A trader in country where their currency 'MONI'(M) is in base five bought 103₅ oranges at M14₅ each. If he sold the oranges at M24₅ each, what will be his gain?

A. 103₅

B. 1030₅

C. 102₅

D. 2002₅

E. 3032₅

Rationalize \(\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}\)

A. -2 \sqrt{35}\)

B. 4\sqrt{7}\) - 6\(\sqrt{5}\)

C. -\(\sqrt{35}\)

D. 4\sqrt{7}\) - 8\(\sqrt{5}\)

E. \(\sqrt{35}\)

Simplify \(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\)

A. 1

B. 6

C. \(\frac{1}{27}\)

D. \(\frac{4}{3}\)

P varies directly as the square of q and inversely as r. If p = 36, when q = 36, when q = 3 and r = 4, find p when q = 5 and r = 2

A. 72

B. 100

C. 90

D. 200

E. 125

Factorize 6x2 - 14x - 12

A. 2(x + 3)(3x - 2)

B. 6(x - 2)(x + 1)

C. 2(x - 3)(3x + 2)

D. 6(x + 2)(x - 1)

E. (3x - 4)(2x + 3)

A straight line y = mx meets the curve y = x2 - 12x + 40 in two distinct points. If one of them is (5, 5) find the other

A. (5, 6)

B. (8, 8)

C. (8, 5)

D. (7,7)

E. (7, 5)

The table below is drawn for a graph y = x³ - 3x + 1
\(\begin{array}{c|c} x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline y = x^3 - 3x + 1 & 1 & -1 & 3 & 1 & -1 & 3 & 1\end{array}\)
From x = -2 to x = 1, the graph crosses the x-axis in the range(s)

A. -1 < x < 0 and 0 < x < 1

B. -2 < x < -1 and 0 < x < 1

C. -2 < x < -1 and -1 < x < 0

D. 0 < x < 1

In a racing competition, Musa covered a distance 5x km in the first hour and (x + 10)km in the next hour. He was second to Nzozi who covered a total distance of 118km in the two hours. Which of the following inequalities is correct?

A. -1 < x < x < 0

B. -3 < x < 3

C. 0 \(\leq\) x < 18

D. 15 < x < 18

If 2x + 3y = 1 and x - 2y = 11, find (x + y)

A. 5

B. -3

C. 8

D. 2

E. -2

Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?

A. x² - 5x - 10 = 0

B. x² - 20x + 360 = 0

C. x² - 21x - 270 = 0

D. 3x² - 65x + 362 = 0