Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}.
Determine (P-Q) β© R
- A. {1, x}
- B. {x y}
- C. {x}
- D. ΙΈ
If the minimum value of y = 1 + hx – 3x2 is 13, find h.
- A. 13
- B. 12
- C. 11
- D. 10
Find the value of x for which the function y = x3 – x has a minimum value.
- A. \(-\sqrt{3}\)
- B. \(-\sqrt{\frac{3}{3}}\)
- C. \(\sqrt{\frac{3}{3}}\)
- D. \(\sqrt{3}\)
Evaluate \(\int^{1}_{-2}(x-1)^{2}dx\)
- A. \(\frac{-10}{3}\)
- B. 7
- C. 9
- D. 11
What is the derivative of t2 sin (3t – 5) with respect to t?
- A. 6t cos (3t - 5)
- B. 2t sin (3t - 5) - 3t2 cos (3t - 5)
- C. 2t sin (3t - 5) + 3t2 cos (3t - 5)
- D. 2t sin (3t - 5) + t2 cos 3t
Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
- A. 81 Ο cubic units
- B. 36 Ο cubic units
- C. 18 Ο cubic units
- D. 9 Ο cubic units
Evaluate: \(\int^{z}_{0}(sin x – cos x) dx \hspace{1mm}
Where\hspace{1mm}letter\hspace{1mm}z = \frac{\pi}{4}. (\pi = pi)\)
- A. \(\sqrt{2 +1}\)
- B. \(\sqrt{2 }-1\)
- C. \(-\sqrt{2 }-1\)
- D. \(1-\sqrt{2}\)
Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
- A. 4 sq units
- B. 2 sq units
- C. \(\frac{4}{3}sq\hspace{1 mm}units\)
- D. \(\frac{1}{3}sq\hspace{1 mm}units\)
Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)
- A. 2x + 2y = 9
- B. 2x + 3y = 8
- C. 2x + y = 9
- D. x + 2y = 8
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
- A. 120m
- B. 140m
- C. 150m
- D. 160m
Find the tangent to the acute angle between the lines 2x + y = 3 and 3x – 2y = 5.
- A. -7/4
- B. 7/8
- C. 7/4
- D. 7/2
In βMNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of angle M meets NO at P, calculate NP.
- A. 4.8 units
- B. 7.2 units
- C. 8.0 units
- D. 18.0 units
A man 1.7m tall observes a bird on top of a tree at an angle of 30Β°. if the distance between the man’s head and the bird is 25m, what is the height of the tree?
- A. 26.7m
- B. 14.2m
- C. \(1.7+(25\frac{\sqrt{3}}{3}m\)
- D. \(1.7+(25\frac{\sqrt{2}}{2}m\)
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.
- A. 1
- B. 2
- C. 3
- D. 4
Divide 4x\(^3\) – 3x + 1 by 2x – 1
- A. 2x2-x+1
- B. 2x2-x-1
- C. 2x2+x+1
- D. 2x2+x-1
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.
- A. 8/5
- B. 8/3
- C. 72/25
- D. 56/9
Express \(\frac{1}{x^{3}-1}\) in partial fractions
- A. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x + 2)}{x^{2} + x + 1})\)
- B. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{x - 2}{x^{2} + x + 1})\)
- C. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 2)}{x^{2} + x + 1})\)
- D. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 1)}{x^{2} - x - 1})\)
Three consecutive positive integers k, l and m are such that l\(^2\) = 3(k+m). Find the value of m.
- A. 4
- B. 5
- C. 6
- D. 7
Tope bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X.
- A. 4β€Xβ€5
- B. 5β€Xβ€8
- C. 5β€Xβ€10
- D. 8β€Xβ€10
Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y – 18\).
- A. (x+y+6)(x+y-3)
- B. (x-y-6)(x-y+3)
- C. (x-y+6)(x-y-3)
- D. (x+y-6)(x+y+3)
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.
- A. 2/3
- B. 1/2
- C. -1/2
- D. -2/3