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Scotland Advanced Higher Mathematics

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