PT3 Mathematics 2016, Question 5

Question 5 (a):
Diagram 5.1 shows a right-angled triangle.


Match cos θ and tan θ to the correct trigonometric ratio.

Answer:

Solution:

Question 5 (b):
Diagram 5.2 shows a trapezium ABCD.

Calculate the area, in cm², of the shaded region.

Solution:
$\begin{array}{l}\text{Area of the shaded region}\\ =\text{ Area }ABCD-\text{Area of parallelogram}\\ =\frac{1}{2}\left(9+12\right)6-\left(3\times 3\right)\\ =63-9\\ =54{\text{ cm}}^2\end{array}$

Question 5 (c):
(i) Simplify a^-2 ÷ a³
(ii) It is given that 5^{3x + 4} ÷ 5³ = 125.
Find the value of x.

Solution:
(i)
a^-2 ÷ a³ = a^-2-3
= a^-5

(ii)
5^{3x + 4} ÷ 5³ = 125
5^{3x + 4 – 3} = 5³
5^{3x + 1} = 5³
3x + 1 = 3
3x = 2
x = ⅔