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)?
Răspuns
(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?
Răspuns
(A)
15
3
If the mean of five consecutive integers is 30, find the largest of the numbers
Răspuns
(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
Răspuns
(D)
6
5
Find the variance of 2x, 2x-1 and 2x+1
Răspuns
(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?
Răspuns
(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?
Răspuns
(D)
N 12 500
8
For what value of n is \(^{n+1}C_3\) = 4(\(^nC_3\))?
Răspuns
(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.
Răspuns
(B)
y = x2 + 7x - 18
10
Differentiate (x\(^2\) - \(\frac{1}{x}\))\(^2\) with respect to x
Răspuns
(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)\(^{-1}\)
Răspuns
(C)
-2
18
If (K2)\(_6\) * 3\(_6\) = 3\(_5\)(K4)\(_5\), what is the value of k?
Răspuns
(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.
Răspuns
(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. [\(\pi = \frac{22}{7}\)]
Răspuns
(A)
89 cm2
26
If tan θ = 5/4, find sin2θ - cos2θ.
Răspuns
(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
Răspuns
(D)
2
28
In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find lYZl.
Răspuns
(B)
\(7\left(\frac{\sqrt{6}}{2}\right)\)
29
In the diagram above, find the value of x
Răspuns
(C)
45o
30
In the diagram above, POQ is a diameter of the circle PQRS. If ∠PSR = 145°, find x°
Răspuns
(A)
55o
31
What is the locus of points equidistant from the lines ax + by + c = 0?
Răspuns
(D)
A line ax + by +q = 0
32
PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS
Răspuns
(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
Răspuns
(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
Răspuns
(A)
14 cm
35
The solution set of the shaded area above is
Răspuns
(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
Răspuns
(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?
Răspuns
(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 \(-5 \ast 3\)
Răspuns
(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
Răspuns
(C)
-10
40
Solve the inequalities for which \(\frac{x+4}{3}-\frac{x-3}{2} < 4\)
Răspuns
(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?
Răspuns
(D)
N810
42
The sum of the first n positive integers is
Răspuns
(D)
1/2 n(n+1)
43
If \(T = 2\pi \sqrt{\frac{l}{g}}\), make g the subject of the formula
Răspuns
(B)
(4π2l) / T2
44
If y = x\(^2\) - x - 12, find the range of values of x for which y \( \geq \) 0
Răspuns
(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\(^8\)?
