The table above shows the scores of a group of students in a physics test. If the mode is m and the number of students who scored 4 or more is n, what is (n, m)?
Answer
(A)
(33, 4)
2
A final examination requires that a student answer any 4 out of 6 questions. In how many ways can this be done?
Answer
(A)
15
3
If the mean of five consecutive integers is 30, find the largest of the numbers
Answer
(C)
32
4
A bag contains 5 black, 4 white and x red marbles. If the probability of picking a red marble is 2/5, find the value of x
Answer
(D)
6
5
Find the variance of 2x, 2x-1 and 2x+1
Answer
(A)
2/3
6
The table above shows the distribution of recharge cards of four major GSM operators. What is the probability that a recharge card selected at random will be GTN or Qtel?
Answer
(C)
2/5
7
The pie chart above shows the expenditure of a family whose income is N30,000. If the expenditure on food is twice that on housing and that on school fees is twice that on transport, how much does the family spend on food?
Answer
(D)
N 12 500
8
For what value of n is \(^{n+1}C_3\) = 4(\(^nC_3\))?
Answer
(D)
3
9
The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.
Answer
(B)
y = x2 + 7x - 18
10
Differentiate (x\(^2\) - \(\frac{1}{x}\))\(^2\) with respect to x
Answer
(C)
4x3 - 2 - 2/x3
11
Find the value of x for which the function 3x\(^3\) - 9x\(^2\) is minimum
Calculate the logarithm to base 9 of 3\(^{-4}\) x 9\(^2\) x (81)\(^{-1}\)
Answer
(C)
-2
18
If (K2)\(_6\) * 3\(_6\) = 3\(_5\)(K4)\(_5\), what is the value of k?
Answer
(D)
2
19
In a small village of 500 people, 350 speak the local language while 200 speak pidgin English. What percentage of the population speak both.
Answer
(B)
10%
20
Find the tax on an income of N20,000 if no tax is paid on the first N10,000 and tax is paid at N50 in N1000 on the next N5000 and at N55 in N1000 on the remainder
In the diagram above, QR is the diameter of the semicircle QR. Find the area of the figure to the nearest whole number. [\(\pi = \frac{22}{7}\)]
Answer
(A)
89 cm2
26
If tan θ = 5/4, find sin2θ - cos2θ.
Answer
(C)
9/41
27
PQ and RS are two parallel lines. If the coordinates of P, Q, R, S are (1,q), (3,2), (3,4), (5,2q) respectively, find the value of q
Answer
(D)
2
28
In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find lYZl.
Answer
(B)
\(7\left(\frac{\sqrt{6}}{2}\right)\)
29
In the diagram above, find the value of x
Answer
(C)
45o
30
In the diagram above, POQ is a diameter of the circle PQRS. If ∠PSR = 145°, find x°
Answer
(A)
55o
31
What is the locus of points equidistant from the lines ax + by + c = 0?
Answer
(D)
A line ax + by +q = 0
32
PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS
Answer
(D)
60o
33
If the locus of the points which are equidistant from point P and Q meets line PQ at point N, then PN equals
Answer
(A)
NQ
34
In the diagram above, PQ = 10 cm, PS = 8 cm and ∠PSR is 60o while ∠SRQ is a right angle. Find SR
Answer
(A)
14 cm
35
The solution set of the shaded area above is
Answer
(D)
y ≤ x, y + x ≤ 4 and y ≥ 0
36
A binary operation \(\oplus\) defined on the set of real number is such that x\(\oplus\)y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6
Answer
(D)
9/5
37
If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?
Answer
(B)
p varies inversely as r6
38
A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)
Answer
(A)
\(\frac{-8}{15}\)
39
Find the value of k if the expression kx3 + x2 - 5x - 2 leaves a remainder 2 when it is divided by 2x + 1
Answer
(C)
-10
40
Solve the inequalities for which \(\frac{x+4}{3}-\frac{x-3}{2} < 4\)
Answer
(B)
x > -7
41
The cost of renovating a 6 m square room is N540. What is the cost of renovating a 9 m square room?
Answer
(D)
N810
42
The sum of the first n positive integers is
Answer
(D)
1/2 n(n+1)
43
If \(T = 2\pi \sqrt{\frac{l}{g}}\), make g the subject of the formula
Answer
(B)
(4π2l) / T2
44
If y = x\(^2\) - x - 12, find the range of values of x for which y \( \geq \) 0
Answer
(B)
x \( \leq \) -3 or x \( \geq \) 4
45
How many terms of the series 3, -6, +12, - 24, + ..... are needed to make a total of 1 - 2\(^8\)?
