Revision examples Unit 1 Topics 1 & 2 (Straight Line, Functions & Trig)

1. Are the lines with equations 2x – y = 3, 3x + y = 2 and 4x –5y = 9 concurrent?

2. a) Find the equation of the line :

i) with gradient ¾ passing through (-4,1)

ii) passing through (7,3) and (10,-1)

b) Prove the two lines in a) are perpendicular, and find their point of intersection.

3. In triangle STU, S is (2,6), T(4,-2) and U(13,7). Find the coordinates of the point of intersection of.

altitude SF and median UE.

4. Find the equations of the lines which bisect the angles between the lines

y = x, and y = 2x.

5. If f(x) = find f ^–1(x) and show that f(f ^–1(x)) = f ^–1(f(x)) = x

6. If g(x) = find g ^–1(x) and show that g(g ^–1(x)) = g ^–1(g(x)) = x

7. On the same diagram sketch y = 5^x and y = log₅x (Put at least three points on each graph).

8. For each graph below, find a and b.

9. Find the exact values of a) sin b) cos c) tan d) cos

10. Solve for 0

a) 2sin(2x) = 1 b) tan(2x) – 1 = 0 c) 2cos(x) + = 0

11. Solve for 0

a) 4tan(2x) + 4 = 0 b) 2sin(3x) – 1 =0 c) 4cos(2x) – 2 = 0