The sum of the 2nd and 5th terms of an arithmetic progression (AP) is 42. If the difference between the 6th and 3rd term is 12, find the

(i) Common difference

(ii) first term

(iii) 20th term.

A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?

• A. y = (3x²/)2 + 2x
• B. y = (3x²)/2 + x
• C. y = 3x² + (x/2)
• D. y = 3x² +2x

During the 2010 PostJamb registration exercise which lasted 15 days the number of candidates registering doubled every day in the last five days but was constant in the first 10 days. If the number of candidates at the beginning was 740, what was the number after the registration?

• A. 326 000
• B. 236 000
• C. 218 000
• D. 118 000

(a) In the diagram, AB is a tangent to the circle with centre O, and COB is a straight line. If CD//AB and < ABE = 40°, find: < ODE.

(b) ABCD is a parallelogram in which |\(\overline{CD}\)| = 7 cm, I\(\overline{AD}\)I = 5 cm and < ADC= 125°.

(i) Illustrate the information in a diagram.

(ii) Find, correct to one decimal place, the area of the parallelogram.

(c) If x = \(\frac{1}{2}\)(1 - \(\sqrt{2}\)). Evaluate (2x\(^2\) - 2x).

A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T

• A. Q`(5, -8)
• B. Q`(-8, 5)
• C. Q`(5, -3)
• D. Q`(-5, -8)

Kweku walked 8m up to slope and was 3m above the ground. If he walks 12m further up the slope, how far above the ground will he be?

• A. 4.5m
• B. 6.0m
• C. 7.5m
• D. 9.0m

A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)

• A. \(\frac{-8}{15}\)
• B. \(\frac{8}{15}\)
• C. \(\frac{17}{15}\)
• D. \(\frac{-17}{15}\)

In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find an expression for tan y.

• A. \(\frac{\sqrt{3} \tan x - 1}{\sqrt{3} + \tan x}\)
• B. \(\frac{\sqrt{3} \tan x}{\sqrt{3} + \tan x}\)
• C. \(\frac{\sqrt{3} \tan x + 1}{\sqrt{3} - \tan x}\)
• D. \(\frac{3 \tan x - 1}{\sqrt{3} - \tan x}\)

A straight line passes through the point P(1,2) and Q(5,8). Calculate the length PQ

• A. \(4\sqrt{11}\)
• B. \(4\sqrt{10}\)
• C. \(2\sqrt{17}\)
• D. \(2\sqrt{13}\)

In how many ways can 3 prefects be chosen out of 8 prefects?

• A. 6
• B. 24
• C. 56
• D. 336