IGCSE Math Revision Notes Algebra

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IGCSE Revision Notes Algebra

Math Syllabus Subtopics covered:

[This is the syllabus to be covered as per the CAIE latest Syllabus]

  1. Use letters to express generalised numbers and express basic arithmetic processes algebraically.
  2. Substitute numbers for words and letters in formulae.
  3. Rearrange simple formulae.
  4. Construct simple expressions and set up simple equations.
  5. Manipulate directed numbers.
  6. Use brackets and extract common factors.
  7. Expand products of algebraic expressions. e.g. expand 3x(2x – 4y) e.g. factorise 9x 2 + 15xy
  8. Two brackets only, e.g. expand (x + 4)(x – 7)
  9. Extended curriculum only.\
  10. Use and interpret positive, negative and zero indices.
  11. Use the rules of indices. e.g. simplify 3x 4 × 5x, 10x 3 ÷ 2x 2 , (x 6 ) 2 C2.
  12.  Derive and solve simple linear equations in one unknown.
  13. Derive and solve simultaneous linear equations in two unknowns.
  14. Use letters to express generalised numbers and express basic arithmetic processes algebraically.
  15. Substitute numbers for words and letters in complicated formulae.
  16. Construct and rearrange complicated formulae and equations.
  17. Notes/Examples e.g. rearrange formulae where the subject appears twice.
  18. Manipulate directed numbers. Use brackets and extract common factors.
  19. Expand products of algebraic expressions.
  20. Factorise where possible expressions of the form:
  21. ax + bx + kay + kby
  22. a 2 x 2 – b2 y 2
  23. a 2 + 2ab + b2
  24. ax 2 + bx + c
  25. e.g. expand 3x(2x – 4y)
  26. e.g. factorise 9x 2 + 15xy
  27. e.g. expand (x + 4)(x – 7) Includes products of more than two brackets,
  28. e.g. (x + 4)(x – 7)(2x + 1)
  29. Manipulate algebraic fractions.
  30. Factorise and simplify rational expressions. 
  31. Use and interpret positive, negative and zero indices.
  32. Use and interpret fractional indices.
  33. Use the rules of indices. 
  34. Derive and solve linear equations in one unknown.
  35. Derive and solve simultaneous linear equations in two unknowns.
  36. Derive and solve simultaneous equations, involving one linear and one quadratic.
  37. Derive and solve quadratic equations by factorisation, completing the square and by use of the formula.
  38. Derive and solve linear inequalities. Including representing and interpreting inequalities on a number line. Interpretation of results may be required.
  39. Continue a given number sequence.
  40. Recognise patterns in sequences including the term to term rule and relationships between different sequences.
  41. Find and use the nth term of sequences.
  42. Recognise sequences of square, cube and triangular numbers.
  43. Linear, simple quadratic and cubic sequences.
  44.  Extended curriculum only.
  45. Extended curriculum only.
  46. Interpret and use graphs in practical situations including travel graphs and conversion graphs.
  47. Draw graphs from given data. e.g. interpret the gradient of a straight line graph as a rate of change.
  48.  Construct tables of values for functions of the form ax + b, ±x 2 + ax + b, x a (x ? 0), where a and b are integer constants.
  49. Draw and interpret these graphs.
  50. Solve linear and quadratic equations approximately, including finding and interpreting roots by graphical methods.
  51. Recognise, sketch and interpret graphs of functions.
  52. Linear and quadratic only. Knowledge of turning points is not required.
  53. Represent inequalities graphically and use this representation to solve simple linear programming problems. Notes/Examples The conventions of using broken lines for strict inequalities and shading unwanted regions will be expected.
  54.  Continue a given number sequence.
  55. Recognise patterns in sequences including the term to term rule and relationships between different sequences.
  56. Find and use the nth term of sequences.
  57. Subscript notation may be used.
  58. Linear, quadratic, cubic and exponential sequences and simple combinations of these.
  59. Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.
  60. Use function notation, e.g. f(x) = 3x – 5, f: x ? 3x – 5, to describe simple functions.
  61. Find inverse functions f –1(x).
  62. Form composite functions as defined by gf(x) = g(f(x)).
  63.  Interpret and use graphs in practical situations including travel graphs and conversion graphs.
  64. Draw graphs from given data.
  65. Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.
  66. Calculate distance travelled as area under a speed–time graph. May include estimation and interpretation of the gradient of a tangent at a point.
  67.  Construct tables of values and draw graphs for functions of the form axn (and simple sums of these) and functions of the form abx + c.
  68. Solve associated equations approximately, including finding and interpreting roots by graphical methods.
  69. Draw and interpret graphs representing exponential growth and decay problems.
  70. Recognise, sketch and interpret graphs of functions. a and c are rational constants, b is a positive integer, and n = –2, –1, 0, 1, 2, 3.
  71. Sums would not include more than three functions.
  72. Find turning points of quadratics by completing the square.
  73. Linear, quadratic, cubic, reciprocal and exponential. Knowledge of turning points and asymptotes is required.
  74. Estimate gradients of curves by drawing tangents.
  75. Understand the idea of a derived function.
  76. Use the derivatives of functions of the form axn , and simple sums of not more than three of these.
  77. Apply differentiation to gradients and turning points (stationary points).
  78. Discriminate between maxima and minima by any method.
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