Correct Answer: c. 512.5cm

Explanation

(a)

(b)

(ci) The number of candidates who scored marks between 24 and 58 = 146 - 14 = 132

(cii) if 12% of the candidates passed with distinction then 88% did not pass with distinction

⇒\(88% of 200 = \frac{88}{100}\times 200=176\)

From the cumulative frequency curve, 176 corresponds to 69 marks

∴ Thelowest mark for distinction = 69 marks

Correct Answer: C. n = 3

Explanation

\(\frac{5^{n +3}}{25^{2n -2}}\) = 5o

\(\frac{5^{n + 3}}{5^{2(2n - 3)}}\) = 5o

n + 3 - 4n + 6 = 0

-3n + 9 = 0

-3n = -9

n = \(\frac{-9}{-3}\)

n = 3

Correct Answer: B. - 22

Explanation

\(\frac{6x + k}{2x^2 + 7x - 15} = \frac{4}{x + 5} - \frac{2}{2x - 3}\)

6x + k = 4 (2x - 3) - 2(x + 5)

6x + k = 8x - 12 - 2x - 10

6x + k = 6x - 22

k = - 22

Explanation

(a)(i) P(A) = \(\frac{2}{3}\) ; P(B) = \(\frac{5}{8}\) ; P(C) = \(\frac{3}{4}\).

\(P(A \cap B \cap C) = P(A) \times P(B) \times P(C)\)

= \(\frac{2}{3} \times \frac{5}{8} \times \frac{3}{4} = \frac{5}{16}\)

(ii) P(A') = \(1 - \frac{2}{3} = \frac{1}{3}\)

P(B') = \(1 - \frac{5}{8} = \frac{3}{8}\)

P(C') = \(1 - \frac{3}{4} = \frac{1}{4}\)

\(P(A' \cap B' \cap C') = P(A') \times P(B') \times P(C')\)

= \(\frac{1}{3} \times \frac{3}{8} \times \frac{1}{4} \)

= \(\frac{1}{32}\)

(iii) P(A and B pass, C fails) = \(\frac{2}{3} \times \frac{5}{8} \times \frac{1}{4} = \frac{5}{48}\)

P( A and C pass, B fails) = \(\frac{2}{3} \times \frac{3}{4} \times \frac{3}{8} = \frac{3}{16}\)

P(B and C pass, A fails) = \(\frac{5}{8} \times \frac{3}{4} \times \frac{1}{3} = \frac{5}{32}\)

P(only two of the boys pass) = \(\frac{5}{48} + \frac{3}{16} + \frac{5}{32} = \frac{43}{96}\)

(b) Let the cost price be x

% gain = \(\frac{\text{actual gain}}{\text{cost price}} \times 100%\)

\(20 = \frac{36,000 - x}{x} \times 100%\)

\(\frac{36,000 - x}{x} = \frac{1}{5}\)

\(5(36,000 - x) = x \implies 180,000 - 5x = x\)

\(180,000 = x + 5x = 6x\)

\(x = N30,000\)

Discount (5%) : \(\frac{5}{100} \times N36,000 = N1,800\)

Selling price : \(N(36,000 - 1,800) = N34,200\)

Actual gain : \(\frac{34,200 - 30,000}{30,000} \times 100% \)

= 14%

(a)(i) P(A) = \(\frac{2}{3}\) ; P(B) = \(\frac{5}{8}\) ; P(C) = \(\frac{3}{4}\).

\(P(A \cap B \cap C) = P(A) \times P(B) \times P(C)\)

= \(\frac{2}{3} \times \frac{5}{8} \times \frac{3}{4} = \frac{5}{16}\)

(ii) P(A') = \(1 - \frac{2}{3} = \frac{1}{3}\)

P(B') = \(1 - \frac{5}{8} = \frac{3}{8}\)

P(C') = \(1 - \frac{3}{4} = \frac{1}{4}\)

\(P(A' \cap B' \cap C') = P(A') \times P(B') \times P(C')\)

= \(\frac{1}{3} \times \frac{3}{8} \times \frac{1}{4} \)

= \(\frac{1}{32}\)

(iii) P(A and B pass, C fails) = \(\frac{2}{3} \times \frac{5}{8} \times \frac{1}{4} = \frac{5}{48}\)

P( A and C pass, B fails) = \(\frac{2}{3} \times \frac{3}{4} \times \frac{3}{8} = \frac{3}{16}\)

P(B and C pass, A fails) = \(\frac{5}{8} \times \frac{3}{4} \times \frac{1}{3} = \frac{5}{32}\)

P(only two of the boys pass) = \(\frac{5}{48} + \frac{3}{16} + \frac{5}{32} = \frac{43}{96}\)

(b) Let the cost price be x

% gain = \(\frac{\text{actual gain}}{\text{cost price}} \times 100%\)

\(20 = \frac{36,000 - x}{x} \times 100%\)

\(\frac{36,000 - x}{x} = \frac{1}{5}\)

\(5(36,000 - x) = x \implies 180,000 - 5x = x\)

\(180,000 = x + 5x = 6x\)

\(x = N30,000\)

Discount (5%) : \(\frac{5}{100} \times N36,000 = N1,800\)

Selling price : \(N(36,000 - 1,800) = N34,200\)

Actual gain : \(\frac{34,200 - 30,000}{30,000} \times 100% \)

= 14%

Correct Answer: A. 24

Correct Answer: C. 15

Explanation

\(=^6C_4\)

\(=\frac{6!}{(4!\times2!)}\)

\(=\frac{6\times5}{2\times1}\)

= 15

Correct Answer: (a) N150,000

Correct Answer: A. 5.7\(ms^{-1}\)

Explanation

\(s = ut + \frac{1}{2}at^{2}\)

\(250 = 6u + \frac{1}{2}(12)(6^{2})\)

\(250 = 6u + 216 \implies 6u = 250 - 216 = 34\)

\(u = \frac{34}{6} \approxeq 5.7ms^{-1}\)

Correct Answer: B. 15:17

Explanation

Divide cash enrollment by their common factors then the answer of each division gives the required ratio. i.e. x = \(\frac{1050}{70}\) = 15

and y = \(\frac{1190}{70}\) = 17

ratio of enrollment of x to y = 15:17