Correct Answer: D. 20

Correct Answer: D. x³ - 7x - 6

Correct Answer: B. 3,-4

Explanation

a. Area of sector MON = \(\frac{MON}{360} \times\pi r^2\)

= \(\frac{60}{360}\times\frac{22}{7}\times7^2\)

= \(\frac{77}{3}cm^2\)

\(\frac{NT}{7}\) = sin60°

NT = 7sin60° = \(7\times\frac{\sqrt{3}}{2}\) = \(7\times\frac{\sqrt{3}}{2}\)cm.

\(\frac{OT}{9} = cos60^0\)

OT = 7cos60° = \(7\frac{1}{2}\)cm

Area of ?ONT = \(\frac{1}{2}\times OT\times NT\)

= \(\frac{1}{2}\times\frac{7}{2}\times\frac{7\sqrt{3}}{2} = 49\sqrt{3}{8}cm^2\)

Area of shaded portion = Area of sector MON - Area of ?ONT

= \(\frac{77}{3} - \frac{49\sqrt{3}}{8}\) = 25.67 - 10.61 = \(15.06cm^2\) = 15.1\(cm^2\)

b. Given : y = mx + c; hence ; x = \(\frac{ y - c }{ m } = \frac{ y }{ m } - \frac{ c }{ m }\)

x-intercept = \(\frac{ - c }{ m } = \frac{ - 3 }{ 4 }\)

Therefore, m = \(\frac{4}{3}\)c ....................... (1)

But y-intercept, c = \(\frac{2}{7}\)

Therefore, m = \(\frac{4}{3}\times\frac{2}{7} = \frac{8}{21}\)

Equation of straight: y = mx + c

y = \(\frac{8}{21}x + \frac{2}{7}\) OR 21y = 8x + 6 = 8x - 21y = - 6

Explanation

(a) finding a = 10\(^{1.3010}\) and b = 10\(^{1.4771}\)

Then, ab = 10\(^{1.3010}\) x 10\(^{1.4771}\) = 10\(^{2.4771}\) = 599.9

(b)(i) they were expected to find < ABC = 180° - 62° = 118°

Exterior < AOC a 2 x 118° - 236° (< at centre is twice angle at the circumference)

Interior < AOC = 360° - 236° = 124°(angle at a point) as required.

(b)(ii) < BAC in 180° - 39° - 118° = 23° (sum of angles of a triangle)

Correct Answer: C. 1.0

Correct Answer: C. 225^o

Explanation

(a) & (b)

Correct Answer: B. 10°

Explanation

tan \(\theta\) = \(\frac{9}{50}\) = 0.18

\(\theta = tan^{-1} 0.18\)

\(\theta\) = 10.20

Correct Answer: C. sec²x