3 2018 June WASSCE Elective Maths Paper 1

1. Simplify $$\displaystyle \frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} + 1}$$
A. 6
B. $$2 \sqrt{3}$$
C. 3
D. $$\frac12$$

2. Find the domain of $$\displaystyle g(x) = \frac{4x^2 - 1}{\sqrt{9x^2 + 1}}$$
A. $$\{x: x \in R\}$$
B. $$\{x: x \in R\}$$
C. $$\{x: x \in R, x \neq -\frac12 \}$$
D. $$\{x: x \in R, x \neq \frac12 \}$$

3. Given that $$f(x) = 3x^2 - 12x + 12$$ and f(x) = 3, find the values of x.
A. -1, 3
B. 1, -3
C. -1, -3
D. 1, 3

4. The binary operation * is defined on the set of real numbers, R, by $$a \ast b = \frac{a}{b} + \frac{b}{a}$$. If $$\left( \sqrt x + 1 \right) \ast \left(\sqrt x - 1 \right) = 4$$, find the value of x.
A. 3
B. 4
C. 5
D. 6

5. If $$4x^2 + 5kx + 10$$ is a perfect square, find the value of $$k$$.
A. $$\frac45 \sqrt{10}$$
B. $$5\sqrt{10}$$
C. $$4\sqrt{10}$$
D. $$\frac54 \sqrt{10}$$

6. If the polynomial $$f(x) = 3x^3 - 2x^2 + 7x + 5$$ is divided by x - 1, find the remainder.
A. 13
B. 5
C. -7
D. -17

7. Given that P = {1, 3, 5, 7, 9, 11},
Q = {2, 4, 6, 8, 10, 12}, and
R = {2, 3, 5, 7, 11} are subsets of
U = {1, 2, 3, …, 12},
which of the following statements is true?
A. n(P’ ∩ R) = 2
B. (R ∩ P) ⊂ (R ∩ U)
C. R ⊂ P
D. Q ∩ R = φ

8. If $$\log_3 a + 2 = 3\log_3 b$$, express a in terms of b.
A. $$a = \frac{b^3}{9}$$
B. $$a = 9b^3$$
C. $$a = b^3 - 9$$
D. $$a = b^3 - 3$$

9. If $$\alpha$$ and $$\beta$$ are the roots of $$2x^2 - 5x + 6 = 0$$, find the equation whose roots are $$\alpha + 1$$ and $$\beta + 1$$.
A. 2x2 - 9x - 15
B. 2x2 - 9x - 13
C. 2x2 - 9x + 13
D. 2x2 - 9x + 15

10. Resolve $$\displaystyle \frac{3x - 1}{(x - 2)^2}, x \neq 2$$ into partial fractions.
A. $$\frac{3}{(x - 2)} - \frac{7}{(x - 2)^2}$$
B. $$\frac{3}{(x - 2)^2} - \frac{7}{(x - 2)}$$
C. $$\frac{3}{(x - 2)} + \frac{5}{(x - 2)^2}$$
D. $$\frac{3}{(x - 2)^2} + \frac{5}{(x - 2)}$$

11. If $$\alpha$$ and $$\beta$$ are the roots of $$2x^2 - 5x + n$$, such that $$\alpha \beta = 2$$, find the value of n.
A. 4
B. 2
C. -2
D. -4

12. Solve $$\log_2(12x - 10) = 1 + \log_2(4x + 3)$$.
A. 1.00
B. 1.75
C. 4.00
D. 4.75