Correct Answer: A. x = 1, y = -2

Explanation

3x - 2y = 7; Solve by elimination method

x + 2y = -3

3x - 2y = 7.....(i)

-3x + 6y = -9.....(ii)

-8y = 16

y = \(\frac{16}{-8} = -2\)

Put y = -2 into equation (i); 3x - 2y = 7

3x - 2(-2) = 7

3x + 4 = 7

3x = 7 - 4

3x = 3

x = \(\frac{3}{3}\) = 1

Correct Answer: C. 40

Explanation

x\(^3\)y\(^2\) in (x-2y)\(^5\)

n = 5, r = 3, p = x, q = -2y

5C\(_3\) * x\(^3\) -2y\(^2\)

5C\(_3\) = \(\frac{5!}{[5-3]!3!}\)

\(\frac{5*4*3!}{2! 3!}\) → \(\frac{5*4}{2}\)

5C\(_3\) = 10

: 5C\(_3\) * x\(^3\) -2y\(^2\) = 10 * x\(^3\) 4y\(^2\)

40x\(^3\)y\(^2\)

the coefficient is 40

Correct Answer: A. 40√3/3m

Correct Answer: B. T = R - \(\frac{15P^3}{Q}\)

Explanation

Cubic both sides; P³ = \(\frac{Q(R - T)}{15}\)

(cross multiplication) Q(R - T) = 15P³

(divide both sides by Q); R - T = 15\(\frac{1}{Q}\)

(subtract r from both sides) - T = \(\frac{15P^3}{Q - R}\)

T = R - \(\frac{15P^3}{Q}\)

Correct Answer: D. 12/5

Explanation

\(\cos \theta = \frac{5}{13}\)

\(\implies\) In the right- angled triangle, with an angle \(\theta\), the adjacent side to \(\theta\) = 5 and the hypotenuse = 13.

\(\therefore 13^2 = opp^2 + 5^2\)

\(opp^2 = 169 - 25 = 144 \implies opp = \sqrt{144}\)

= 12.

\(\tan \theta = \frac{opp}{adj} = \frac{12}{5}\)

Correct Answer: B. \(\frac{19}{35}\)

Correct Answer: C. (2,6)

Correct Answer: D. 17

Explanation

Students that scored 4 and above = 5 + 3 + 3 + 0 + 2 + 2 + 2 = 17

Explanation

(a) \((x - 2)(x - 3) = 12\)

\(x^{2} - 3x - 2x + 6 = 12 \implies x^{2} - 5x + 6 - 12 = 0\)

\(x^{2} - 5x - 6 = 0\)

\(x^{2} - 6x + x - 6 = 0 \implies x(x - 6) + 1(x - 6) = 0\)

\( (x - 6)(x + 1) = 0 \implies \text{x = 6 or -1}\)

(b) The shaded portion comprises two shaded segments labelled A and B.

Area of segment A = \(\frac{60°}{360°} \times \pi r^{2} - \frac{1}{2} r^{2} \sin 60°\)

\(\frac{1}{6} \times \frac{22}{7} \times 7 \times 7 - \frac{1}{2} \times 7 \times 7 \times 0.8660\)

= \(25.667 - 21.217\)

= \(4.45 cm^{2}\)

Also, the area of the segment B = \(4.45 cm^{2}\).

Hence, the area of the shaded portion = \(4.45 cm^{2} + 4.45 cm^{2}\)

= \(8.9 cm^{2}\)

\(\approxeq 9 cm^{2}\) (to the nearest whole number).

Correct Answer: C. 90km/hr

Explanation

\(speed = \frac{distance}{time}\\

72 = \frac{60}{time}\\

t = \frac{60}{72} = \frac{5}{6}hr\)

time lost = 10mis \(= \frac{10}{60}hr = \frac{1}{6}\)

Time required for the journey

\(=\frac{5}{6}-\frac{1}{6} = \frac{2}{3}\\

speed \hspace{1mm}=60 \div \frac{2}{3} = 90km/hr\)