Find the volume of a cone which has a base radius of 5 cm and slant height of 13 cm.

• A. \(300\pi\) cm\(^2\)
• B. \(325\pi\) cm\(^2\)
• C. \(\frac{325}{3}\pi\) cm\(^2\)
• D. \(100\pi\) cm\(^2\)

Correct Answer: D. \(100\pi\) cm\(^2\)

Explanation

Volume of a cone = \(\frac{1}{3}\pi r^2 h\)

r = 5 cm

l = 13 cm

Using Pythagoras theorem

⇒ \(13^2 = 5^2 + h^2\)

⇒ \(169 = 25 + h^2\)

⇒ \(169 - 25 = h^2\)

⇒ \(h^2 = 144\)

⇒ \(h = \sqrt144 = 12 cm\)

∴ Volume of the cone = \(\frac{1}{3} \times\pi\times 5^2 x 12 = 100\pi\) cm\(^2\)

Solve the inequality y² - 3y > 18

• A. -3< y< 6
• B. y< -3 or y > 6
• C. y > -3 or y > 6
• D. y< 3 or y< 6

Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.

• A. 24°
• B. 56°
• C. 127°
• D. 156°

Ten coins were tossed together a number of times. The distribution of the number of heads obtained is given in the following table :

Calculate, correct to three decimal places, the :

(a) mean number of heads ;

(b) probability of getting an even head ;

(c) probability of getting an odd number.

Add the lowest and the highest of these numbers and find the average. 20, 48, 0, 100 and 10

• a. 50
• b. 100
• c. 55
• d. 18

A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?

• A. 43.7% loss
• B. 13.2% gain
• C. 13.2% loss
• D. 43.7% gain

The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newton’s is 2cm, find the extension produced by a tension of 12 newton’s.

• A. 2
• B. 1
• C. 0
• D. 3

Make u the subject of formula, E = \(\frac{m}{2g}\)(v² - u²)

• A. u = \(\sqrt{v^2 - \frac{2Eg}{m}}\)
• B. u = \(\sqrt{\frac{v^2}{m} - \frac{2Eg}{4}}\)
• C. u = \(\sqrt{v- \frac{2Eg}{m}}\)
• D. u = \(\sqrt{\frac{2v^2Eg}{m}}\)

Consider the following statement:

x: All wrestlers are strong

y: Some wresters are not weightlifters.

Which of the following is a valid conclusion?

• A. All strong wrestlers are weightlifters
• B. Some strong wrestlers are not weightlifters
• C. Some weak wrestlers are weightlifters
• D. All weightlifters are wrestlers

Find the lower quartile of the distribution illustrated by the cumulative frequency curve

• A. 17.5
• B. 19.0
• C. 27.5
• D. 28.0