### Mathematics Past Questions

16

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. $$\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 1)}{x^{2} - x - 1})$$
17
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
18

Divide 4x$$^3$$ - 3x + 1 by 2x - 1

• A. 2x2-x+1
• B. 2x2-x-1
• C. 2x2+x+1
• D. 2x2+x-1
19

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
20
A man 1.7m tall observes a bird on top of a tree at an angle of 300. 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. $$1.7+(25\frac{\sqrt{2}}{2}m$$