Form 4 Additional Mathematics
Coursework Examination – 20%
1. Given that, SIN A =
𝟑
𝟓
express COS A as a fraction in its lowest terms.
(2 MARKS)
2. Solve the following equations for all values of θ where 00 ≤ θ ≤ 3600 :
a. SIN θ = - 0.25
b. COS θ = 0.762
c. SIN 2θ = 0.67
d. 3 COS 2θ = 2
e. TAN
2𝜃
+2=0
3
3. If SIN A =
𝟒
𝟓
and COS B =
( 2 MARKS EA.)
𝟏𝟐
𝟏𝟑
Calculate, without tables or calculators the
values of SIN(A +B) when both A and B are acute.
(3 MARKS)
4. Prove that:
a. tan θ ≡
sin 2𝜃
1+cos 2𝜃
b. ( 1 + tan2 θ) cos2 θ ≡ 1
(5 MARKS)
th
th
5. The 5 term of an AP is 10 and the 10 term is 5, find
(a) the first term
(b) the common difference.
(c) an expression for the term n
(5 marks)
6. If x +1, 2x – 1 , and x +5 are three consecutive terms of an AP,
a. Find the value of x.
b. hence write down the AP
(3 marks)
7. The sum of the first 8 terms of an AP is 12 and the sum of the first 16 terms
is 56. Find the AP
(5 marks)
2
8. (a) Find the value of the 6th term of a GP 60, 40, 26 …..
3
(b) Find the sum of the first 10 terms of the GP 12, 8 and 2
1
3
(c) If the Sum to infinity of a GP is twice the first term, find the common
ratio.
(7 marks)