Explanation

(a) \(2Ax - Kx^{2}\)

When x = 1, \(2A(1) - K(1^{2}) = 7\)

\(2A - K = 7 ... (1)\)

When x = 2, \(2A(2) - K(2^{2}) = 4\)

\(4A - 4K = 4 \implies A - K = 1 ... (2)\)

From (2), \(A = 1 + K\)

(1) becomes : \(2(1 + K) - K = 7\)

\(2 + 2K - K = 7 \implies 2 + K = 7\)

\(\therefore K = 5\)

\(A = 1 + K = 1 + 5 = 6\)

\(A, K = 6, 5\)

(b) \(x^{2} - 3x - 1 = 0\)

\(a = 1, b = -3, c = -1\)

Using the quadratic formula,

\(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

\(x = \frac{-(-3) \pm \sqrt{(-3)^{2} - 4(1)(-3)}}{2(1)}\)

\(x = \frac{3 \pm \sqrt{9 + 12}}{2}\)

\(x = \frac{3 \pm \sqrt{21}}{2} = \frac{3 \pm 4.583}{2}\)

\(x = \frac{3 + 4.583}{2} ; x = \frac{3 - 4.583}{2}\)

\(x = \frac{7.583}{2} = 3.7915 \approxeq 3.8\) (to 1 d.p)

\(x = \frac{-1.583}{2} = -0.7915 \approxeq -0.8\) (to 1 d.p)

Correct Answer: (b)LX

Correct Answer: A. 5%

Explanation

(a)

(b) Mode = 33.5

Correct Answer: B. 12√2 cm

Correct Answer: C. 9

Correct Answer: A. 40°

Explanation

In the diagram above,

∠MNO = 140° and angles on a straight line is 180°

: ∠NMO = (180 - 140)° = 40°

Hence; ∠POM = 40° ( alternate angle ∠S)

Correct Answer: A. 25m/s

Explanation

\(\frac{720 \times 1000}{8 \times 60 \times 60}\) = \(\frac{20 \times 10}{8}\)

= \(\frac{200}{8}\)

= 25 m/s

Correct Answer: A.¹/₄

Explanation

log₈x - 4log₈x = 2; log₈x - log₈x⁴ = 2

log₈x/x⁴ = 2

x/x⁴ = 8² = 1/x³ = 64

x³ = (1/4)³; x = 1/4

Correct Answer: A. \(\frac{5}{33}\)

Explanation

Total number of balls = 5 + 3 + 4

= 12 balls

P(first ball is red) = \(\frac{5}{12}\)

P(second ball is red) = \(\frac{4}{11}\)

\(\therefore\) P(both balls are red) = \(\frac{5}{12} \times \frac{4}{11}\)

= \(\frac{5}{33}\)