Answers

  1. (a)   (b)   (c)   (d)

  2. (a)   (b)   (c)

  3. (a) 8a6b-1  (b)   (c)   (d) ab-1  (e)   (f)

  4. (a)   (b)   (c)   (d)

  5. (a) log2(5(x+1))  (b) log23  (c) 25

  6. (a)   (b) -x  (c) 2 log10x

  7. (a)   (b)   (c)   (d)   (e)   (f)

  8. (a) y - (-1) = (x - (-2))2  (b)   (c)

  9. (a) x4(x - 4)(x + 4)  (b) (x - 2)(2x - 5)(2x + 5)  (c) (2x + 3)(4x2 - 6x + 9)  (d) (x - 1)(x + 1)(x2 + 1)

  10. (a)   (b)   (c)

  11. (a) , or   (b) , or   (c) , or , where k is any integer

  12. (a)   (b)   (c)   (d)   (e)   (f)   (g)   (h)

  14. (a)   (b) or -3  (c)

  15. (a) -89  (b) x2 + 3

  16. (a) or   (b) , or

  17. (a)   (b) or   (c) all x

  18. (a)   (b) 2 or   (c) or 2

  19. (a) 7x + 3y = 2  (b) 3x + 2y = 1  (c) y = 3

  20. (a) (2, -1)  (b)
  21. (a) (x - 1)2 + (y - 2)2 = 18  (b)

  22. (a) centre = (-3,2) radius   (b) x + 3y = 13.

  23. (a) 9  (b) (x - 5)2 + (y - 3)2 = 25

  24. 8x2 - 38x + 8y2 + 20y + 43 = 0 (a circle).

  25. (a)x < -2 or x > 1  (b) i. D: all numbers, R: {7} ii. D: all numbers except , R: all numbers except
  26. D: all numbers except 0; Range: {-1,1}

  27. (a) 2   (b)   (c) 2x + h

  30. (a) y = -x2 + 2x + 3  (b)

  31. (a) y = x2 - 3x + 2  (b) y = x(x2 + 3x + 3)(x + 1)3  (c) x2 + y2 = 1

  32. (a)   (b)   (c)

  34. (a)   (b)

  35. (a)   (b)   (c)   (d) km  (e) or 30°

  36. (a) 1 = cos(x - x) = ...  (b) Use D.  (c) Use B.  (d) Use (c) then (a).

    (e) Use (c) then (a)   (f) Replace x by in (d).  (g) Replace x by in (e).