Correct Answer: A. 0.117

Explanation

log\(_{10}\) x = \(\bar{2}.3675\) => x = 0.023

log\(_{10}\) y = \(\bar{2}.9738\) => y = 0.094

x + y = 0.117

Explanation

(a)

(b) (i) 60th percentile is where the line from the cumulative frequency of 60 touches the curve i.e. 60th percentile = 58.5

(ii) If the pass mark was fixed at 35%, then the frequency will be 13 with the class mark 31 - 40.

(a)

(b) (i) 60th percentile is where the line from the cumulative frequency of 60 touches the curve i.e. 60th percentile = 58.5

(ii) If the pass mark was fixed at 35%, then the frequency will be 13 with the class mark 31 - 40.

Correct Answer: C. 8

Explanation

(a) Let the sum of \(3\frac{2}{3}\) and \(2\frac{1}{5}\) be less than 7 by z.

Then z = \(7 - (3\frac{2}{3} + 2\frac{1}{5})\)

= \(7 - (\frac{11}{3} + \frac{11}{5})\)

= \(7 - \frac{88}{15}\)

= \(\frac{17}{15} = 1\frac{2}{15}\)

Hence, the sum of \(3\frac{2}{3}\) and \(2\frac{1}{5}\) is less than 7 by \(1\frac{2}{15}\).

(b) \(h = 6 + 4\cos (15p)°\) (Given)

(i) When p = 4,

\(h = 6 + 4\cos (15 \times 4)°\)

\(h = 6 + 4 \cos 60°\)

= \(6 + 4 \times 0.5\)

= \(6 + 2 = 8 m\)

(ii) When h = 9 m, the given equation becomes

\(9 = 6 + 4\cos (15p)°\)

\(9 - 6 = 4 \cos (15p)°\)

\(\cos (15p)° = \frac{3}{4}\)

\((15p)° = \cos^{-1} (0.75)\)

\((15p)° = 41.4°\)

\(p° = \frac{41.4}{15}\)

\(p° = 2.76°\)

\(p \approxeq 2.8°\) (2 significant figures).

Correct Answer: B. 55°

Correct Answer: D. \(\frac{2 - \sqrt{3}}{3}\)

Explanation

Sin 60 = \(\frac{\sqrt{3}}{2}\); cos 60^o = \(\frac{1}{2}\)

= \(\frac{1 - \sin 60}{1 + \cos 60} = \frac{1 - \frac{\sqrt{3}}{2}}{1 + \frac{1}{2}}\)

= \(\frac{2 - \sqrt{3}}{3}{2}\div \frac{2 + 1}{2}\)

= \(\frac{2 - \sqrt{3}}{2} \times \frac{2}{3}\)

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

Explanation

(a)(i) R is the required region.

(iii) Coordinates of the point of intersection of the two graphs = (1.1, 3.8)

(b) Assuming \(y - \frac{3x}{4} = 3\)

If x = 0, \(y - \frac{3}{4}(0) = 3 \implies y = 3\)

If y = 0, \(0 - \frac{3}{4}x = 3 \implies -3x = 12 ; x = - 4\)

Assuming \(y + 2x = 6\)

If x = 0, \(y + 2(0) = 6 \implies y = 6\)

If y = 0, \(0 + 2x = 6 \implies 2x = 6 ; x = 3\)

(b) \((x + 2)(x + c) = x^{2} + 2x + cx + 2c\)

\(x^{2} + (2 + c)x + 2c = x^{2} + bx + 18\)

\( 2c = 18 ; c = 9\)

\(b = 2 + c = 2 + 9 = 11\)

(b, c) = (11, 9).

Correct Answer: A. 1.5

Explanation

Numerator: 96 → 37.5% of 96 = 36

Decreased by 36 → 96 - 36

New numerator = 60

Denominator: 50 → 20% of 50 = 10

Decreased by 10 → 50 - 10 = 40

New Denominator = 40

New fraction = \(\frac{60}{40}\) or 1.5

Correct Answer: A. 10 cm

Explanation

Volume of a cylinder = \(\pi r^2h\)

40\(\pi cm^3\) = \(\pi. 4^2h\)

40\(cm^3\) = 16h

h = 2.5cm/sec

In 4 seconds, 2.5cm x 4

= 10cm

Correct Answer: B. \(\log_{10}^2\)

Explanation

log\(_{10}\) 6 - log\(_{10}\)3\(^3\) + log\(_{10}\) (\(\sqrt[3]{27}\))\(^2\)

= log \(_{10}\) 6 - log \(_{10}\) 27 + log\(_{10}\) 9

= log\(_{10}\) \(\frac{6 \times 9}{27}\)

= log\(_{10}\)2