QUESTION 1 [12 Marks]
Workout the following without a calculator:
(a)
(b) Solve for a and 6 if a— 3bi = (1+7%)7!
(c) i2 + L - +24“ leave your answer in the form a + bi.
QUESTION 2 [21 Marks]
(a) Work out the following without a calculator:
pl2\\ tf p9\\73
i) Simplify ~ (=) (-F] (¢2~*)
ii) 67 -1-—6!-” =0
(e8@t1)2 _ 10
iii) a
(b) Using the laws of logarithms:
i) show that log, a -log.b = log.a
ii) solve log7(logy x”) = 0
QUESTION 3 [30 Marks]
Solve:
(a) ) 22 —5|)+x2=2
( b) 327+ 36 = 31z by completing the square
(6)
(c) ) log,(a% + 3) + log.(x — 3) < 4 and write the answer in interval notation. [12|
(d) c+ Vr—4=4
[5]
QUESTION 4 [14 Marks]
Given the following sequences:
a) 9,14,19,24,...
b) 1024, 512, 256, 128,...