A ladder, 6m long, leans against a vertical wall at an angle 53° to the horizontal. How high up the wall does the ladder reach?

• A. 3.611m
• B. 4.521m
• C. 4.792m
• D. 7.962m

Evaluate ∫\(^{\pi}_{2}\)(sec² x - tan²x)dx

• A. \(\frac{\pi}{2}\)
• B. \(\pi\) - 2
• C. \(\frac{\pi}{3}\)
• D. \(\pi\) + 2

Simplify; \(\frac{a}{b} - \frac{a}{a} - \frac{c}{b}\)

• A. \(\frac{a - b + c}{ab}\)
• B. \(\frac{ab - bc - ac}{ab}\)
• C. \(\frac{a^2 - b^2 + ac}{ab}\)
• D. \(\frac{a^2 - b^2 - ac}{ab}\)

(a) A bus travels with a velocity of \(6 ms ^{-1}\). It then accelerates uniformly and travels a distance of 70 m. If the final velocity is \(20 ms ^{-1}\), find, correct toone decimal place, the:

acceleration;

(b) A bus travels with a velocity of \(6 ms ^{-1}\). It then accelerates uniformly and travels a distance of 70 m. If the final velocity is \(20 ms ^{-1}\), find, correct toone decimal place, the:

time to travel this distance.

XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120^o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)]

• A. 14.67cm
• B. 22.67cm
• C. 29.33cm
• D. 37.33cm

X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X

• A. 240°
• B. 150°
• C. 60°
• D. 270°

Express the square root of 0.000144 in the standard form

• A. 1.2 x 10^-4
• B. 1.2 x 10^-3
• C. 1.2 x 10^-2
• D. 1.2 x 10^-1

Factorize: x + y - ax = ay

• A. (x - y)(1 - a)
• B. (x + y)(1 + a)
• C. (x + y)(1 - a)
• D. (x - y)(1 + a)

In a class of 80 students, every students studies Economics or Geography or both. If 65 students study Economics and 50 study Geography, how many study both subjects?

• A. 15
• B. 30
• C. 35
• D. 45

Solve without using tables log₅(62.5) - log₅(\(\frac{1}{2}\))

• A. 3
• B. 4
• C. 5
• D. 8