# Advanced Higher Mathematics – Scotland

### Scotland Advanced Higher Mathematics

# | TOPIC | TITLE |
---|---|---|

1 | Initial Assessment | Initial Assessment |

2 | Surds | Graphing irrational roots |

3 | Roots | Solving simultaneous quadratic equations graphically |

4 | Graphs | Quadratic polynomials of the form y = ax. + bx + c. |

5 | Graphs | Graphing perfect squares: y=(a-x) squared |

6 | Graphs | Solve by graphing |

7 | Graphs | Graphing complex polynomials: quadratics with no real r… |

8 | Graphs | General equation of a circle: determine and graph the e… |

9 | Graphs | Graphing cubic curves |

10 | Graphs | Graphs of polynomials |

11 | Modulus | Absolute value equations |

12 | Matrices | Vectors |

13 | Proofs | Inductive and deductive reasoning |

14 | Proofs | Definition and use of counter examples |

15 | Proofs | Indirect proofs |

16 | Proofs | Mathematical induction |

17 | Proofs | Conditional statements (converse, inverse and contrapos… |

18 | Circles | The equation of a circle: to find radii of circles |

19 | Circles | The semicircle: to select the equation given the semi c… |

20 | Surds | Binomial expansions |

21 | Binomial | Binomial products. |

22 | Binomial | Binomial products with negative multiplier |

23 | Binomial | Binomial products [non-monic]. |

24 | Binomial | Squaring a binomial. [monic] |

25 | Binomial | Squaring a binomial [non-monic]. |

26 | Probability | Binomial Theorem – Pascal’s Triangle |

27 | Differentiation | Function of a function rule, product rule, quotient rul… |

28 | Differentiation | Increasing, decreasing and stationary functions. |

29 | Differentiation | First Derivative – turning points and curve sketching |

30 | Differentiation | The second derivative – concavity. |

31 | Differentiation | Curve sketching |

32 | Differentiation | Practical applications of maxima and minima |

33 | Differentiation | Limits |

34 | Integration | Computation of volumes of revolution |

35 | Integration | The Trapezium rule and Simpson’s rule |

36 | Trigonometry | Graphing the trigonometric ratios – I Sine curve. |

37 | Trigonometry | Graphing the trigonometric ratios – II Cosine curve. |

38 | Trigonometry | Graphing the trigonometric ratios – III Tangent curve. |

39 | Trigonometry | Graphing the trigonometric ratios – IV Reciprocal ratio… |

40 | Trigonometry | Trigonometric identities |

41 | Trigonometry | Using one ratio to find another. |

42 | Trigonometry | Solving trigonometric equations – Type I. |

43 | Trigonometry | Solving trigonometric equations – Type II. |

44 | Trigonometry | Solving trigonometric equations – Type III. |

45 | Trigonometry | Plotting polar coordinates and converting polar to rect… |

46 | Trigonometry | Converting rectangular coordinates to polar form |

47 | Trigonometry | Write and graph points in polar form with negative vect… |

48 | Trigonometry | Sin(A+B) etc sum and difference identities (Stage 2) |

49 | Trigonometry | Double angle formulas (Stage 2) |

50 | Trigonometry | Half angle identities (Stage 2) |

51 | Trigonometry | t Formulas (Stage 2) |

52 | Functions | Definition, domain and range |

53 | Functions | Notation and evaluations |

54 | Functions | More on domain and range |

55 | Functions | Domain and range from graphical representations |

56 | Functions | Evaluating and graphing piecewise functions |

57 | Functions | Functions combinations |

58 | Functions | Composition of functions |

59 | Functions | Inverse functions |

60 | Functions | Rational functions Part 1 |

61 | Functions | Rational functions Part 2 |

62 | Functions | Parametric equations (Stage 2) |

63 | Functions | Polynomial addition etc in combining and simplifying fu… |

64 | Functions | Parametric functions (Stage 2) |

65 | Exponentials | The exponential function. |

66 | Logarithms | Logarithmic functions. |

67 | Logarithms | Equations of type log x to the base 3 = 4. |

68 | Logarithms | Equations of type log 32 to the base x = 5. |

69 | Logarithms | Laws of logarithms. |

70 | Logarithms | Using the log laws to expand logarithmic expressions. |

71 | Logarithms | Using the log laws to simplify expressions involving lo… |

72 | Logarithms | Using the log laws to find the logarithms of numbers. |

73 | Logarithms | Equations involving logarithms. |

74 | Logarithms | Using logarithms to solve equations. |

75 | Logarithms | Change of base formula |

76 | Logarithms | The graph of the logarithmic curve |

77 | Logarithms | Working with log curves. |

78 | Approximation | Newton’s method of approximation |

79 | Complex numbers | Imaginary numbers and standard form |

80 | Complex numbers | Complex numbers – multiplication and division |

81 | Complex numbers | Plotting complex number and graphical representation |

82 | Complex numbers | Absolute value |

83 | Complex numbers | Trigonometric form of a complex number |

84 | Complex numbers | Multiplication and division of complex numbers in trig … |

85 | Complex numbers | DeMoivre’s theorem (Stage 2) |

86 | Complex numbers | The nth root of real and complex numbers (Stage 2) |

87 | Complex numbers | Fundamental theorem of algebra (Stage 2) |

88 | Matrices | Basic concepts – Matrices |

89 | Matrices | Addition and subtraction of matrices |

90 | Matrices | Scalar matrix multiplication |

91 | Matrices | Multiplication of one matrix by another matrix |

92 | Matrices | Translation in the number plane |

93 | Matrices | Translation by matrix multiplication |

94 | Matrices | Number of solutions (Stage 2) |

95 | Matrices | 2 vector addition in 2 and 3D (stage 2) |

96 | Matrices | Optimal solutions (Stage 2) – Vectors |

97 | Matrices | Linear systems with matrices (Stage 2) |

98 | Matrices | Row-echelon form (Stage 2) |

99 | Matrices | Gauss Jordan elimination method (Stage 2) |

100 | Parabola | The parabola: to describe properties of a parabola from… |

101 | Conic sections | The rectangular hyperbola. |

102 | Conic sections | Introduction to conic sections and their general equati… |

103 | Conic sections | The parabola x. = 4ay |

104 | Conic sections | Circles |

105 | Conic sections | Ellipses |

106 | Conic sections | Hyperbola |

107 | End of Course Assessment | End of Course Assessment |