### 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.
26 Roots Completing the square
27 Roots Solving quadratic equations by completing the square
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
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