Basic Mathematics Final Exams Year 1.

UNIVERSITY OF NAIROBI
SCHOOL OF MATHEMATICS
XEQ 101: BASIC MATHEMATICS – DRAFT EXAMINATION
INSTRUCTION: ANSWER QUESTION ONE AND ANY OTHER TWO QUESTION
QUESTION ONE – 30 MARKS
5 8
a. If sin 𝐴 = , sin 𝐵 = 17 , where 𝐴 and 𝐵 are acute angles, find without using tables the values
13

of:
i. cos(𝐴 + 𝐵) (3 marks)
ii. sin(𝐴 − 𝐵) (3 marks)
iii. tan(𝐴 + 𝐵) (3 marks)
b. Given the following set 𝐴 = {1,2,3,4,5,6} and 𝐵 = {2,5 7,3,8,9}. Find the following:
i. |𝐴 ∪ 𝐵 | (3 marks)
ii. |𝐴 ∆ 𝐵| (3 marks)
c. Given the complex number 𝑧 = 1 − 𝑖. Find
i. The modulus of 𝑧 (2 marks)
ii. The argument of 𝑧 (2 marks)
iii. Plot it on an argand diagram (2 marks)
d. A class in made up of 11 students. A team of 8 students is supposed to be assembled from the
11 students. How many teams can be assembled? (5 marks)
e. Show that the product of two odd integers in odd. (4 marks)


QUESTION TWO – 20 MARKS
a. Consider the following subset of real numbers:
2 1
{−8, −√5, 1, , 0, − , √3, 𝜋, 9}
3 7
List the numbers in this set that are:
i. Natural numbers (3 marks)
ii. Integers (3 marks)
iii. Rational numbers (3 marks)
iv. Irrational numbers (3 marks)
b. Solve sin 5𝑥 + sin 3𝑥 = 0 (8 marks)