Problem 1
(a) Perform the required operation in each of the following and write
your answer in the form of a + bi (3 Marks)
i. (−3 + 2i)(5 + 11i)
ii. −1+i
−2+2i
iii. (6 + 2i) − (2 − 4i)
(b) Factorize the following expressions (2 Marks)
i. 27x
3 + 1
ii. 4x
2 − 25
(c) Solve the quadratic equation using the factoring method (1
Mark)
x
2 + 7x + 12 = 0
(d) Simplify the following exponents (2 Marks)
i. (a
5
b
10)
3
ii. (2a
−2
b
4
)(3a
2
b
−5
)
(e) Solve for x in (1 Mark)
2(x − 1) + x = 5(2x + 3)
(f) Let the sets A and B be as follows A = {1, 2, 3} B = {2, 3}.
Find A∆B and the corresponding cardinality ( 1 Mark)
Problem 2
(a) Perform the indicated operation (3 Marks)
3y + 12
3y
2 − 15y
÷
y
2 − 16
y
2 − 3y − 10
(b) Represent the following complex numbers on an argand diagram
(2 Marks)
i. −2 + 3i
2
ii. −1 − 4i
(c) Solve the following quadratic equation by completing the square
method (2 Marks)
x
2 + 7x + 12 = 0
(d) Solve the following system of equation (2 Marks)
(
3
x
x
−
+
2
y
y
= 7
= 5
(e) Simplify (1 Mark):
(−2 − 3i) − (−8 − 7i)
Problem 3
(a) Solve for the unknown in the following system of equation (3
Marks)
x
2 + y + 2z = 3
2x − y −
3
2
z = 1
x −
y
2 −
3z
2 =
5
2
(b) Let sets A and B be as follows A = {7, 5, 6} B = {9, 5, 7, 8}.Evaluate
the following and their corresponding cardinalities (5 Marks)
i. B \ A
ii. A ∩ B
iii. A ∪ B
iv. A∆B
(c) Rationalize the denominator (1 Mark)
1
4 −
√
2
(d) Simplify the following expression (1 Mark)
x
2 + 7x + 12
x
2 − 9
3
Problem 4
(a) Find the sum of the first 40 terms of the arithmetic sequence
(2 Marks)
3, 7, 11, 15, · · ·
(b) Expand using binomial theorem (2 Marks)
(2a − 3b)
6
(c) Solve the following quadratic equation (3 Marks)
i. 2x
2 + 28x − 26 = 0 using the quadratic formula
ii. −15x−9 = −14x
2 using the completing the square method
(d) Simplify the following compound expression (2 Marks)
(1 − x
2
)
1
2 + x
2
(−x
2 + 1) −
2
1
3(1 − x
2
)
3
2
(e) Rational
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