Prelim Revision Mixed questions Exercise 1 Questions 1 - 10

1. By completing the square, find the co-ordinates of the turning point of the function

y = -2x² + 7x – 6

2. Use the addition formulae to prove:

a) sin 75^o = b) sin 15^o =

3. Calculate the area between the curves: y = x² – 2x and y = 6x – x²

4. A sector of a circle with radius r cm has area 16cm². Show that the perimeter P cm of the sector is:

P(r) = 2()

Find the minimum value of P.

5. Show that x – 4 is a factor of 2x⁴ – 9x³ + 5x² - 3x – 4.

6. The triangle ABC has vertices A(1,2), B(5,6) and C(1,6). Show that ABC is a right angled triangle,

a) By using gradients

b) By using the converse of Pythagoras

7. Show that x + 3y + 1 = 0 is a tangent to the circle x² + y² + 10x + 4y + 19 = 0.

8. Given that tan (x – y) = show that

tan (x – y) =

9. If tan x = and tan y = prove that tan (x-y) =

10. Find the maximum and the minimum value of f(x) in the given interval, and sketch the graph of

f(x) = 2x² - x⁴ , {x: }