What is the number whose logarithm to base 10 is \(\bar{3}.4771\)?
Answer
(D)
0.003
10
A house bought for N100,000 was later auctioned for N80,000. Find the loss percent.
Answer
(A)
20%
11
A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error.
Answer
(D)
\( 3\frac{1}{8} \)%
12
The sum of the 1st and 2nd terms of an A.P. is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms.
Answer
(B)
20
13
E = (integers \(\leq\) 20), P = (multiples of 3), Q = (multiples of 4), what are the elements of P'∩Q?
Answer
(B)
(4, 8, 16, 20)
14
Given that 2p - m = 6 and 2p + 4m = 1, find the value of (4p + 3m).
Answer
(D)
7
15
Which of the following is a point on the curve y = x\(^2\) - 4x + 7?
Answer
(B)
(1,4)
16
If 8x- 4 = 6x- 10, find the value of 5x,
Answer
(B)
-15
17
For what value of x is the expression \(\frac{x^2 + 15x + 50}{x - 5}\) not defined ?
Answer
(D)
5
18
If x is positive, for what range of values of x is 4 + 3x < 10?
Answer
(B)
x < 2
19
In the graph above, the gradient of the curve at the point P is
Answer
(A)
-113
20
What is the equation of the line PQ?
Answer
(C)
y = x + 5
21
Which of the following equations can be solved by the points of intersection P and Q of the curve and the line PQ?
Answer
(B)
x2 - 4 = 0
22
Which of the following is not a factors of 2p\(^2\) - 2?
Answer
(E)
2p + 1
23
Find the quadratic equation whose roots are 3 and \(\frac{2}{3}\).
Answer
(E)
3x2 - 11x + 6 = 0
24
Which of the following is a root of the equation x\(^2\) +6x = 0?
Answer
(A)
0
25
Factorise: 6x\(^2\) + 7xy - 5y\(^2\)
Answer
(D)
(3x + 5y)(2x - y)
26
Solve the equation log8x - 4log8x = 2
Answer
(A)
1/4
27
The angle subtended at the centre by a chord of a circle radius 6cm is 120°. Find the length of the chord.
Answer
(E)
\(6\sqrt{3}\) cm
28
A cuboid of base 12.5cm by 20cm holds exactly 1 litre of water. What is the height of the cuboid? (1 litre =1000cm3)
Answer
(B)
4cm
29
Two ships on the equator are on longitudes 45oW and 45oE respectively. How far are they apart along the equator, correct to 2 significant figures? (Take the radius of earth = 6400km and π = 22/7)
Answer
(B)
10,000km
30
Calculate, correct to 2 significant figures, the length of the arc of a circle of radius 3.5cm which subtends an angle of 75° at the centre of the circle. [Take π = 22/7].
Answer
(B)
4.6cm
31
A circle has radius x cm. What is the area of a sector of the circle with angle 135°, leaving the answer in terms of x and π?
Answer
(B)
\( \frac{3\pi x^2}{8} \)
32
In the diagram, PQRS is a trapezium with PQ||SR. STR is a straight line, PSHQT, PTHQR. If |PQ| = 12cm and the height of the trapezium is 9cm, find its area.
Answer
(D)
162cm2
33
Two solid spheres have volumes 250cmo and 128cmo respectively. Find the ratio of their radii.
Answer
(E)
5:4
34
In the diagram ST and QR are parallel. |PS| = 6cm, |SQ| = 8cm and |PR] = 18 2/3. Find |PT|
Answer
(B)
8cm
35
In the diagram, PQ||RS and angles are as shown. Find x
Answer
(E)
165o
36
IF the exterior angles of a quadilateral are yo, (2y + 5)o , (y + 15)o and (3y - 10)o, find yo
Answer
(E)
50
37
The sum of the angles of regular polygon is 2520o. How many sides does the polygon have?
Answer
(D)
16
38
Which of the following is not a property of all parallelogram?
Answer
(C)
the diagonal cut at right angles
39
In the diagram above, PQ is the tangent to the circle RST at T.|ST| = ST and ∠RTQ = 68o. Find ∠PTS
Answer
(D)
56o
40
The diagram above shows a circle PQRS in which ∠PRQ = 54o and ∠SPQ = 97o. Find ∠PQS
Answer
(E)
29o
41
In the diagram |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP = 74o. Find ∠QPS
Answer
(D)
53o
42
A ladder 6m long leans against a vertical wall so that it makes an angle of 60o with the wall. Calculate the distance of the foot of the ladder from the wall
Answer
(D)
3√3m
43
The bearing of Q from P is 122o, what is the bearing of P from Q?
