# Higher Mathematics – Scotland

### Scotland Higher Mathematics

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

1 | Initial Assessment | Initial Assessment |

2 | Surds | Introducing surds |

3 | Surds | Some rules for the operations with surds |

4 | Surds | Simplifying surds |

5 | Surds | Creating entire surds |

6 | Surds | Adding and subtracting like surds |

7 | Surds | Expanding surds |

8 | Surds | Conjugate binomials with surds |

9 | Surds | Rationalising the denominator |

10 | Surds | Rationalising binomial denominators |

11 | Surds | Graphing irrational roots |

12 | Equations | Applications of simultaneous equations |

13 | Inequalities | Solving Inequalities. |

14 | Simplifying | Simplifying algebraic fractions. |

15 | Simplifying | Simplifying algebraic fractions using the index laws. |

16 | Simplifying | Algebraic fractions resulting in negative indices. |

17 | Simplifying | Cancelling binomial factors in algebraic fractions. |

18 | Factorising | Expansions leading to the difference of two squares |

19 | Factorising | Common factor and the difference of two squares |

20 | Factorising | Factorising quadratic trinomials [monic] – Case 2. |

21 | Factorising | Factorisation of non-monic quadratic trinomials |

22 | Factorising | Factorisation of non-monic quadratic trinomials – moon … |

23 | Roots | Difference of two squares |

24 | Roots | Quadratic equations with factorisation. |

25 | Roots | Solving quadratic equations. |

26 | Roots | Completing the square |

27 | Roots | Solving quadratic equations by completing the square |

28 | Roots | The quadratic formula |

29 | Roots | Problem solving with quadratic equations |

30 | Roots | Solving simultaneous quadratic equations graphically |

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

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

33 | Graphs | Solve by graphing |

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

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

36 | Graphs | Graphing cubic curves |

37 | Graphs | Graphs of polynomials |

38 | Polynomials | Introduction to polynomials |

39 | Polynomials | The sum, difference and product of two polynomials. |

40 | Polynomials | Polynomials and long division. |

41 | Polynomials | Polynomial equations |

42 | Factor theorem | The factor theorem |

43 | Factor theorem | More on the factor theorem |

44 | Factor theorem | Complete factorisations using the factor theorem |

45 | Remainder theorem | The remainder theorem. |

46 | Remainder theorem | More on remainder theorem |

47 | Modulus | Absolute value equations |

48 | Roots | Sum and difference of two cubes. |

49 | Roots | Sum and product of roots of quadratic equations |

50 | Roots | Sum and product of roots of cubic and quartic equations |

51 | Roots | Methods of approximating roots |

52 | Matrices | Vectors |

53 | Proofs | Inductive and deductive reasoning |

54 | Proofs | Definition and use of counter examples |

55 | Proofs | Indirect proofs |

56 | Proofs | Mathematical induction |

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

58 | Transformations | Use grids to enlarge/reduce 2D shapes |

59 | Transformations | Special transformations – reflections, rotations and en… |

60 | Transformations | Transformations – reflections |

61 | Transformations | The definition and concept of combined transformations … |

62 | Co-ordinate Geometry | Triangle inequality theorem |

63 | Coordinate geometry | Distance formula. |

64 | Coordinate geometry | Mid-point formula |

65 | Coordinate geometry | Gradient |

66 | Coordinate geometry | Gradient formula. |

67 | Coordinate geometry | The straight line. |

68 | Coordinate geometry | Lines through the origin. |

69 | Coordinate geometry | General form of a line and the x and y Intercepts. |

70 | Coordinate geometry | Slope intercept form of a line. |

71 | Coordinate geometry | Point slope form of a line |

72 | Coordinate geometry | Two point formula: equation of a line which joins a pai… |

73 | Coordinate geometry | Intercept form of a straight line: find the equation wh… |

74 | Coordinate geometry | Parallel lines: identify equation of a line parallel to… |

75 | Coordinate geometry | Perpendicular lines. |

76 | Coordinate geometry | Perpendicular distance |

77 | Coordinate geometry | Line through intersection of two given lines |

78 | Coordinate geometry | Angles between two lines |

79 | Coordinate geometry | Internal and external division of an interval |

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

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

82 | Surds | Binomial expansions |

83 | Binomial | Binomial products. |

84 | Binomial | Binomial products with negative multiplier |

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

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

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

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

89 | Speed | Average speed |

90 | Speed | Using subscripted variables |

91 | Speed | Uniform motion with equal distances |

92 | Speed | Uniform motion adding the distances |

93 | Speed | Uniform motion with unequal distances |

94 | Speed | Uniform motion of all types |

95 | Speed | Motion under gravity – objects in vertical motion |

96 | Speed | Introducing initial velocity |

97 | Differentiation | Differentiation from first principles. |

98 | Differentiation | Differentiation of y = x to the power of n. |

99 | Differentiation | Meaning of dy over dx – equations of tangents and norma… |

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

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

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

103 | Differentiation | The second derivative – concavity. |

104 | Differentiation | Curve sketching |

105 | Differentiation | Practical applications of maxima and minima |

106 | Differentiation | Limits |

107 | Integration | Integration – anti-differentiation, primitive function |

108 | Integration | Computation of an area |

109 | Integration | Computation of volumes of revolution |

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

111 | Series and sequences | The arithmetic progression |

112 | Series and sequences | Finding the position of a term in an A.P. |

113 | Series and sequences | Given two terms of A.P., find the sequence. |

114 | Series and sequences | Arithmetic means |

115 | Series and sequences | The sum to n terms of an A.P. |

116 | Series and sequences | The geometric progression. |

117 | Series and sequences | Finding the position of a term in a G.P. |

118 | Series and sequences | Given two terms of G.P., find the sequence. |

119 | Series and sequences | Geometric means. |

120 | Series and sequences | The sum to n terms of a G.P. |

121 | Series and sequences | Sigma notation |

122 | Series and sequences | Limiting sum or sum to infinity. |

123 | Series and sequences | Recurring decimals and the infinite G.P. |

124 | Series and sequences | Superannuation. |

125 | Series and sequences | Time payments. |

126 | Series and sequences | Applications of arithmetic sequences |

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

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

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

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

131 | Trigonometry | Trigonometric ratios. |

132 | Trigonometry | Using the calculator. |

133 | Trigonometry | Using the trigonometric ratios to find unknown length. … |

134 | Trigonometry | Using the trigonometric ratios to find unknown length. … |

135 | Trigonometry | Using the trigonometric ratios to find unknown length. … |

136 | Trigonometry | Unknown in the denominator. [Case 4]. |

137 | Trigonometry | Angles of elevation and depression. |

138 | Trigonometry | Trigonometric ratios in practical situations. |

139 | Trigonometry | Using the calculator to find an angle given a trigonome… |

140 | Trigonometry | Using the trigonometric ratios to find an angle in a ri… |

141 | Trigonometry | Trigonometric ratios of 30., 45. and 60. – exact ratios… |

142 | Trigonometry | The cosine rule to find an unknown side. [Case 1 SAS]. |

143 | Trigonometry | The cosine rule to find an unknown angle. [Case 2 SSS]. |

144 | Trigonometry | The sine rule to find an unknown side. Case 1. |

145 | Trigonometry | The sine rule to find an unknown angle. Case 2. |

146 | Trigonometry | The area formula |

147 | Trigonometry | Reciprocal ratios. |

148 | Trigonometry | Trigonometric identities |

149 | Trigonometry | Angles of any magnitude |

150 | Trigonometry | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° |

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

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

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

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

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

156 | Trigonometry | Converting rectangular coordinates to polar form |

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

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

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

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

161 | Trigonometry | t Formulas (Stage 2) |

162 | Functions | Definition, domain and range |

163 | Functions | Notation and evaluations |

164 | Functions | More on domain and range |

165 | Functions | Domain and range from graphical representations |

166 | Functions | Evaluating and graphing piecewise functions |

167 | Functions | Functions combinations |

168 | Functions | Composition of functions |

169 | Functions | Inverse functions |

170 | Functions | Rational functions Part 1 |

171 | Functions | Rational functions Part 2 |

172 | Functions | Parametric equations (Stage 2) |

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

174 | Functions | Parametric functions (Stage 2) |

175 | Exponentials | The exponential function. |

176 | Logarithms | Logarithmic functions. |

177 | Logarithms | Powers of 2. |

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

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

180 | Logarithms | Laws of logarithms. |

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

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

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

184 | Logarithms | Equations involving logarithms. |

185 | Logarithms | Using logarithms to solve equations. |

186 | Logarithms | Change of base formula |

187 | Logarithms | The graph of the logarithmic curve |

188 | Logarithms | Working with log curves. |

189 | End of Course Assessment | End of Course Assessment |