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1 Topic 1: Number and algebra
1.1 Using standard form
1.2 Arithmetic sequences and series
1.3 Geometric sequences and series
1.4 Financial applications - compound interest, annual depreciation
1.5 Introduction to logarithms
1.6 Approximating and estimating
1.7 Loan repayments and amortization
1.8 Use of technology to solve systems of linear equations and polynomial equations
1.9 Laws of logarithms
1.10 Expressions with non-integer exponents
1.11 Sum of infinite geometric sequences
1.12 Introduction to complex numbers
1.13 Polar and Euler form
1.14 Introduction to matrices
1.15 Eigenvalues and eigenvectors
2 Topic 2: Functions
2.1 Equations of straight lines, parallel and perpendicular lines
2.2 Functions, notation domain, range and inverse as reflection
2.3 Graphing
2.4 Key features of graphs, intersections using technology
2.5 Modelling skills
2.7 Composite functions, finding an inverse function including domain restriction
2.8 Transformations of graphs, composite transformations
2.9 HL modelling functions
2.10 Scaling large numbers, log-log graphs
3 Topic 3: Geometry and trigonometry
3.1 3d space, volume angles, midpoints
3.1 2d and 3d trigonometry
3.3 Angles of elevation and depression
3.4 The circle, arc and area of a sector, degrees only
3.5 Intersection of lines, equations of perpendicular bisectors
3.6 Voronoi diagrams
3.7 Radians
3.8 Unit circle, Pythagorean identity, solving trigonometric equations graphically
3.9 Matrix transformations
3.10 Vector definitions
3.11 Vector equation of a line in 2d and 3d
3.12 Vector applications to kinematics
3.13 Scalar and vector products
3.14 Graph theory
3.15 Adjacency matrices and tables
3.16 Tree and cycle algorithms, Chinese postman, travelling salesman
4 Topic 4: Statistics and probability
4.1 Concepts, reliability and sampling techniques
4.2 Histograms, CF graphs, box plots
4.3 Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
4.4 Pearson's , scatter diagrams, equation of y on x
4.5 Probability concepts, expected numbers
4.6 Combined, mutually exclusive, conditional, independence, probability diagrams
4.7 Discrete random variables
4.8 Binomial distribution
4.9 Normal distribution and calculations
4.10 Spearman's rank correlation coefficient
4.11 Expected, observed, hypotheses, chi squared, gof, t-test
4.12 Data collection, reliability and validity tests
4.13 Non-linear regression
4.14 Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators
4.15 Central limit theorem
4.16 Confidence intervals
4.17 Poisson distribution
4.18 T and Z test, type I and II errors
4.19 Transition matrices - Markov chains
5 Topic 5: Calculus
5.1 Introduction to differential calculus
5.2 Increasing and decreasing functions
5.3 Differentiating polynomials, n E Z
5.4 Tangents and normal
5.5 Introduction to integration, areas between curve and x axis
5.6 Stationary points, local max and min
5.7 Optimisation
5.8 Trapezoid rule
5.9 Differentiating standard functions and derivative rules
5.10 Second derivatives, testing for max and min
5.11 Indefinite integration, reverse chain, by substitution
5.12 Areas under a curve onto x or y axis. Volumes of revolution about x and y
5.13 Kinematic problems
5.14 Setting up a differential equation, solve by separating variables
5.15 Slope fields
5.16 Euler's method for 1st order differential equations
5.17 Phase portrait
5.18 Euler's method for 2nd order differential equations
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