If log\(_{10}\) 2 = m and log\(_{10}\) 3 = n, find log\(_{10}\) 24 in terms of m and n.
Answer
(A)
3m + n
5
Find the 5th term of the sequence 2,5,10,17....?
Answer
(D)
26
6
if p = {-3<x<1} and Q = {-1<x<3}, where x is a real number, find P n Q.
Answer
(A)
0
7
Factorize 6pq-3rs-3ps+6qr
Answer
(C)
3(2q - s)(p + r)
8
What number should be subtracted from the sum of 2 \(\frac{1}{6}\) and 2\(\frac{7}{12}\) to give 3\(\frac{1}{4}\)?
Answer
(B)
1\(\frac{1}{2}\)
9
Mensah is 5 years old and joyce is thrice as old as mensah. In how many years will joyce be twice as old as Mensah?
Answer
(C)
5 years
10
If 16 * 2\(^{(x + 1)}\) = 4\(^x\) * 8\(^{(1 - x)}\), find the value of x.
Answer
(D)
-1
11
The circumference of a circular track is 9km. A cyclist rides round it a number of times and stops after covering a distance of 302km. How far is the cyclist from the starting point?
Answer
(A)
5km
12
Simplify 2√7- \(\frac{14}{√7} + \frac{7}{√21}\)
Answer
(C)
\(\frac{√21}{3}\)
13
If 4x+2y=16 and 6x-2y=4 , find the value of (y-x).
Answer
(B)
2
14
In the diagram, ∠ABC and ∠BCD are right angles, ∠BAD = t and ∠EDF = 70°. Find the value of t.
Answer
(D)
110°
15
The sum of the interior angles of a regular polygon with k sides is (3k-10) right angles. Find the size of the exterior angle?
Answer
(A)
60°
16
make u the subject in x =\(\frac{2u-3}{3u + 2}\)
Answer
(C)
u = \(\frac{2x + 3}{2 - 3x}\)
17
A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of #22,800.00 was paid as import duty, calculate the cost of the engine.
Answer
(A)
#60,000.00
18
The height of an equilateral triangle of side is 10 3√ cm. calculate its perimeter.
Answer
(B)
60cm
19
In △LMN, |LM| = 6cm, ∠LNM = x and sin x = sin x = \(\frac{3}{5}\).
Find the area of △LMN
Answer
(C)
24cm\(^2\)
20
consider the statements:
P = All students offering Literature(L) also offer History(H);
Q = Students offering History(H) do not offer Geography(G).
Which of the Venn diagram correctly illustrate the two statements?
Answer
(C)
C
21
Find The quadratic Equation Whose Roots Are -2q And 5q.
Answer
(D)
x\(^2\) - 3qx - 10q\(^2\)
22
if tanθ = \(frac{3}{4}\), 180° < θ < 270°, find the value of cosθ.
Answer
(C)
-\(\frac{4}{5}\)
23
If \(\frac{2}{x-3}\) - \(\frac{3}{x-2}\) = \(\frac{p}{(x-3)(x -2)}\), find p.
Answer
(A)
5 - x
24
The diagonal of a rhombus are 12cm and 5cm. calculate its perimeter
Answer
(A)
26cm
25
In the diagram, △XYZ is produced to T. if |XY| = |ZY| and ∠XYT = 40°, find ∠XZT
Answer
(A)
110°
26
A solid brass cube is melted and recast as a solid cone of height h and base radius r. If the height of the cube is h, find r in terms of h.
Answer
(B)
r = √\(\frac{3h^2}{π}\)
27
Which of the following is not an exterior angle of a regular polygon?
Answer
(A)
66°
28
From a point T, a man moves 12km due west and then moves 12km due south to another point Q. Calculate the bearing of T from Q.
Answer
(C)
045°
29
In the diagram, O is the centre of the circle PQRS, ∠PQR = 72° and OR is parallel to PS. Find ∠ OPS.
Answer
(D)
36°
30
A trapezium of parellel sides 10cm and 21cm and height 8cm is inscribed in a circle of radius 7cm. calculate the area of the region not covered by the trapezium.
π =\(\frac{22}{7}\)
Answer
(C)
30cm\(^2\)
31
Find, correct to two decimal, the mean of 1\(\frac{1}{2}\), 2\(\frac{2}{3}\), 3\(\frac{3}{4}\), 4\(\frac{4}{5}\), and 5\(\frac{5}{6}\).
Answer
(A)
3.71
32
A cyclist moved at a speed of Xkm/h for 2 hours. He then increased his speed by 2 km/h for the next 3 hours.
If the total distance covered is 36 km, calculate his initials speed.
Answer
(D)
6km/h
33
find the value of (x+y)
Answer
(A)
215°
34
In the diagram, \(\overline{MP}\) is a tangent to the circle NQR, ∠NQR, ∠PNQ = 64 and | \(\overline{RQ}\) | = | \(\overline{RN}\) |. Find the angle market t.
Answer
(C)
58°
35
find the first quartile of 7,8,7,9,11,8,7,9,6 and 8.
Answer
(B)
7.0
36
In the diagram, PQRS is a circle. find the value of x.
Answer
(A)
50°
37
A cone has a base radius of 8cm and height 11cm. calculate , correct to 2d.p, the curved surface area
Answer
(A)
341.98cm\(^2\)
38
Given that sin x = \(\frac{3}{5}\), 0 ≤ x ≤ 90, evaluate (tan x + 2cosx)
Answer
(B)
2\(\frac{7}{20}\)
39
In the diagram, line \(\overline{EC}\) is a diameter of the circle ABCDE.
If angle ABC equals 158°, find ∠ADE
Answer
(C)
68
40
Height(cm)
160
161
162
163
164
165
No. of players
4
6
3
7
8
9
the table shows the height of 37 players of a basketball team calculates correct to one decimal place the mean height of the players.
Answer
(A)
163.0
41
\(\overline{XY}\) is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of \(\overline{XY}\) is (-4,-2) find the coordinates of Y.
Answer
(B)
(0,8)
42
500 tickets were sold for a concert tickets for adults and children were sold at $4.50 and $3.00 respectively if the total receipts for the concerts was $1987.50 how many tickets for adults were sold?
Answer
(A)
325
43
The distance d between two villages east more than 18 KM but not more than 23KM.
which of these inequalities represents the statements?
Answer
(D)
18 < d ≤ 23
44
The pie chart represents the distribution of fruits on display in the shop if there are 60 apples on display how many oranges are there?
Answer
(D)
90
45
A box contains 40 identical balls of which 10 are red and 12 are blue. if a ball is selected at random from the box what is the probability that it is neither red nor blue?
