If \(P344_{6} – 23P2_{6} = 2PP2_{6}\), find the value of the digit P.
- A. 2
- B. 3
- C. 4
- D. 5
Simplify \(\frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n}\)
- A. 2n+1
- B. 2n-1
- C. 4
- D. 1/4
If 314\(_{10}\) – 256\(_7\) = 340\(_x\), find x.
- A. 7
- B. 8
- C. 9
- D. 10
A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit?
- A. N112,000.50
- B. N96,000.00
- C. N85,714.28
- D. N76,800.00
Evaluate \(\frac{(2.813 \times 10^{-3} \times 1.063)}{(5.637 \times 10^{-2})}\) reducing each number to two significant figures and leaving your answer in two significant figures.
- A. 0.056
- B. 0.055
- C. 0.054
- D. 0.54
In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?
- A. 8
- B. 24
- C. 62
- D. 86
If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), find the values of m and n respectively.
- A. 1, -2
- B. -2, 1
- C. \(\frac{-2}{5}\), 1
- D. 2, 3/5
If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000?
- A. 480,000
- B. 249,696
- C. 249,600
- D. 244,800
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. \(1.7+(25\frac{\sqrt{2}}{2}m\)