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(a) Formula : Volume = \(\frac{1}{3} \pi r^{2} h\) \(\pi = 3.142; r = 4cm; h = 6cm\) \(Volume = \frac{1}{3} \times 3.142 \times 4^{2} \times 6 = 100.544 cm^{3}\) (b) Volume of hemisphere = \(\frac{1}{2} \times \frac{4}{3} \pi r^{3}\) = \(\frac{2}{3} \times \frac{22}{7} \times 5^{3}\) = \(\frac{5500}{21} cm^{3} = 261.905 cm^{3}\) Volume of water discharged per second = \(\pi r^{2} h\) = \(\frac{22}{7} \times 0.2m \times 0.2m \times 2m = \frac{1.76}{7}\) = \(0.2514 m^{3} / sec\) \(\therefore \text{The time to fill the tank = } \frac{261.905}{0.2514 \times 60}\) = \(\frac{261.905}{15.084} = 17.363 mins\) \(\approxeq 17.4 mins\)

(a) Class Interval Tally Freq 45 - 49 |||| | 6 50 - 54 |||| |||| 9 55 - 59 |||| |||| 10 60 - 64 |||| |||| || 12 65 - 69 |||| || 7 70 - 74 |||| | 6 (b) Class Interval Mid-value (x) x - 62 \((x - 62)^{2}\) \(f\) \(f(x - 62)\) \(f(x - 62)^{2}\) 45 - 49 47 -15 225 6 -90 1350 50 - 54 52 -10 100 9 -90 900 55 - 59 57 -5 25 10 -50 250 60 - 64 62 0 0 12 0 0 65 - 69 67 5 25 7 35 175 70 - 74 72 10 100 6 60 600 \(\sum\) 50 -135 3275 \(Mean (\bar{x}) = A + \frac{\sum f(x - A)}{\sum f}\) = \(62 + \frac{-135}{50}\) = \(62 - 2.7 = 59.3\) Standard deviation = \(\sqrt{\frac{\sum f(x - A)}{\sum f}}\) = \(\sqrt{\frac{3275}{50}}\) = \(\sqrt{65.5}\) = \(8.093 \approxeq 8.1\) (to 1 decimal place)

(b) |AC| = 7cm ; |QB| = 2.9cm.

(a) Let S = sample space = integers from 5 to 25 inclusive. F = multiple of 5 ; T = multiple of 3. S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25} F = {5, 10, 15, 20, 25}; T = {6, 9, 12, 15, 18, 21, 24} P(F or T) = \(\frac{5}{21} + \frac{7}{21} = \frac{12}{21} = \frac{4}{7}\) (b) Let B = blue balls and R = red balls n(B) = 4 ; n(R) = 6. (i) P(both are red) = \(\frac{6}{10} \times \frac{6}{10} = \frac{36}{100}\) = \(\frac{9}{25}\) (ii) P(both are same colour) = P(both are red) or P(both are blue) = \(\frac{9}{25} + (\frac{2}{5} \times \frac{2}{5})\) = \(\frac{9}{25} + \frac{4}{25}\) = \(\frac{13}{25}\)

(a) \(y = 2x^{2} - 5x + 1\) x -3 -2 -1 0 1 2 3 4 5 y 34 19 8 1 -2 -1 4 13 26 Table of value for \(y = x + 6\) x -2 0 2 y 4 6 8 (b) (d) (i) Least value of y = -2 occurs at x = 1 (ii) Solution of \(2x^{2} - 5x + 1 = x + 6\) are x = -0.7 and x = 3.7.

(a) The number that speak Hausa = n(H) = 25 The number that speak Igbo = n(I) = 16 The number that speak Yoruba = n(Y) = 21 Total no of students = U = 40 \(n(H \cap I) = 8 ; n(H \cap Y) = 11 ; n(Y \cap I) = 6\) (b) \(U = n(H) + n(I) + n(Y) - n(H \cap Y) - n(H \cap I) - n(I \cap Y) + n(H \cap Y \cap I)\) \(40 = 6 + x + 2 + x + 4 + x + 8 - x + 11 - x + 6 - x + x\) \(40 = 37 + x \implies x = 40 - 37 = 3\)

(a) Distance along arc PQ = \(\frac{\theta}{360^\circ} \times 2 \pi r\) where \(r = R \cos \theta\) \(|PQ| = \frac{60^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 6400 \times \cos 40^\circ\) \(|PQ| = \frac{1}{6} \times 2 \times \frac{22}{7} \times 6400 \times 0.7660\) = \(5134.74 km \approxeq 5135km\) (to the nearest whole number) (b) Difference in latitude between Q and T = 40^\circ - 28^\circ = 12^\circ \(\therefore |QT| \text{along the line of longitude} = \frac{12}{360} \times 2 \times \frac{22}{7} \times 6400\) \(\frac{1}{30} \times 2 \times \frac{22}{7} \times 6400 = 1340.95km \approxeq 1341km\) (c) Average speed = \(\frac{\text{Total distance covered}}{\text{Total time taken}}\) = \(\frac{5134.74 + 1340.95}{12} = 539.64km/hr\) \(\approxeq 540km/hr\) (to 3 significant figures)

No expanded working has been attached for this question yet. The verified answer is Option B.

Agitated means disturbed, anxious, upset or restless. The word opposite in meaning (antonym) of agitated is calm, which means peaceful, composed and free from disturbance.

Since obstacles are things that hinder progress or success, the opposite would be advantages, which are things that support progress or success.

The word "sobbed" indicates a deep and loud cry, usually accompanied by convulsive breaths. The opposite of crying or sobbing is laughing. Therefore, option D, "laughed," is the most appropriate choice as it represents the opposite action, indicating a joyful or amused expression rather than the distress implied by "sobbed."

No expanded working has been attached for this question yet. The verified answer is Option A.

No expanded working has been attached for this question yet. The verified answer is Option B.

No expanded working has been attached for this question yet. The verified answer is Option D.

No expanded working has been attached for this question yet. The verified answer is Option A.