Explanation

(a) Let the cost of the car to the dealer be x.

Sales of car to a man with 15% profit : (115% of x = 1.15 x\)

Sale of the car to the woman by the man at 5% loss : (95% of 1.15x = N120,175.00)

\(0.95 \times 1.15x = N120,175.00\)

\(1.0925x = N120,175.00\)

\(x = \frac{120,175.00}{1.0925}\)

\(x = N110,000\)

The original cost of the car to the dealer = N110,000.00.

(b) Circumference of a circle = \(2\pi r\)

Distance covered by the wheel = 1.05 km

Radius of the wheel = 18cm

Circumference of the wheel = \(2 \times \frac{22}{7} \times 18\)

= \(113.14 cm\)

Note : 1.05 km = 105,000 cm

Number of revolution = \(\frac{105,000}{113.14}\)

= \(928.05 revs\)

\(\approxeq 928 revs\)

Correct Answer: C. N4,400:00k

Correct Answer: B. \(\frac{3}{2}\)

Explanation

9(2 - x) = 3

3^{2(2 - x)} = 3

2(2 - x) = 1

4 - 2x = 1

-2x = 1 - 4

-2x = -3

x = \(\frac{-3}{-2}\)

x = \(\frac{3}{2}\)

Correct Answer: D. 50°

Explanation

< Q = < R (OQ = OR = radii)

< QOR = 180° - 2(40°) = 100°

< QSR = < RPQ = \(\frac{1}{2}\) < QOR

= \(\frac{100}{2} = 50°\)

Correct Answer: D. 672

Explanation

Let the power of \(2x^{2}\) be t and the power of \(\frac{1}{x} \equiv x^{-1}\) = 9 - t.

\((2x^{2})^{t}(x^{-1})^{9 - t} = x^{0}\)

Dealing with x alone, we have

\((x^{2t})(x^{-9 + t}) = x^{0} \implies 2t - 9 + t = 0\)

\(3t - 9 = 0 \therefore t = 3\)

The binomial expansion is then,

\(^{9}C_{3} (2x^{2})^{3}(x^{-1})^{6} = \frac{9!}{(9-3)! 3!} \times 2^{3}\)

= 84 x 8

= 672

Explanation

(a)

\(\theta = \frac{60°}{2} = 30°\)

Area of trapezium = \(\frac{a + b}{2} h\)

\(60 = \frac{15 + 25}{2} h \implies 60 = 20h\)

\(h = \frac{60}{20} = 3 cm\)

(ii) Considering \(\Delta PSR\),

\(\sin \theta = \frac{Opp}{Hyp}\)

\(\sin 30 = \frac{3}{|PS|}\)

\(|PS| = \frac{3}{\sin 30}\)

= \(\frac{3}{0.5} = 6 cm\)

(b) Let the total amount to be shared = k.

Ade's share = \(\frac{3}{5} k \)

Remainder = \(k - \frac{3}{5}k \)

= \(\frac{2}{5}k\)

Nelly's share : \(\frac{1}{3} \times \frac{2}{5}k\)

= \(\frac{2}{15}k\)

Austin's share : \(\frac{2}{5}k - \frac{2}{15}k\)

= \(\frac{4}{15}k\)

\(\frac{4}{15}k - \frac{2}{15}k = \frac{2}{15}k\)

\(\frac{2}{15}k = N3,000\)

\(\implies k = \frac{3,000 \times 15}{2}\)

= \(N22,500\)

Ade's share = \(\frac{3}{5}k\)

= \(\frac{3}{5} \times N22,500 = N13,500\).

Explanation

(c) |XP| = 3.8 cm.

Correct Answer: C. 336

Explanation

\(^3{P}_3\) = \(\frac{8!}{8-3}!\)

= \(\frac{(8 * 7 * 6 * 5)!}{5!}\)

= 336

Correct Answer: C. 1.455

Correct Answer: A. 7:4

Explanation

\(\frac{4m + 3n}{4m - 3n} = \frac{5}{2}\)

\(5(4m - 3n) = 2(4m + 3n)\)

\(20m - 15n = 8m + 6n\)

\(20m - 8m = 6n + 15n\)

\(12m = 21n\)

\(\frac{21}{12} = \frac{m}{n}\)

\(m : n = 7 : 4\)