SS3 Mathematics Examination Questions and Answers [Free]

TOPIC: ARITHMETIC AND GEOMETRIC PROGRESSION

DIRECTION: Choose the correct answer from the lettered options.

1. Find the number of term of the sequence that will make up 240. The given

sequence are 13, 16, 19, 22, ……………

 A. 9

 B. 17

 C. 27

 D. 29

The correct answer is option [A]. Solution: Hint [The question forms A.P.]. Using the

equation Sn = – 1) d]/2, where a = 13, d = 3, Sn = 240. Solve using the formula

given.

2. If the second and fourth terms of a G.P. are 8 and 32 respectively, what is the sum

of the first four terms?

 A. 28

 B. 40

 C. 48

 D. 60

The correct answer is option [D].

The general form of a G.P. is a, ar, ar2,…., arn – 1 (for n terms).

Here ar =second term = 8; ar3

 = fourth term = 32. [ar3

/ar = r2

]

32/8 = 4 = r2 (r = (4 = 2 (where r=common ratio, a = 1st term).

For ar = 8

2a = 8

a = 4

For r >1, sum =

a[rn – 1]/r – 1,

where n = 4, r = 2, a = 4.

Then 4[24 – 1]/2 – 1 = 4 x 15/1 = 60.

3. Calculate the sum of the tenth terms of the G.P. 5, -21

⁄2, 11

⁄4 ……………

4. If the 8th term of an A.P. is twice the 4th term and the sum of the first 5 terms is 47,

find the common difference.

 A. 6.31

 B. 3.13

 C. 4.42

 D. 2.24

The correct answer is option [B]. Solution: Un = a + [n – 1]d; U8 = 2U4; U8 = a + [n – 1]d,

where n = 8; 2U4 = 2[a + (n – 1)d], where n = 4; a + [8 – 1]d

= 2[a + (4 – 1)d]; a + 7d = 2[a + 3d]; a + 7d = 2a + 6d; 7d – 6d = 2a -a; d = a………[i];

Sn = -1 )d]/2; S5 = – 1)d]/2 = 47; 2.5[2a + 4d]; recall that a = d,

therefore, 2d + 4d = 47/2.5; 6d = 18.8; d = 18.8/6 = 3.13.

5. The 4th term of an A. P. is 13 while the 10th term is 31. Find the 21st term.

 A. 175.

 B. 85.

 C. 64.

 D. 45.

The correct answer is option [C]. Solution:

The 4th term = a + 3d;

The 10th term = a + 9d;

a + 3d = 13 —— [i];

TOPIC: BEARINGS

DIRECTION: Choose the correct answer from the lettered options.

1. The bearing of a point A from a point B is 042o. Calculate the bearing of B from A.

 A. 228o

 B. 222o

 C. 138o

 D. 48o

The correct answer is option [B].

2. A ladder of length 5m rests against a vertical wall and makes an angle of 60o with

the ground. How far is the foot of the ladder from the wall?

 A. √3/2m

 B. 2 1

/2m

 C. 5√3/2m

 D. 5m

The correct answer is option [B].

3. The angle of depression of a tree when compared to the length of its shadow on

the level ground is 28o

 and the length of its shadow is 9.78m. What is the height of

the tree?

 A. 6.64m

 B. 5.50m

 C. 5.20m

 D. 4.20m

The correct answer is option [C].

4. The bearing of a bird on a tree from a hunter on the ground is N72°E. What is the

bearing of the hunter from the bird?

 A. S18°W

 B. S72°W

 C. S72°E

 D. S27°E

The correct answer is option [B].

5. The angle of elevation of a storey building from a point X on the ground is  o and

the distance from the point X to the foot of the building is 80cm. If the height of the

 A. 90.9o

 B. 81.3o

 C. 41.2o

 D. 39.1o

The correct answer is option [C].

6. Three villages X, Y and Z, are connected by level roads. |XY| =5km, |YZ| = 4km and

XŶZ = 160o. Find |XZ| to 2 significant figures

 A. 12.4km

 B. 11.4km

 C. 8.9km

 D. 3.4km

The correct answer is option [C].

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