Mathematics Past Questions and Answers

If x⁴ - kx³ + 10x² + 1x - 3 is divisible by (x - 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and 1

A K = -7, 1 = -15
B K = -15, 1 = -7
C K = \(\frac{15}{3}\) , 1 = -7
D K = \(\frac{7}{3}\) , 1 = -17

Question 42:

Evaluate without using tables sin(-1290^o)

A \(\frac{3}{2}\)
B -\(\frac{3}{2}\)
C \(\frac{2}{2}\)
D 1
E \(\frac{1}{2}\)

Question 43:

The angle of elevation of the top of a vertical tower from a point A on the ground is 60^o. From a point B, 2 units of distance further away from the foot of the tower, the angle of elevation of the tower is 45^o. Find the distance of A from the foot of the tower

A 3 + \(\sqrt{3}\)
B 5 + \(\sqrt{3}\)
C 3 - \(\sqrt{3}\)
D 1
E \(\sqrt{3}\) - 1

Question 44:

The vectors a and b are given in terms of two perpendicular units vectors i and j on a plane by a = 2i - 3j, b = -i + 2j. Find the magnitude of the vector a + 3b

A 2
B 4
C \(\sqrt{10}\)
D 35
E 2.2

Question 45:

Add the same number to the numerator and denominator of \(\frac{3}{18}\). If the resulting fraction is \(\frac{1}{2}\), then the number added is

A 13
B 14
C 15
D 12
E 11