In the diagram O is the center of the circle. Reflex angle XOY = 210° and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.
Svar
(A)
8m
2
A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is \(2\sqrt{3}\) cm. Calculate the volume of the pyramid
Svar
(B)
\(10\frac{2}{3}cm^3\)
3
The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area
Svar
(B)
\(15\pi cm^2\)
4
In the diagram above, ∠PQU=36°, ∠QRT = 29°, PQ||RT. Find ∠PQR
If \(M5_{ten} = 1001011_{two}\) find the value of M
Svar
(C)
7
9
The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x- axis at P and R and the y- axis at Q.
What is the value of y at Q?
Svar
(A)
\(6\frac{1}{3}\)
10
The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x-axis at P and R and the y-axis at Q.
When \(y = 3\frac{1}{3}\), what is the positive value of x?
Svar
(B)
\( 2\frac{1}{5}\)
11
The length, in cm, of the sides of a right angled triangle are x, (x+2) and (x+1) where x > 0. Find , in cm, the length of its hypotenuse
Svar
(B)
5
12
If log 2 = 0.3010 and log 2\(^y\) = 1.8062, find; correct to the nearest whole number, the value of y.
Svar
(A)
6
13
Points X, Y and Z are located in the same horizontal plane such that Y is 12 km north of X and Z is on a bearing of 270° from X. If |XZ| = 6km, calculate, correct to one decimal place, lYZl
Svar
(B)
13.4km
14
The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?
Svar
(B)
5
15
If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?
Svar
(A)
1
16
From the diagram, find the bearing of Q from P.
Svar
(A)
236o
17
Find the nth term of the sequence 4, 10, 16 ,...
Svar
(A)
2(3n- 1)
18
If (-3, -4) is a point on the line y = mx + 2 find the value of m.
Svar
(C)
2
19
Which of the following is represented by the above sketch?
Svar
(B)
y = x2 - x - 6
20
In the diagram, SQ is a tangent to the circle at P, XP||YQ, ∠XPY = 56 o and ∠PXY = 80 o.Find angle PQY
Svar
(A)
34o
21
For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?
Svar
(D)
\(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\)
22
Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\)
Svar
(C)
\(\frac{3-x}{1-x^2}\)
23
The lengths of the parallel sides of a trapezium are 9 cm and 12 cm. lf the area of the trapezium is 105 cm2, find the perpendicular distance between the parallel sides.
Svar
(C)
10cm
24
The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. [Taken \(\pi = \frac{22}{7}\)]
Svar
(D)
9cm
25
A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime.
Svar
(A)
\(\frac{1}{4}\)
26
The median of the distribution is
Svar
(C)
15
27
The range of the distribution is
Svar
(C)
25
28
The upper quartile of the distribution is
Svar
(D)
17.75
29
In the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|.
Svar
(B)
19.04cm
30
In the diagram O is the centre of the circle. Which of the following is/are not true? I. a = b II. b + c = 180o III. a + b = c
In the diagram, |SR| = |RQ| and ∠PRQ = 58o ∠VQT = 19o, PQT, SQV and PSR are straight lines. Find ∠QPS
Svar
(A)
42o
33
The angle of depression of a point Q from a vertical tower PR, 30m high, is 40°. If the foot P of the tower is on the same horizontal level as Q, find, correct to 2 decimal places, |PQ|.
Svar
(A)
35.75m
34
The volume of a cylinder of radius 14cm is 210cm3. What is the curved surface area of the cylinder?
If q oranges are sold for t Naira, how many oranges can be bought for p naira?
Svar
(D)
\(\frac{pq}{t}\)
38
In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = \(6\sqrt{3}cm\), calculate |RT|
Svar
(C)
3cm
39
In the diagram, calculate the value of x
Svar
(C)
100o
40
In the diagram, \(\bar{PS}\hspace{1mm} and \hspace{1mm}\bar{QT}\) are two altitudes of ∆PQR. Which of the following is equal to ∠RQT?
Svar
(D)
∠SPR
41
In the diagram, |QR| = 10cm, PR⊥QS, angle PSR = 30° and angle PQR = 45°. Calculate in meters |QS|
Svar
(A)
\(10(1+\sqrt{3})\)
42
Calculate and correct to two significant figures, the percentage error in approximating 0.375 to 0.4
Svar
(D)
6.7
43
To arrive on schedule, a train is to cover a distance of 60km at 72km/hr. If it starts 10 minutes late, at what speed must it move to arrive on schedule?
Svar
(C)
90km/hr
44
In the diagram, \(QR||TP and W\hat{P}T = 88^{\circ} \). Find the value of x
Svar
(C)
67o
45
In the diagram O is the center of the circle, ∠SOR = 64° and ∠PSO = 36°. Calculate ∠PQR
