AI HL · IB Mathematics: Applications and Interpretation HL

12.1 · 2 weeks Sequences & Series Arithmetic and geometric sequences, sigma notation, financial applications and time value of money. 12.1.1 Arithmetic Sequences 12.1.2 Arithmetic Series 12.1.3 Geometric Sequences 12.1.4 Series & Sigma Notation 12.1.5 Geometric Series 12.1.6 Mixed Practice & Exam Prep 12.1.7 Infinite geometric series: the sum to infinity 12.1.8 Infinite series: the range of x, r and the first term 12.1.9 Infinite series in context: bouncing balls and nested squares 12.1.10 Sequences and series: revision 12.1.11 Unit review 0 0 of 120 skills done

12.2 · 3 weeks Finance Compound interest, depreciation, annuities and amortization, with approximation and percentage error. 12.2.1 Finance Solver: compound interest and depreciation 12.2.2 Amortisation and annuities 12.2.3 When PpY ≠ CpY 12.2.4 Rounding and percentage error 0 0 of 58 skills done

12.5 · 1 week Functions Introduction to functions, domain and range, inverses, graphing and systems of equations. 12.5.1 Function notation, domain and range 12.5.2 Key features and models of graphs 12.5.3 Composite functions 12.5.4 Inverse functions 12.5.5 Translations of graphs 12.5.6 Stretches and reflections 12.5.7 Composite transformations 12.5.8 Closest point on a graph 12.5.9 Review: the approach model and graph transformations 12.5.10 Unit review 0 0 of 45 skills done

12.4 · 2 weeks Solving Equations with Technology Systems of linear equations and polynomial equations, solved on the GDC. 12.4.1 Solving systems of equations 12.4.2 Modelling with systems of equations 12.4.3 Polynomial equations with the solver 12.4.4 Solving and forming polynomial equations 12.4.5 Graphs of polynomial equations 12.4.6 Where two graphs meet 12.4.7 Mixed practice: equations and systems 12.4.8 Unit review 0 0 of 45 skills done

12.7 · 8 weeks Mathematical Models Linear, quadratic, exponential, cubic and sinusoidal models with GDC applications. 12.7.1 Linear, quadratic, cubic, variation and exponential models 12.7.2 Exponential models, half-life and logarithmic models 12.7.3 Sinusoidal models: Ferris wheels, tides and daylight 12.7.4 Sinusoidal and logistic models 12.7.5 Piecewise models and continuity 12.7.6 Mixed modelling practice 12.7.7 Unit review 0 0 of 36 skills done

12.3 · 1 week Coordinate Geometry Straight lines in two dimensions and three-dimensional coordinate geometry. 12.3.1 3D coordinates: distance and midpoint 12.3.2 Straight lines: gradient, parallel and perpendicular 0 0 of 20 skills done

12.10 · 2 weeks Geometry & Trigonometry 3D trigonometry, sine and cosine rules, radians, unit circle and sector calculations. 12.10.1 Right-angled trigonometry and angles between lines 12.10.2 Sine rule and cosine rule 12.10.3 Area of a triangle 12.10.4 Mixed practice: rules of trigonometry 12.10.5 Angles in 3D shapes 12.10.6 Bearings 12.10.7 Angles of elevation and depression 12.10.8 Applications of trigonometry: 3D, bearings, elevation 12.10.9 Volumes and surface areas of solids 12.10.10 Radians and degrees 12.10.11 The unit circle and trigonometric equations 12.10.12 Arc length and sector area 12.10.13 The sine rule: the ambiguous case 12.10.14 Grazing goat problems: sectors round a shed 12.10.15 Grazing goat problems: sector and triangle area 12.10.16 Unit review 0 0 of 79 skills done

12.6 · 2 weeks Exponents & Logarithms Exponential expressions, logarithms, log laws and logarithmic scales. 12.6.1 Laws of exponents: negative and fractional indices 12.6.2 Logarithms and solving exponential and log equations 12.6.3 Mixed exponent and logarithm practice 12.6.4 Logarithmic scales on graphs 12.6.5 Unit review 0 0 of 42 skills done

AHL 1 · 2 weeks Graph Theory Graphs, trees, algorithms, adjacency matrices and optimisation problems. AHL 1.1 What is a graph? Vertices, edges and trees AHL 1.2 Adjacency matrices and degree AHL 1.3 Walks, trails, paths, circuits and cycles AHL 1.4 Counting walks with powers of the adjacency matrix AHL 1.5 Eulerian and Hamiltonian graphs AHL 1.6 Weighted graphs and shortest routes AHL 1.7 Random walks, transition matrices and page rank AHL 1.8 Minimum spanning trees: Kruskal's algorithm AHL 1.9 Minimum spanning trees: Prim's algorithm AHL 1.10 The Chinese postman problem AHL 1.11 The travelling salesman: nearest neighbour AHL 1.12 Travelling salesman: bounds and practical problems AHL 1.13 Exam practice: the whole unit AHL 1.14 Unit review 0 0 of 43 skills done

12.8 · 2 weeks Voronoi Diagrams Voronoi diagrams, perpendicular bisectors, nearest neighbour interpolation. 12.8.1 Voronoi diagrams in the real world 12.8.2 Equation of a perpendicular bisector 12.8.3 Sites, cells, edges and vertices 12.8.4 Adding a site: the incremental algorithm 12.8.5 Nearest neighbour interpolation 12.8.6 The toxic waste dump problem 12.8.7 Unit review 0 0 of 19 skills done

12.9 · 2 weeks Differentiation Introduction to differentiation, power rule, tangents, normals and optimisation. 12.9.1 Gradient, increasing and decreasing 12.9.2 From the graph of f to the graph of f′12.9.3 From the graph of f′ back to f 12.9.4 Sketching f and f' from graphs 12.9.5 Differentiating powers of x 12.9.6 Expanding, splitting fractions and increasing or decreasing 12.9.7 Gradient at a point and where the gradient equals a value 12.9.8 Equation of a tangent and of a normal 12.9.9 Tangents, normals and gradient with technology 12.9.10 Harder tangent and normal problems 12.9.11 Stationary points: where the gradient is zero 12.9.12 Maximum and minimum points on a domain 12.9.13 Optimisation in context 12.9.14 Unit review 0 0 of 48 skills done

13.5 · 2 weeks Integration Anti-derivatives, trapezium rule and integrals as accumulation. 13.5.1 Distance as area under a speed-time graph 13.5.2 Anti-differentiation: reversing the power rule 13.5.3 Expanding, splitting fractions and boundary conditions 13.5.4 Definite integrals and area under a curve 13.5.5 Accumulation: rate in, amount out 13.5.6 Unit mixed practice: areas, rates and accumulation 13.5.7 The trapezium rule 13.5.8 The trapezium rule with data, and its error 13.5.9 Unit review 0 0 of 42 skills done

AHL 2 · 3 weeks Further Derivatives Chain rule, product/quotient rules, related rates, concavity and stationary points. AHL 2.1 Differentiating powers, trig, e^x and ln x AHL 2.2 Tangents, normals and gradient problems AHL 2.3 The chain rule AHL 2.4 The product and quotient rules AHL 2.5 Related rates with the chain rule AHL 2.6 Related rates: ladders, cones and circles AHL 2.7 The second derivative and concavity AHL 2.8 Classifying stationary points and inflection AHL 2.9 Kinematics: displacement, velocity and acceleration AHL 2.10 Mixed practice: stationary points, concavity and models AHL 2.11 Derivatives: exam-style practice AHL 2.12 Unit review 0 0 of 69 skills done

AHL 3 · 3 weeks Further Integration Integration techniques, areas, volumes of revolution and kinematics. AHL 3.1 Integrating powers and standard functions AHL 3.2 Integrating f(ax+b) and by inspection AHL 3.3 Further integration: substitution and boundary conditions AHL 3.4 Definite integrals by hand and with the calculator AHL 3.5 Area between a curve and the x-axis AHL 3.6 Mixed practice: definite integrals and areas AHL 3.7 Area between a curve and the y-axis AHL 3.8 Volumes of revolution about the x-axis AHL 3.9 Volumes of revolution about the y-axis AHL 3.10 Harder volumes and areas of revolution AHL 3.11 Integration by substitution AHL 3.12 Integrals under transformations of the graph AHL 3.13 Exam practice: transformations, areas and volumes AHL 3.14 Unit review 0 0 of 78 skills done

13.3 · 3 weeks Statistics Data types, central tendency, dispersion, histograms and regression. 13.3.1 Data, sampling and averages 13.3.2 Spread and standard deviation 13.3.3 Changing every value 13.3.4 Quartiles, box plots and outliers 13.3.5 Histograms and cumulative frequency graphs 13.3.6 Scatter diagrams and correlation 13.3.7 Linear regression and prediction 13.3.8 Spearman's rank correlation and comparison with Pearson's r 13.3.9 Statistics review: exam questions 13.3.10 Unit review 0 0 of 44 skills done

13.1 · 2 weeks Probability Tree diagrams, Venn diagrams, two-way tables and conditional probability. 13.1.1 Theoretical and experimental probability 13.1.2 Venn diagrams for probability 13.1.3 Tree diagrams and sample spaces 13.1.4 Probability from two-way tables 13.1.5 Combined events and mutually exclusive events 13.1.6 Conditional probability 13.1.7 Independent events 13.1.8 Mixed practice: choosing the right tool 13.1.9 Probability review: the boy or girl problem 13.1.10 Unit review 0 0 of 48 skills done

13.2 · 2 weeks Probability Distributions Discrete random variables, binomial and normal distributions. 13.2.1 Discrete random variables and distribution tables 13.2.2 Expected value of a discrete random variable 13.2.3 Fair games and further distributions 13.2.4 The binomial distribution 13.2.5 Binomial probabilities with the calculator 13.2.6 Mean, variance and binomial practice 13.2.7 The normal distribution: properties and when it is a good model 13.2.8 Normal probability calculations with the GDC 13.2.9 Inverse normal calculations and normal practice 13.2.10 The Poisson distribution and its conditions 13.2.11 Poisson probabilities, mean and variance, and rescaling the rate 13.2.12 The sum of two independent Poisson variables 13.2.13 Mixed practice: Poisson distribution 13.2.14 Distributions review: chapter 8 checklist and short quiz 13.2.15 Unit review 0 0 of 64 skills done

13.4 · 3 weeks Hypothesis Testing Chi-squared tests, t-tests and Spearman's rank correlation. 13.4.1 What a hypothesis test is 13.4.2 Chi-squared goodness of fit 13.4.3 Testing the fit of a model 13.4.4 Chi-squared test for independence 13.4.5 One-sample t-test for a mean 13.4.6 Two-sample pooled t-test 13.4.7 Spearman's rank correlation 13.4.8 Combining categories in a chi-squared test 13.4.9 Goodness of fit when parameters are estimated 13.4.10 Testing a mean: z-test or t-test 13.4.11 Critical values and critical regions for a test of a mean 13.4.12 Two-sample tests for means: z and pooled t 13.4.13 The paired-sample t-test 13.4.14 Hypothesis tests for a mean: mixed practice 13.4.15 Testing a proportion: the binomial test 13.4.16 Testing a Poisson mean 13.4.17 Testing for correlation 13.4.18 Binomial and Poisson tests: mixed practice 13.4.19 Type I errors 13.4.20 Type II errors and how they link to Type I 13.4.21 Exam question: sums of normals, a test for a mean and Type II error 13.4.22 Unit review 0 0 of 100 skills done

AHL 4 · 3 weeks Vectors Vector operations, equations of lines, dot product, kinematics and eigenvalues. AHL 4.1 Column vectors and base vectors i, j, k AHL 4.2 Adding and subtracting vectors AHL 4.3 Scalar multiplication and parallel vectors AHL 4.4 Magnitude of a vector and unit vectors AHL 4.5 Position vectors, displacement vectors and distance AHL 4.6 Mixed practice: parallel vectors, unit vectors, displacement, distance and parameters AHL 4.7 Collinear points and parallel lines with vectors AHL 4.8 The vector equation of a line AHL 4.9 Parametric form, intersecting lines and skew lines AHL 4.10 Mixed practice: lines in 3D, parametric form and intersections AHL 4.11 Constant velocity: speed, position and closest approach AHL 4.12 Mixed practice: kinematics with constant velocity AHL 4.13 The scalar product: definition and component form AHL 4.14 The angle between two vectors; perpendicular and parallel vectors AHL 4.15 The acute angle between two lines AHL 4.16 Shortest distance from a point to a line AHL 4.17 The vector product AHL 4.18 Parallel vectors, perpendicular vectors and area AHL 4.19 Components of a vector: along and perpendicular AHL 4.20 Mixed practice: scalar and vector products, lines and distances AHL 4.21 Kinematics on a line: derivatives and integrals AHL 4.22 Motion on a line: direction changes, distance and speed AHL 4.23 Variable velocity in two dimensions AHL 4.24 Projectiles and constant acceleration AHL 4.25 Projectiles: launch angle, launch height and clearing a wall AHL 4.26 Circular motion AHL 4.27 An object that starts later AHL 4.28 Mixed practice: projectiles, circular motion and delayed objects AHL 4.29 Exam practice: circular motion with changing speed AHL 4.30 Unit review 0 0 of 160 skills done

AHL 5 · 3 weeks Matrices Matrix arithmetic and multiplication, determinants and inverses, systems of equations, eigenvalues and powers, and matrices as transformations. AHL 5.1 Definition and arithmetic of matrices AHL 5.2 Matrix multiplication AHL 5.3 Determinants AHL 5.4 Inverse matrices AHL 5.5 Systems of equations using the inverse matrix AHL 5.6 Eigenvalues and eigenvectors AHL 5.7 Diagonalisation and powers of matrices AHL 5.8 Matrices as transformations AHL 5.9 Composite transformations, area and invariant lines AHL 5.10 Mixed Practice & Exam Prep 0 0 of 63 skills done

AHL 6 · 2 weeks Complex Numbers Complex number forms, operations, De Moivre's theorem and geometric representations. AHL 6.1 The number i and Cartesian form AHL 6.2 Conjugates, division and equating parts AHL 6.3 The complex plane and the modulus AHL 6.4 Complex roots of quadratic equations AHL 6.5 Cartesian form: mixed practice AHL 6.6 Modulus-argument (polar) form AHL 6.7 Products, quotients and powers in cis form AHL 6.8 Exponential form AHL 6.9 Powers and de Moivre's formula AHL 6.10 Adding sinusoidal functions with complex exponentials AHL 6.11 Mixed practice: polar and exponential form AHL 6.12 Geometry on the Argand diagram AHL 6.13 Unit review 0 0 of 66 skills done

AHL 7 · 2 weeks Markov Chains & Transition Matrices Transforming variables, CLT, Poisson distribution and Markov chains. AHL 7.1 States, transition matrices and transition diagrams AHL 7.2 Powers of the transition matrix and initial state vectors AHL 7.3 Steady state and long-term probabilities AHL 7.4 Markov chain problems, absorbing states and eigenvalues AHL 7.5 Unit review 0 0 of 36 skills done

AHL 8 · 3 weeks Statistics 2 Advanced hypothesis testing, confidence intervals and error analysis. AHL 8.1 Non-linear regression with the calculator AHL 8.2 Sum of squared residuals and R² AHL 8.3 Paper 3 modelling: a logistic investigation AHL 8.4 Linear combinations of random variables AHL 8.5 The sample mean and its standard error AHL 8.6 Mixed practice: linear combinations and the sample mean AHL 8.7 Linear combinations of independent normal variables AHL 8.8 The sample mean and the central limit theorem AHL 8.9 Mixed practice: normal combinations, sample means and the central limit theorem AHL 8.10 Unbiased estimates of the mean and variance; validity and reliability AHL 8.11 The t-interval for a mean AHL 8.12 z-intervals, t-intervals and choosing between them AHL 8.13 Unit review 0 0 of 56 skills done

AHL 9 · 2 weeks Differential Equations Separation of variables, Euler's method, slope fields and coupled systems. AHL 9.1 Setting up differential equations and integrating dy/dx = f(x)AHL 9.2 Separation of variables: general and particular solutions AHL 9.3 Separable equations in context: growth, decay and harder forms AHL 9.4 Slope fields and solution curves AHL 9.5 Euler's method for dy/dx = f(x, y)AHL 9.6 Euler's method for coupled systems AHL 9.7 Euler's method: accuracy and contexts AHL 9.8 Solving coupled linear systems exactly AHL 9.9 Phase portraits for real eigenvalues AHL 9.10 Complex eigenvalues: foci and centres AHL 9.11 Equilibrium points that are not the origin AHL 9.12 Euler's method for a coupled system: graphs and phase portraits AHL 9.13 Coupled systems and phase portraits: mixed practice AHL 9.14 Euler's method for second order equations AHL 9.15 Stability of second order equations AHL 9.16 Second order equations: exact solutions, error and models AHL 9.17 Unit review 0 0 of 66 skills done

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