How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
6.5 units
13.0 units
3.5 units
7.0 units
Correct answer is A
PQ\(^2\) = (x2 - x1)\(^2\) + (y2 - y1)\(^2\)
= 12\(^2\) + 5\(^2\)
= 144 + 25
= 169
PQ = √169 = 13
But PQ = diameter = 2r, r = PQ/2 = 6.5 units
Find the number of sides of a regular polygon whose interior angle is twice the exterior angle.
6
2
3
8
Correct answer is A
Let the ext. angle = x
Thus int. angle = 2x
But sum of int + ext = 180 (angle of a straight line).
2x + x = 180
3x = 180
x = 180/3 = 60
Each ext angle = 360/n
=> 60 = 360/n
n = 360/60 = 6
4
6
3
0
Correct answer is A
The line joining (P, 4) and (6, -2).
Gradient: \(\frac{-2 - 4}{6 - P} = \frac{-6}{6 - P}\)
The line joining (2, P) and (-1, 3)
Gradient: \(\frac{3 - P}{-1 - 2} = \frac{3 - P}{-3}\)
For perpendicular lines, the product of their gradient = -1.
\((\frac{-6}{6 - P})(\frac{3 - P}{-3}) = -1\)
\(\frac{6 - 2P}{6 - P} = -1 \implies 6 - 2P = P - 6\)
\(6 + 6 = P + 2P \implies P = \frac{12}{3} = 4\)
100°
120°
30°
60°
Correct answer is B
Cos θ° = t2 + t2 -(√3t)2
= 2t2 - 3t2
= -t2/2t2
= -1/2
Thus θ = cos-1 (-0.5) = 120°
y = (x/10) + 5
y = x + 5
√3y = - x + 5√3
√3y = x + 5√3
Correct answer is D
Cos 30 = 5/x
x cos 30 = 5, => x = 5√3
Coordinates of P = -5, 3, 0
Coordinates of Q = 0, 5
Gradient of PQ = (y2 - y1) (X2 - X1) = (5 - 0)/(0 -5√3)
= 5/5√3 = 1/√3
Equation of PQ = y - y1 = m (x -x1)
y - 0 = 1/√3 (x -(-5√3))
Thus: √3y = x + 5√3