Algebra Revision Worksheet

Section A — Algebra Foundations

Simplify or answer each question.

1. In the expression 7x + 4, identify:
   
   a) the variable
   b) the coefficient
   c) the constant
2. How many terms are in:
   5x² − 3x + 8
3. Write an algebraic expression for:
   A number x increased by 9
4. Write an algebraic expression for:
   Five times a number y, then subtract 4
5. Simplify:
   4x + 7x
6. Simplify:
   9a − 3a + 5
7. Simplify:
   6x + 4y − 2x + 3y
8. Simplify:
   3x² + 5x − x² + 2x
9. State whether the terms 5x and 5x² are like terms. Give a reason.
10. If x = 4, evaluate:
    3x + 7

Section B — Substitution and Formulae

11. Evaluate:
    2x² − 3x + 1
    when x = 3.
12. Evaluate:
    4a − 2b
    when a = 5 and b = −3.
13. The perimeter of a rectangle is given by:
    P = 2l + 2w
    Find P when l = 8 cm and w = 5 cm.
14. The distance travelled is given by:
    d = vt
    Find d when v = 12 m/s and t = 7 seconds.
15. Use:
    A = ½bh
    to calculate the area of a triangle with base 10 cm and height 7 cm.
16. Make x the subject:
    y = x + 6
17. Make a the subject:
    b = 3a
18. Make r the subject:
    C = 2πr
19. Make h the subject:
    A = ½bh
20. Make x the subject:
    y = 4x − 7

Section C — Expanding and Factorising

21. Expand:
    3(x + 5)
22. Expand:
    4(2x − 3)
23. Expand and simplify:
    3(x + 2) + 2(x − 1)
24. Expand:
    (x + 3)(x + 5)
25. Expand:
    (x − 4)(x + 2)
26. Expand:
    (2x + 3)(x − 4)
27. Factorise fully:
    6x + 12
28. Factorise fully:
    15x² − 10x
29. Factorise:
    x² + 7x + 12
30. Factorise:
    x² − 9x + 20
31. Factorise:
    x² − 16
32. Factorise:
    2x² + 7x + 3

Section D — Linear Equations and Word Problems

33. Solve:
    x + 8 = 17
34. Solve:
    5x = 35
35. Solve:
    3x + 4 = 19
36. Solve:
    4x − 7 = 2x + 9
37. Solve:
    3(x + 2) = 21
38. Solve:
    2(x − 3) + 5 = 13
39. A number is increased by 7. The result is 19. Form an equation and find the number.
40. Three times a number, decreased by 4, is equal to 20. Form an equation and find the number.
41. The length of a rectangle is 3 cm greater than its width. The perimeter is 30 cm. Find the length and width.
42. Tariro buys 4 identical exercise books and pays $12. Write and solve an equation to find the cost of one exercise book.

Section E — Simultaneous Equations and Inequalities

43. Solve:
    x + y = 8
    x − y = 2
44. Solve:
    2x + y = 11
    x − y = 1
45. Solve:
    x + y = 9
    y = x + 3
46. Solve:
    3x + 2y = 16
    x + y = 6
47. Solve:
    4x − 5 > 15
48. Solve:
    2x + 3 ≤ 11
49. Solve:
    −3x > 12
50. Represent:
    x ≥ 4
    on a number line.
51. Represent:
    −2 < x ≤ 5
    on a number line.

Section F — Quadratic Equations

52. Factorise:
    x² + 8x + 15
53. Factorise:
    x² − 5x − 14
54. Solve by factorisation:
    x² + 5x + 6 = 0
55. Solve by factorisation:
    x² − 9x + 20 = 0
56. Solve:
    2x² + 10x = 0
57. Solve by completing the square:
    x² + 6x − 7 = 0
58. Solve using the quadratic formula:
    2x² + 3x − 2 = 0
59. Solve using the quadratic formula:
    x² − 4x − 1 = 0
60. State the discriminant of:
    x² − 6x + 9 = 0
    What does it tell you?
61. State the discriminant of:
    x² + 2x + 5 = 0
    What does it tell you?

Section G — Algebraic Fractions

62. Simplify:
    6x / 9
63. Simplify:
    (x² − 9)/(x − 3)
64. Simplify:
    (x² + 7x + 12)/(x + 3)
65. Simplify:
    (2x² + 8x)/(2x)
66. Simplify:
    (x² − 16)/(x + 4)
67. Evaluate:
    (x + 2)/3
    when x = 7.