METHODIST GILRS’ HIGH SCHOOL, YABA, LAGOS.

FIRST TERM EXAMINATION, 2023/2024 ACADEMIC SESSION

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SUBJECT: MATHEMATICS CLASS: SS 3 TIME: 3 HRS.
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SECTION A: OBJECTIVES, INSTUCTION: ANSWER ALL QUESTIONS IN THIS SECTION (1 HOURS)
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D. { 1 , 2, 3 , 5 ,7 ,8 , 9 }
−1
1. Evaluate (0.064 ) 3 log 3 9−log 2 8
5 6. Evaluate
A. log 3 9
2 −1
2 A.
B. 3
5 1
−2 B.
C. 2
5 1
5 C.
D. - 3
2 −1
D.
2
2. The ages, in years, of four boys are 10, 12,
14, and 18. What is the average age of the 7. Evaluate 2√ 28−3 √ 50 +√ 72.
boys? A. 4√ 7−21 √ 2
A. 12 years B. 4√ 7−¿ 11√ 2
1 C. 4√ 7−¿ 9√ 2
B. 12 years
2 D. 4√ 7 + √ 2
C. 13 years
1 8. If 6, P and 14 are consecutive terms in an
D. 13
2 arithmetic progression (A.P), find the value
of P
y+ 1 2 y−1 A. 9
3. Solve − =4 B. 10
2 3
A. y = 19 C. 6
B. y = - 19 D. 8
C. y = - 29
D. y = 29 9. If m : n = 2 : 1 , evaluate 3m2 – 2n2
m2 + mn
4. If sin θ = 3/5, find cos θ. 3
A.
A. 4/5 4
B. 5/4 5
B.
C. 1/5 3
3
D. 2/5 C.
4
3
5. If T = { prime nunbers } and M= { odd numbers } D.
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are subsets of ʮ=
{ x : 0< x ≤ 10 ,∧x is aninteger } , find ( T ' ∩ M ' ) . 10.Solve 4x2 – 16x + 15 = 0
A. { 4 , 6 , 8 ,10 } 1 1
B. { 1 , 4 , 6 , 8 , 10 } A. 1 or −¿2
2 2
C. { 1 , 2, 4 , 6 , 8 ,10 }

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 1 1 15.From the top of a vertical cliff 20m high, a
B. 1 or 2
2 2 boat at sea can be sighted 75m away and on
1 1 the same horizontal position as the foot of
C. −1 or 1
2 2 the cliff. Calculate, correct to the nearest
1 1 degree, the angle of depression of the boat
D. −1 or −¿ 2
2 2 from the top of the cliff.
A. 560
11.Find the equation of a straight line passing B. 750
through the point (1,-5) and having C. 160
3 D. 150
gradient of .
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A. 3x + 4y – 23 = 0 The following are the scores obtained by
B. 3x + 4y + 23 = 0 some students in a test. Use the information
C. 3x – 4y + 23 = 0 to answer questions 16 to 20
D. 3x – 4y – 23 = 0 8 18 10 14 18 11 13
14 13 17 15 8 16 13
12.A box contain 2 white and 3 blue identical
balls. If two balls are picked at random from 16.Find the mode of the distribution.
the box, one after the other with A. 18
replacement, what is the probability that B. 14
they are of the different colours? C. 13
2 D. 8
A.
3
3 17.Find the range of the distribution.
B. A. 10
5
7 B. 12
C. C. 15
20
12 D. 9
D.
25
18.Calculate the mean of the distribution.
13.The foot of a ladder is 6m from the base of A. 13.4
an electric pole. The top of the ladder rest B. 28.3
against the pole at a point 8m above the C. 11.4
ground. How long is the ladder? D. 15.0
A. 14m
B. 12m 19.Find the median score.
C. 10m A. 14.5
D. 7m B. 14.0
C. 13.5
3 cos x D. 13.0
14.If tan x = , 0 < x < 900 , evaluate .
4 2sin x
8 20.How many students scored above the mean
A. 3 score?
3 A. 10
B. 2 B. 9
4 C. 8
C. 3 D. 7
2
D. 3

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21.The fourth term of a linear sequence (A.P) is B. 600
37 and the first term is – 20. Find the C. 400
common difference. D. 300
A. 63
B. 57 27.A rectangular board has length 15cm and
C. 19 width x cm. If its sides are doubled, find its
D. 17 new area.
A. 60x cm2
22.If log x 2 = 0.3, evaluate log x 8. B. 45x cm2
A. 2.4 C. 30x cm2
B. 1.2 D. 15x cm2
C. 0.9
D. 0.6 28.Yinka sold an article for #6,900.00 and
made a profit of 15%. Calculate his
23.Make b the subject of the relation percentage profit if he had sold it for
1 #6,600.00
l b = (a+ b)h
2 A. 5%
ah B. 10%
A. C. 12%
2l−h
D. 13%
2l−h
B. 29.If 3p = 4q and 9p = 8q –12, find the value of
al
al pq.
C. A. 12
2l−h
al B. 7
D. C. -7
2−h
D. -12y

30.If (0.25) y = 32, find the value of y.

24.Charles sold his house through an agent
−5
who charged 8% commission on the selling A. y =
price. If Charles received $117,760.00 after 2
the sale, what was the selling price of the −3
B. y =
house? 2
A. $130,000.00 3
C. y =
B. $128,000.00 2
C. $125,000.00
D. $120,000.00 5
D. y =
2
25.Factorize completely:
31. Z
(2x + 2y)(x – y) + (2x – 2y)(x+ y)
A. 4(x-y)(x+ y) 32cm
B. 4(x- y)
C. 2(x-y)(x+y) Y X
D. 2(x-y)
In ∆ XYZ ,|YZ| = 32cm, < YXZ = 520 and <XYZ =
26.The interior angles of a polygon are 3x0, 2x0, 900. Find correct to the nearest cm, |XY|.
4x0, 3x0 and 6x0. Find the size of the smallest A. 31 cm
angle of the polygon. B. 25 cm
A. 800 C. 20 cm

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D. 13 cm D. -1

b 37.If 23y = 1111two, find the value of y.

32.If 2a = √ 64 and = 3, evaluate a2 + b2
a A. 4
A. 250 B. 3
B. 160 C. 6
C. 90 D. 7
D. 48
38.H varies directly as p and inversely as the
33.The total surface area of a solid cylinder is square of y. If H = 1, p=8 and y=2, find H in
165cm2. If the base diameter is 7cm, term of p and y.
22 p
calculate the height. (Take π = ) A. H =
7 4y
2

A. 7.5cm 2p
B. 4.5cm B. H = 2
y
C. 4.0cm p
D. 2.0cm C. H = 2
2y
p
34.There are 8 boys and 4 girls in a lift. What is D. H = 2
y
the probability that the first person who
steps out of the lift will be a boy?
0.0048 × 0.81
3 39.Evaluate: , leaving your
A. 0.0027 ×0.004
4
1 answer in standard form.
B. A. 3.6×10 1
4
2 B. 3.5 ×10
C. C. 3.6 ×10 4
3
1 D. 3.7 ×10 5
D.
3
40.Find the truth set of x2 + 4x + 3 = 0
2
x −5 x−14 A. {−1 }
35.Simplify 2 B. {−1 ,−3 }
x −9 x+14
x−7 C. {−2 , 2 }
A.
x+ 7 D. { 1 , 3 }
x+ 7 41.The length of a side of an equilateral
B.
x−7 triangle is 10cm. Find the height of the
x−2 triangle.
C.
x+ 2 A. 11.18cm
x+ 2 B. 10.00cm
D.
x−2 C. 8.66cm
D. 5.00cm
3 p−1
36.Which of these values would make 2
p −p log 10 8
undefined? 42.Simplify
log 1 o 4
A. 1 log 10 2
A.
1
B. B. log 10 4
3
1 C. 2
C. - 3
3 D.
2

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 2
d y
43.Factorize 6x + 2x + 4x
3 4 5 47.Given that y = 4x2 -8x +6. Find 2 .
dx
A. 2x3 (3 + x + 2x2) A. 9 B. 8 C. 8x-8 D. 8x3 – 8x2
B. 2x2 (3 + x + 2x3)
C. 2x (3 + x2 + 2x3)
D. 2x3 (3 + x + 2x) 48.If A = (−83 −75 ) and B= (−48 −6
7
, )
44.Simplify 3(2n +1) – 4(2n−1) Find A + B
2n+1 – 2n
A. 2n+1
B. 2n-1
A. (−87 −74 ) B. (−10 −10 )
c. 4
D.
1
4
C. ( 01 −01 ) D. (01 −1
0 )
49.A binary operation ⍟ is defined as x ⍟ y=
45.If log 10 2 = 0.3010 andlog 10 3 = 0.4771, 2 2
x −y
evaluate log 10 4.5 .
x+ y
A. 0.4771
Find -3 ⍟ 5
B. 0.3010
A. 9
C. 0.6532
B. -8
D. 0.9542
C. 12
D. 16
46.What is the square root of 0.0081
A. 0.9 50. The distance S meters travelled by a
B. O.009
particle after t seconds is given by S = t2 + 3t
C. 0.09
D. 0.03 + 8.
Find the velocity after 5 sec.
A. 13m/s B. 10m/s C. 7m/s D. 5m/s

PART I (40 marks): Answer ALL questions in this part. EACH QUESTION CARRIES 8 MARKS
1. (a) Solve, (i) log4 (x2 + 6x + 11) = ½ (ii) 25(2x – 1) x (1/5) – (3x+2) = 625 (x +3)
(b) Find the equation of the line passing through the points (2, 5) and (-4, - 7).

mt
2. (a) (i). Factorize px-2qx – 4qy + 2py (ii). Make m the subject of the relations h=
d (m+ p)
(b) A dealer sold a car to a woman and made a profit of 15% and the woman sold it to a man for ₦
120,175.00 at a loss of 5%. How much did the dealer buy the car?

3. (a) P varies directly as Q and inversely as the square of R. If P= 1 when Q = 8 and R = 2, find the value
of Q when P = 3 and R = 5.
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(b) (i) Given that Sin x = , 00¿ x <900. Find the value of 5 cosx – 4 tanx.
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(ii) If 2N4seven = 15Nnine, find the value of N.

4. (a) log10 2 = 0.3010 and log10 3= 0.4771, calculate without using table, the value of log10 0.72.

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 (b) A basket contains 80 mangoes and 60 oranges. If two fruits are picked one after the other without
replacement, what is the probability that
(i) One of each fruit is picked?
(ii) One type of fruit is picked?
5. The table below gives the frequency distribution of marks obtained by some students in a
scholarship examination.
Scores(x) 15 25 35 45 55 65 75
Frequency(f) 1 4 12 24 18 8 3

(a) Calculate correct to 3 significant figures, the mean mark

(b) Find the: (i) mode (ii) Range of the distribution.

PART II (60 marks): Answer any FIVE questions from this part. All questions carry equal mks.
6. In a class of 80 students, 20 offered Accounts, 21 offered chemistry, 18 offered Economics, 7
chemistry and Accounts, 8 offered Accounts and Economics,11 offered Economics and chemistry. If
each student offered at least one of the subjects, how many students offered:
(i) All the three subjects? (ii). exactly two of the subjects (iii). Accounts only

7. (a) Copy and complete the table of values for the relation y = 2sinx + 1.
x 00 300 600 900 1200 1500 1800 2100 2400 2700
y 1.0 2.7 0.0 -0.7

(b) Using a scale of 2cm: 300 on X-axis, 2cm:1 unit on Y-axis, draw graph of y= 2sinx +1 for 00 < x < 2700.
(c) Use the graph to find the values of x for which sinx = ¼

8. (a) The present ages of a man and his son are 47 and 17 years respectively. In how many years would
the man’s age be twice that of his son?
(b) The lengths of two ladders, L and M are 10m and 12m respectively. They are placed against a wall
such that each ladder makes the same angle with the horizontal ground. If the foot of L is 8m from
the foot of the wall.
(i) Draw a diagram to illustrate this information
(ii) Calculate the height at which M touches the wall.

9. (a)
T
S S

Q
P R

In the diagram, PQR is a tangent to the circle QST at Q. if /QT/ = /ST/ and ¿SQR = 56o, Find

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 (i) ¿ PQT . (ii) ¿ STQ .

(b). A (lat. 430N, long.770E), B (lat. 430N, long. 1030W) and C (lat. 570S, long.770E) are three points on the
earth surface. Calculate the distance between:
(i). A and B along latitude 430 N.
(ii). A and C along the great circle. Hence, find
(iii). the total distance covered throughout the journey. (Take R = 6400Km, Ꙥ= 22/7)
10. (a) Use a ruler and a pair of compasses only to Construct an inscribed circle in a ∆PQR of sides PQ =
8.5cm , PR = 7cm and ¿QPR = 1200.
(b) Measure the radius of the circle.
(c) Calculate the area of the inscribed circle.
11. (a). The angles of pentagon are x0, 2x0, 3x0, 2x0, and (3x – 10)0. Find the value of x.
(b). The following are the lengths of 30 pieces of iron in cm
45 55 65 60 61 68 59 54 64 76
50 68 72 68 80 67 70 62 79 67
63 71 59 64 53 57 74 55 57 64
I. Using the class 45 – 49, 50 – 54, 55 –59,.. , construct a frequency table of the data.
II. Draw the histogram for the distribution.
III. Calculate the mean of the distribution.
IV. What is the probability of selecting an iron rod whose length is the modal class?

12. (a) Copy and complete the table of values for y= 2x2 +x – 10 for x= -5 to 4.

X -5 -4 -3 -2 -1 0 1 2 3 4
Y 5 -9 -10 0

(b) Using the scale of 2cm to 1 unit on the x -axis and 2cm to 5 units on the y- axis, draw the graph of y
= 2x2 + x = 10 for -5 ≤x ≤ 4.
(c) Use the graph to find the solution of:
I. 2x2 + x = 10;
II. 2x2 + x – 10 = 2x.
13. (a) Solve the quadratic equation 2x2 + x = 10, using completing the square method.
(b). A water reservoir in the form of a cone mounted on a hemisphere is built such that the plane face of
the hemisphere fits exactly to the base of the cone and the height of the cone is 6 times the radius of
its base.
(i) Illustrate the information in a diagram
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(ii) If the volume of the reservoir is calculated to be 333 π m3, calculate correct to the nearest
2
whole number (a) the volume of the hemisphere (b) the total surface area of the reservoir.