the arc at the centre of the circle. (b) the area of the sector enclosed by this arc.
23.
A model of a tent consists of a cube and a pyramid on a square base as shown below: Calculate the total surface area of the model (floor inclusive)
24.
Solve the equation am + bn = r, given that m =
(
-
3
-
2
)
n =
(
0
4
)
r =
(
-
6
0
)
and a and b are scalars.
25.
Find the volume of a prism 15 cm long and whose cross-section is a regular heptagon of side 10 cm.
26.
In the figure below, 0 is the centre of the circle,
∠
POQ = 90° and PQ = 24 cm: Find: (a) the area of the sector POQ. (b) the area of the shaded region.
27.
Find the area of the figure below if AD = 15 cm, BC = 10 cm,
∠
AED =
∠
ADB =
∠
BCD = 90° and
∠
BDC = 30°.
28.
John walks 4.8 km due north from point A to B and then covers a further 6 km due east to C. What is the shortest distance from A to C?
29.
The figure below is a cube of side 6 cm: Calculate the length: (a) AC (b) AG (c) AF
30.
The area of a rhombus is 442
c
m
2
. If one of its diagonal is 34 cm long, find: (a) the length of the other diagonal (b) the length of the side of the rhombus
31.
The base of a solid right pyramid is a regular hexagon of side 8 cm. If the slant edges are 10 cm, find the: (a) surface area of the pyramid. (b) volume of the pyramid.
32.
The cross-section of a prism is a triangle with sides 3 cm, 5 cm, and 7 cm. If the prism is 12 cm long, find its volume.
33.
Given that cos x = sin (3x + 10), find: (a) x (b) tan x
34.
A television aerial is held upright by a wire 16 m long which is fixed to the top of the aerial and to the ground 3 metres from the foot of the aerial. Find the angle of inclination of the wire to the ground.
35.
A frustum of height 6 cm is cut from a pyramid whose base is a square of side 20 cm and height 14 cm. Find the volume of the frustum.
36.
The radius and height of a cylinder are 3.5 cm and 6.5 cm respectively. Calculate the surface area, the height and the radius of a similar cylinder whose volume is 2 002
c
m
3
. (take
π
=
22
7
)
37.
In the figure below AG=GH=EJ=ED=4 cm. AH=BH=CJ=DJ and AB=CD. Calculate: (a) CJ and DC. (b) the ratio of the area of AGH to ABH. (c) the ratio of the volume of AHJDEG to ABCDJH. (d) the volume and the surface area of the whole block if GE = BC = 2DJ.
38.
The area of the figure below is A
c
m
2
and its perimeter is P cm. If A = P+8, find x.
39.
Find the surface area of a cone whose height is 5.2 cm and volume 49
c
m
3
.
40.
A boy's shadow is 2.2 m long when the angle of elevation is from the tip of the shadow to his head is 30°. Calculate the height of the boy.
41.
Calculate the volume of a cone whose base radius is 5 cm and curved surface area is 109.9
c
m
2
.
42.
Find the length of a side of a regular pentagon whose vertices lie on the circumference of a circle of radius 5 cm.
43.
A man walks 1 km on a bearing of 140°. How far is he; (a) east of the starting point? (b) south of the starting point?
44.
A triangle ABC is such that
∠
BCA = 90°, BC = 48 cm and
∠
ABC =60°. Determine lengths AB and AC.
45.
An observer stationed 20 m away from a tall building finds that the angle of elevation of the top of the building is 68° and the angle of depression of its foot is 50°. Calculate the height of the building.
46.
Calculate the volume of metal required to make a hemispherical bowl with internal and external radii 8.4 cm and 9.1 cm respectively.
47.
Onyango observed a hawk exactly overhead at the same time as Kamau observed it at an angle of elevation of 50°. If Onyango and Kamau were 25 m apart on a level ground, how high was the hawk above the ground, given that Kamau's eye level was 172 cm above the ground?
48.
A straight road rises steadily at an angle of 4° to the horizontal. If a car travels 2 km up the road, calculate its vertical and horizontal displacement.
49.
A pyramid PQRST has a rectangular base QRST. If the base of the pyramid measures 8 cm by 4 cm and perpendicular height is equal to the diagonal of the base, find its volume and surface area.
50.
A ladder 8m long is leaning against a vertical wall. The ladder makes an angle of 70° with level ground. Calculate the distance of the top of the ladder from the ground.
51.
Find the value of the unknown lengths in each of the following diagrams:
52.
The figure below shows a cone in which angle VYX = 30° and VY = 46 cm. Calculate the height and diameter of the cone.
53.
AB is a chord of a circle with centre 0 and radius 12.3 cm. If
∠
OAB 70° calculate the length AB and the distance of 0 and AB.
54.
Find the radius of a cone whose height is 8 cm and volume 115
c
m
3
.
55.
The two parallel sides of a trapezium measure 12 cm and 9 cm. A third side measures 10.4 cm and makes an angle of 50° with the longest side. Calculate the area of the trapezium.
56.
A bucket is 44 cm in diameter at the top and 24 cm in diameter at the bottom. Find its capacity in litres if it is 36 cm deep.
57.
The figure below shows a tetrahedron ABCD in which AC = 8 cm and BC = 7 cm. AD and BD are perpendicular to CD and
∠
CAD = 36°. (a) Calculate: (i) AD (ii) CD (iii) BD (iv)
∠
BCD
58.
Find the radius of a hemispherical bowl which can hold 0.5 litres of liquid.
59.
The dimensions, in centimetres, of a rectangle are (2n + 3) by (n + 1) and its area is 817
c
m
2
. Determine the length of the diagonal.
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