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