Mathematics

1. 1.

   Solve |2x - 3| < 7.

   [3 marks] · no calculator
2. 2.

   Given f(x) = 3x + 2 and g(x) = x^2 - 1, find fg(x) and gf(x), and show that fg and gf are not the same function.

   [3 marks] · no calculator
3. 3.

   Express (5x + 1) / ((x - 1)(x + 2)) in partial fractions.

   [4 marks] · no calculator
4. 4.

   The function f is defined by f(x) = (2x + 1)/(x - 3), x != 3. Find f^-1(x) and state its domain.

   [4 marks] · no calculator
5. 5.

   The curve y = f(x) has a maximum point at (2, 5). Write down the coordinates of the corresponding turning point on each of: (a) y = 2f(x - 3), (b) y = f(2x) + 4, (c) y = -f(x + 1). State the nature of the turning point in (c).

   [5 marks] · no calculator
6. 6.

   Solve 2^(2x+1) - 9(2^x) + 4 = 0, giving exact values of x.

   [5 marks]

Original, unofficial practice questions from SubjectScout — not official past-paper questions.