Solve the inequality x² + 2x > 15.

• A. x< -3 or x > 5
• B. -5< x< 3
• C. x< 3 or x > 5
• D. x > 3 or x< -5

Given that G is directly proportional to the square of H. If G is 5 when H is 3, Find H when G is 100

• (A)150
• (B)125
• (C)180
• (D)225

(a) Find the coordinates of the point which divides the line joining (7, -5) and (-2, 7) externally in the ration 3 : 2.

(b) Without using calculators or mathematical tables, evaluate \(\frac{2}{1 + \sqrt{2}}\) - \(\frac{2}{2 + \sqrt{2}}\), leaving the answer in the form p + q\(\sqrt{n}\), where p, q and n are integers.

Three boys shared some oranges. The first received 1/3 of the oranges and the second received 2/3 of the remaining. If the third boy received the remaining 12 oranges, how many oranges did they share

• A. 60
• B. 54
• C. 48
• D. 42

Evaluate ∫sin2xdx

• A. cos 2x + k
• B. 1/2cos 2x + k
• C. −1/2cos 2x + k
• D. -cos 2x + k

Simplify: \(\frac{54k^2 - 6}{3k + 1}\)

• A. 6(1 - 3k²)
• B. 6(3k² - 1)
• C. 6(3k - 1)
• D. 6(1 - 3k)

Factorize x² - 2x - 3xy completely

• A. (x - 2)(3x - y)
• B. (x - 3y)(x - 2)
• C. (x - 3y)(x - 3y)
• D. (3x + y)(x - 2)

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).

• A. -2
• B. -\(\frac{3}{2}\)
• C. \(\frac{3}{2}\)
• D. 2

(a) Simplify : \((2a + b)^{2} - (b - 2a)^{2}\)

(b) Given that \(S = K\sqrt{m^{2} + n^{2}}\); (i) make m the subject of the relations ; (ii) if S = 12.2, K = 0.02 and n = 1.1, find, correct to the nearest whole number, the positive value of m.

A chord of a circle of a diameter 42cm subtends an angle of 60o at the centre of the circle. Find the length of the mirror arc

• A. 22cm
• B. 44cm
• C. 110cm
• D. 220cm