A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?
答え
(A)
25
2
If log\(_810\) = X, evaluate log\(_85\) in terms of X.
答え
(C)
X-\(\frac{1}{3}\)
3
Find the value of X if \(\frac{\sqrt{2}}{x+\sqrt{2}}=\frac{1}{x-\sqrt{2}}\)
答え
(A)
3√2+4
4
If \(\frac{(a^2 b^{-3}c)^{\frac{3}{4}}}{a^{-1}b^{4}c^{5}}=a^{p} b^{q} c^{r}\) What is the value of p+2q?
答え
(D)
-10
5
If \(\frac{({a^2b^{-3}c})^{3/4}}{a^{-1}b^4c^5}\) = \(a^p b^q c^r\); what is the value of p+2q?
答え
(D)
-10
6
A trader bought 100 oranges at 5 for N1.20, 20 oranges got spoilt and the remaining were sold at 4 for N1.50. Find the percentage gain or loss.
答え
(B)
25% gain
7
What is the answer when 2434\(_6\) is divided by 42\(_6\)?
答え
(B)
356
8
If 2\(_9\) x (Y3)\(_9\) = 3\(_5\) x (Y3)\(_5\), find the value of Y.
If \(m*n = (\frac{m}{n} - \frac{n}{m}\)) for m, n belong to R, evaluate -3*4
答え
(C)
\(\frac{7}{12}\)
11
The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers
答え
(B)
3p/2
12
A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.
The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.
答え
(C)
72/25
17
Divide 4x\(^3\) - 3x + 1 by 2x - 1
答え
(D)
2x2+x-1
18
Find a positive value of \(\alpha\) if the coordinate of the centre of a circle x\(^2\) + y\(^2\) - 2\(\alpha\)x + 4y - \(\alpha\) = 0 is (\(\alpha\), -2) and the radius is 4 units.
答え
(C)
3
19
A man 1.7m tall observes a bird on top of a tree at an angle of 30°. if the distance between the man's head and the bird is 25m, what is the height of the tree?
答え
(B)
14.2m
20
In ∆MNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of angle M meets NO at P, calculate NP.
答え
(B)
7.2 units
21
Find the tangent to the acute angle between the lines 2x + y = 3 and 3x - 2y = 5.
答え
(C)
7/4
22
From a point P, the bearings of two points Q and R are N670W and N230E respectively. If the bearing of R from Q is N680E and PQ = 150m, calculate PR
答え
(C)
150m
23
Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)
答え
(D)
x + 2y = 8
24
Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
答え
(C)
\(\frac{4}{3}sq\hspace{1 mm}units\)
25
Evaluate: \(\int^{z}_{0}(sin x - cos x) dx \hspace{1mm}
Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
答え
(B)
36 π cubic units
27
What is the derivative of t2 sin (3t - 5) with respect to t?
答え
(C)
2t sin (3t - 5) + 3t2 cos (3t - 5)
28
Evaluate \(\int^{1}_{-2}(x-1)^{2}dx\)
答え
(C)
9
29
Find the value of x for which the function y = x\(^3\) - x has a minimum value.
答え
(C)
\(\frac{\sqrt{3}}{3}\)
30
If the minimum value of y = 1 + hx - 3x\(^2\) is 13, find h.
答え
(B)
12
31
The shaded portion in the graph above is represented by
答え
(A)
y + x - x3 ≥ 0, y - x ≤ 0
32
Find the length XZ in the triangle above.
答え
(A)
√7 m
33
In the figure above, PQRS is a circle with ST//RQ. Find the value of x PT = PS.
答え
(B)
55o
34
In the diagram above, EFGH is a cyclic quadrilateral in which EH//FG, EG and FH are chords. If ∠FHG = 42o and ∠EFH = 34o, calculate ∠HEG
答え
(C)
52o
35
In the figure above, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units
答え
(A)
3
36
Find the value of l in the frustrum above
答え
(A)
5cm
37
The diagram above is the graph of y = x\(^2\), the shaded area is
答え
(C)
64/3 square units
38
The table above shows the frequency distribution of the ages (in years) of pupils in a certain secondary school. What percentage of the total number of pupils is over 15 years but less than 21 years?
答え
(C)
50%
39
the shaded portion in the graph is represented by
答え
(C)
y + x - 3 \(\geq\) 0, y + x \(\leq\) 0
40
In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG, and FH are chords. If < FHG = 42º and < EFH = 34º, calculate < HEG.
