Correct Answer: C. 3

Explanation

Volume of sphere = Volume of cylinder

i.e. \(\frac{4}{3} \pi r^3 = \pi r^2 h\)

\(\frac{4}{3} \pi r^3 = \pi \times 3^2 \times 4\)

r³ = \(\frac{\pi \times 9 \times 4 \times 3}{4 \pi}\)

r = 3\(\sqrt{27}\)

= 3

Explanation

\(Mean = \frac{\sum fx}{\sum f} = \frac{3350}{70} = 47.8571\)

\(\approxeq 47.9\) (to 3 sig. figs)

(b)(i) Mode = 45 (score with the highest frequency)

(ii) Range = Highest mark - Lowest mark

= 75 - 15 = 60.

Correct Answer: A. (x+5y)(7x+y)

Correct Answer: A. 9

Explanation

\(f(x) = mx^{2} - 6x - 3\)

\(f '(x) = \frac{\mathrm d y}{\mathrm d x} = 2mx - 6\)

\(f'(1) = 2m - 6 = 12\)

\(2m = 18 \implies m = 9\)

Correct Answer: A. -2

Explanation

\(\int_{1}^{2} (2 + 2x - 3x^{2}) \mathrm {d} x\)

= \((2x + x^{2} - x^{3})|_{1}^{2}\)

= \((2(2) + 2^{2} - 2^{3}) - (2(1) + 1^{2} - 1^{3})\)

= \(0 - 2 = -2\)

Correct Answer: C. -\(\frac{4}{11}\), 2

Correct Answer: C. 0.8

Explanation

\(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\)\(\begin{pmatrix} 5 \\ 4 \end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\)

\(\begin{pmatrix} 10 + 4 \\ 20 + 12\end{pmatrix}\) = \(\begin{pmatrix} 14 \\ 32\end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\)

k = \(\frac{14}{17.5} = \frac{32}{40} = 0.8\)

Correct Answer: B. 2

Correct Answer: D. \(\frac{x + 2}{x - 2}\)

Explanation

\(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\)

\(\frac{(x - 7)(x + 2)}{(x - 7)(x - 2)}\)

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

Explanation

(a)

(i) In the diagram,

\(x° + 90° = (3x + 15)°\) (Sum of opposite interior angles)

Thus, \(90° - 15° = 3x - x \implies 75° = 2x\)

\(x = 37.5°\)

(ii)

< RSQ = 90° - 37.5° = 52.5°

(b) \(2N4_{seven} = 15N_{nine}\)

\(2N4_{seven} = (2 \times 7^{2}) + (N \times 7^{1}) + (4 \times 7^{0})\)

= \(98 + 7N + 4\)

= \(102 + 7N\)

\(15N_{nine} = (1 \times 9^{2}) + (5 \times 9^{1}) + (N \times 9^{0})\)

= \(81 + 45 + N\)

= \(126 + N\)

\(\implies 102 + 7N = 126 + N\)

\(7N - N = 126 - 102 = 24\)

\(6N = 24 \implies N = 4\)

Therefore, \(244_{seven} = 154_{nine}\).