Prelim Revision Mixed questions Section B Questions 21 - 31

21. Try to find the coordinates of the point of intersection of the lines 2x – y + 5 = 0 and 4x – 2y – 7 = 0. Explain.

22. Copy and complete the following table:

f(x)	x^2 + 1
f(3)
f(-2)
f(1/2)
domain

23. A triangle has vertices P(0,4), Q(-2,-6) and R(6,-2). Find the point of intersection of the altitude to P from QR, and the perpendicular bisector of PR.

24. Find the value of a and b in each diagram below.

a)

b)

25. Solve the following equations for 0 < x < 360 x:

a) cos(2x) + cos(x) = 0

b) 5cos(2x) + 7sin(x) + 7 = 0

26. The distance s metres of a train from its starting point after t seconds is given by the formula

s = t³ - 2t² + 3t

Calculate: a) the average speed of the train over the interval t = 1 to t = 2

b) the speed of the train at the end of the 2 seconds.

27. Find the intervals in which each of the following functions is increasing or decreasing.

a) f(x) = 2x² – 10x b) f( x) = x³ – 3x² – 6

28. Show that the point A() lies on the curve y = .

The tangent at A meets the x and y axes at C and D. Show that the length of CD is units.

29. Find the shaded area below.

30. If sin(x+30)^o = sin(x), show that tan(x)^o = 2 +

31. If f(x) = 3x + 1 and g(x) = 4 – x², find f(g(x)) and g(f(x))