If P = {3, 5, 6} and Q = {4, 5, 6} then P∩Q equals
Answer
(D)
{5, 6}
3
A and B are two sets. The number of elements in A∪B is 49, the number in A is 22 and number in B is 34. How many elements are in A ∩ E?
Answer
(E)
7
4
A student found the approximate value of 0.02548 correct to two places of decimal instead of two significant figures. Find the percentage error.
Answer
(E)
20%
5
Simplify log39 + log315 - log35
Answer
(C)
3
6
Solve me equation: 2/3 (x + 5) = 1/4(5x - 3)
Answer
(E)
7
7
Which of the following equations has its roots as 4 and -5?
Answer
(D)
x2 + x - 20 = 0
8
Solve the equations: 4x -y = 11; 5x + 2y = 4.
Answer
(D)
x = 2, y = -3
9
Make q the subject of the relation t = √(pq/r - r\(^2\)q)
Answer
(A)
q = \(\frac{rt^2}{(p - r^3)}\)
10
P varies inversely as the square of W. When W = 4, P = 9. Find the value of P when W = 9
Answer
(D)
16/9
11
If x varies over the set of real numbers, which of the following is illustrated in the diagram above?
Answer
(B)
-2 < x ≤ 3
12
In the triangle XYZ , XM is the altitude from X to YZ.XY = 13cm, XZ = 15cm and YM = 5cm. Find the length of YZ
Answer
(C)
14cm
13
Two points P and Q are on longitude 67°W. Their latitudes differ by 90°. Calculate their distance apart in terms of π. (Take radius of the earth = 6400km).
Answer
(C)
3200πkm
14
The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium
Answer
(B)
4Ocm2
15
Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π
Answer
(C)
184πcm2
16
The cross-section of a prism is a right-angled triangle 3cm by 4cm by 5cm. The height of the prism is 8cm. Calculate its volume
Answer
(A)
48cm3
17
Find the radius of a circle in which an arc of length 44cm subtends angle 200° at the centre of the circle. [Take π = 22/7]
Answer
(B)
12.6cm
18
The diagram above is a triangle XYZ whose area is 23.5cm2. XY =1Ocm and YZ = 8cm, calculate θ correct to the nearest degree.
Answer
(C)
36o
19
Which of the following is not necessarily sufficient for the construction of a triangle?
Answer
(C)
Two sides and a right angle
20
In the diagram, EF//QR, PE = 2cm, EQ = 4cm and FR = 6cm. Find x
Answer
(B)
3cm
21
Which of the following statements is/are true when two straight lines intersect?
I. Adjacent angles are equal II. Vertically opposite angles are equal III. Adjacent angles are supplementary
Answer
(C)
II and III only
22
PQRS and GHRS are parallelograms on the same base SR and between the same parallel straight line PH and SR. Which of the following is true?
Answer
(E)
Parallelogram PQRS = Parallelogram GHRS
23
From the diagram above, which of the following is true?
Answer
(D)
a + b = x + 180
24
The interior angles of a pentagon are 126o, 114o, y, 92o and 83o. Find the value of y.
Answer
(E)
125o
25
Solve the inequality 3x - 8 ≥ 5x
Answer
(C)
x ≤ -4
26
Divide 3.6721 by 4
Answer
(A)
0.9180
27
The eleventh term of an AP, is 25 and its first term is -3. Find its common difference.
Answer
(E)
24/5
28
Find the common ratio in the GP: log 3, log 9, log 81 ..........
Answer
(B)
2
29
Find the value of t for which \(\frac{64}{27} = (\frac{3}{4})^{t - 1}\)
Answer
(B)
-2
30
O is the centre of the circle PQRS. PR and QS intersect at T POR is a diameter, ∠PQT = 42o and ∠QTR = 64o; Find ∠QRT
Answer
(A)
68o
31
TR is the tangent to the circle PQR with centre O. Find the size of ∠PRT
Answer
(C)
60o
32
Given that \(\frac{1}{2} \log_{10} P = 1\), find the value of P.
Answer
(C)
102
33
If two triangles are similar, which of the following is true? Their
Answer
(B)
corresponding angles are equal
34
Which of the following is not necessarily true of a rectangle?
Answer
(C)
The diagonals are perpendicular
35
A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord
Answer
(C)
24cm
36
The angle of elevation of a point T on a tower from a point U on the horizontal ground is 30o. If TU = 54m, how high is T above the horizontal ground?
Answer
(E)
27m
37
Express the true bearing of 250° as a compass bearing
Answer
(D)
S70oW
38
lf sin θ= \(\frac{-1}{2}\), find all the values of θ between 0° and 360°.
Answer
(D)
210o,330o
39
Cos 65o has the same value as
Answer
(E)
Cos 295o
40
Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the nearest degree, the smallest angle of the triangle.
