Topic 1: Number and algebra
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1.1 Scientific notation (10:44)
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1.2.1 Arithmetic sequences and series (12:13)
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1.2.2 Sigma notation (5:05)
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1.3 Geometric sequences and series (13:52)
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1.4.1 Compound interest (11:51)
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1.4.2 Depreciation (6:21)
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1.4.3 Inflation (5:28)
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1.5.1 Laws of exponents (4:04)
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1.5.2 Introduction to logs (7:55)
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1.5.3 The number e (10:25)
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1.6.1 Rounding (10:05)
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1.6.2 Upper and lower bounds (8:09)
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1.6.3 Percentage error (5:51)
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1.7.1 Loans (8:35)
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1.7.2 Annuities (10:16)
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1.7.3 Change of base (8:37)
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1.8.1 System of linear equations (3:17)
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1.8.2 Roots of a polynomial (6:03)
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1.9.1 Laws of logs (10:01)
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1.9.2 Change of base (8:37)
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1.10 More exponents (12:35)
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1.11 Sum of an infinite geometric sequence (7:45)
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1.12.1 Complex numbers introduction (10:59)
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1.12.2 Operations with complex numbers (10:17)
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1.12.3 Complex solutions to polynomial equations (14:14)
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1.13.1 Modulus-argument form (20:10)
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1.13.2 Euler form (17:47)
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1.13.3 Adding sinusoidal functions (12:21)
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1.13.4 Operations and geometric interpretation (13:26)
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1.14.1 Introduction to matrices (3:39)
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1.14.2 Algebra of matrices (3:33)
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1.14.3 Multiplication of matrices (6:58)
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1.14.4 Identity matrix (3:40)
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1.14.5 Properties of matrices (2:47)
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1.14.6 Determinant and inverse of a matrix (8:15)
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1.14.7 System of linear equations (6:00)
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1.15.1 Eigenvalues and eigenvectors combined (18:09)
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1.15.2 Powers of matrices (11:04)
Topic 2: Functions
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2.1.1 Gradient of a line (8:34)
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2.1.2 Equation of a straight line (5:58)
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2.1.3 Parallel and perpendicular lines (8:25)
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2.2.1 Functions introduction (13:26)
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2.2.2 Evaluating functions (6:08)
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2.2.3 Inverse functions (11:21)
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2.3 Sketching functions (9:07)
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2.4.1 Features of graphs (12:22)
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2.4.2 Asymptotes (9:01)
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2.5.1 Linear modelling (10:39)
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2.5.2 Quadratic functions (6:34)
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2.5.3 Quadratic modelling (10:14)
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2.5.4 Exponential modelling (14:33)
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2.5.5 Direct and inverse variation (14:55)
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2.5.6 Cubic modelling (11:29)
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2.5.7 Sinusoidal graphs (13:13)
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2.5.8 Creating a sinusoidal model (8:56)
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2.6 Finding the parameters of a model (6:22)
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2.7.1 Composite functions (11:11)
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2.7.2 Finding inverse functions (9:44)
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2.8.1 Transformations (14:13)
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2.8.2 Composite transformations (12:46)
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2.9.1 Half life (12:56)
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2.9.2 Logarithmic functions (8:27)
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2.9.3 Logistic modelling (12:52)
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2.9.4 Piecewise functions (8:40)
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2.10.1 Scaling with logs (13:16)
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2.10.2 Log log graphs (10:24)
Topic 3: Geometry and trigonometry
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3.1.1 Midpoint of a line segment (4:54)
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3.1.2 Distance between 2 points (5:37)
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3.1.3 Volume and surface area (14:44)
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3.1.4 Trigonometry in 3d (15:12)
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3.2.1 Pythagoras' theorem (3:00)
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3.2.2 Soh cah toa (8:21)
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3.2.3 Sine rule (6:16)
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3.2.4 Cosine rule (6:59)
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3.2.5 Area of a triangle (2:58)
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3.3.1 Bearings (10:46)
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3.3.2 Angles of elevation and depression (8:22)
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3.4 Arcs and Sectors (5:10)
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3.5 Perpendicular bisectors (15:59)
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3.6.1 Voronoi diagrams intro (11:09)
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3.6.2 Voronoi examples (14:53)
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3.7.1 Radians (8:14)
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3.7.2 Arcs and sectors (9:12)
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3.8.1 Mr. Flynn's exact triangles (8:06)
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3.8.2 Unit circle (18:37)
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3.8.3 The CAST diagram (15:41)
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3.8.4 Graphs of sin, cos and tan (10:45)
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3.8.5 Sine rule (ambiguous case) (6:00)
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3.8.6 Trig identities (5:11)
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3.8.7 Solving Trigonometric Equations (12:50)
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3.9.1 Matrix transformations (intro and stretches) (7:33)
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3.9.2 Translations (3:35)
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3.9.3 Enlargements (4:53)
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3.9.4 Rotations (9:58)
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3.9.5 Reflections (14:56)
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3.9.6 Composite matrix transformations (6:32)
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3.9.7 Determinant of a transformation matrix (9:58)
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3.10.1 Vectors introduction (11:56)
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3.10.2 Operations with vectors (15:47)
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3.10.3 Magnitude and unit vectors (12:38)
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3.11 Vector equation of a line (17:58)
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3.12.1 Vectors and kinematics (10:40)
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3.12.2 Motion with variable velocity (9:53)
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3.13.1 Scalar product and angle between vectors (13:52)
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3.13.2 Angle between two lines (6:45)
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3.13.3 Vector product (9:45)
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3.13.4 Areas using vector product (9:25)
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3.13.5 Components of vectors (10:07)
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3.14 Introduction to graph theory (16:02)
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3.15.1 Adjacency matrices (9:33)
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3.15.2 Weighted adjacency tables (5:12)
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3.15.3 Walks (20:13)
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3.16.1 Graph routes (5:32)
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3.16.2 Kruskal's algorithm (8:07)
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3.16.3 Prim's algorithm (5:05)
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3.16.4 Prim's algorithm with adjacency table (5:00)
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3.16.5 Eulerian graphs (5:45)
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3.16.6 Chinese postman problem (17:20)
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3.16.7 Hamiltonian graphs (3:02)
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3.16.8 Travelling salesman problem (7:10)
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3.16.9 TSP practical problems (5:52)
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3.16.10 Nearest neighbour algorithm (5:32)
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3.16.11 Deleted vertex algorithm (5:28)
Topic 4: Statistics and probability
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4.1.1 Discrete v continuous data (7:28)
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4.1.2 Sampling techniques (10:44)
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4.2.1 Histograms and Cumulative Frequency Curves (21:04)
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4.2.2 Box and whisker diagram (6:37)
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4.2.3 Interpreting box plots (8:23)
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4.2.4 Outliers (9:30)
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4.3.1 Averages and spread (11:22)
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4.3.2 Frequency tables (14:10)
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4.3.3 Constant changes to data (8:42)
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4.3.4 Variance and standard deviation by hand (8:12)
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4.4 Linear regression and correlation (21:52)
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4.5 Probability formulae (9:47)
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4.6.1 Venn diagrams (19:15)
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4.6.2 Tree diagrams (16:15)
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4.7 Discrete random variables (13:41)
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4.8 Binomial distribution (17:18)
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4.9 Normal distribution (28:45)
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4.10 Spearman's rank correlation coefficient (17:09)
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4.11.1 Chi squared intro (10:34)
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4.11.2 Chi squared test for independence (16:57)
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4.11.3 Chi squared goodness of fit (11:45)
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4.11.4 t test (19:21)
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4.12.1 Surveys and questionnaires (4:20)
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4.12.2 Reliability v validity (6:25)
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4.12.3 Chi squared (categorising data) (12:13)
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4.12.4 Chi squared (degrees of freedom) (16:54)
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4.13.1 Non linear regression (6:08)
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4.13.2 Sum of square residuals (10:30)
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4.13.3 The coefficient of determination (14:20)
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4.14.1 Linear transformations of X (11:35)
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4.14.2 Linear combinations of n random variables (10:29)
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4.14.3 Unbiased estimates for the mean and variance (11:42)
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4.14.4 Unbiased estimates example questions (8:29)
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4.15.1 Linear combination of n independent normal random variables (19:28)
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4.15.2 Normal distribution sampling (11:39)
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4.15.3 The central limit theorem (12:56)
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4.16.1 Confidence intervals (known variance) (9:06)
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4.16.2 Confidence intervals (unknown variance) (5:04)
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4.17 Poisson distribution (14:59)
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4.18.1 Z-test one tailed (9:28)
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4.18.2 Z-test two tailed (8:58)
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4.18.3 T-test (4:45)
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4.18.4 Matched pairs (5:52)
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4.18.5 Testing for population proportion (6:02)
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4.18.6 Test for mean using Poisson distribution (8:19)
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4.18.7 Testing for correlation (7:25)
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4.18.8 Type I an II errors Intro (9:14)
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4.18.9 Normal errors (9:51)
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4.18.10 Poisson errors (11:50)
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4.18.11 Binomial errors (9:02)
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4.19.1 Markov chains introduction (12:02)
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4.19.2 Transition matrices (13:17)
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4.19.3 Steady state and long term probabilities (15:11)
Topic 5: Calculus
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5.1.1 Introduction to differentiation (13:20)
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5.1.2 Introduction to limits (16:17)
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5.2.1 Increasing and decreasing functions (12:49)
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5.3.1 Differentiation power rule (9:37)
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5.3.2 Derivative at a point (6:03)
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5.4 Tangents and normals (9:49)
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5.5.1 Integration (power rule) (11:50)
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5.5.2 Finding f(x) (5:24)
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5.5.3 Area under the curve (6:44)
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5.6 Stationary points (11:27)
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5.7 Optimization (16:10)
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5.8 Trapezoidal rule (14:16)
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5.9.1 Derivative of sinx,cosx,lnx,e^x (5:19)
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5.9.2 Differentiation (rational exponents) (10:27)
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5.9.3 Chain rule (14:11)
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5.9.4 Product rule (5:47)
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5.9.5 Quotient rule (8:54)
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5.9.6 Related rates of change (11:18)
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5.10.1 Relationship between graphs and derivatives (13:27)
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5.10.2 Sketching derivatives (14:23)
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5.10.3 Classifying stationary points (13:40)
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5.10.4 Points of inflexion (7:14)
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5.11.1 Integration power rule (rational power) (10:07)
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5.11.2 Integrating sin and cos (2:57)
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5.11.3 Integrating e^x and 1/x (5:33)
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5.11.4 Inverse chain rule (10:18)
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5.11.5 Integration by substitution (19:09)
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5.12.1 Area under the curve (15:03)
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5.12.2 Area between curve and y-axis (11:37)
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5.12.3 Volume of revolution intro and x-axis (12:26)
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5.12.4 Volume of revolution about y-axis (12:39)
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5.13.1 Kinematics (28:12)
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5.13.2 Kinematics 2 (6:14)
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5.14.1 Setting up a differential equation (5:04)
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5.14.2 Separation of variables (6:34)
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5.15 Slope fields (11:40)
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5.16.1 Euler's method (17:03)
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5.16.2 Euler's method example (16:42)
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5.16.3 Euler's method for coupled systems (13:36)
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5.17.1 Phase portraits intro (11:48)
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5.17.2 Solutions of coupled differential equations (p1) (12:27)
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5.17.3 Solutions of coupled differential equations (p2) (11:07)
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5.17.4 Sketching phase portraits introduction (5:33)
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5.17.5 Sketching phase portraits (source) (6:01)
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5.17.6 Sketching phase portraits (sink) (3:58)
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5.17.7 Sketching phase portraits (spiral sink) (3:58)
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5.17.8 Sketching phase portraits (spiral source) (7:47)
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5.17.9 Sketching phase portraits (centre) (5:04)
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5.18.1 Second order DE (Euler's method) (10:10)
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5.18.2 Second order DE (exact solution) (11:01)
Internal assessment
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1.1 IA Introduction (10:22)
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1.2 A Presentation (12:45)
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1.3 B Mathematical communication (9:25)
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1.4 C Personal engagement (11:04)
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1.5 D Reflection (5:34)
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1.6 E Use of mathematics (8:42)
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1.7 Choosing a topic 1 (17:52)
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1.8 Choosing a topic 2 (19:57)
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2.1 Quadratic from basketball video (8:04)
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2.2 basketball analysis (11:26)
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2.3 Quadratic fit on photo (13:57)
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2.4 Sinusoidal fit on photo (4:33)
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2.5 Data modelling with Excel (7:41)
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2.6 Data modelling with Geogebra (10:34)
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2.7 Modelling a skateboard ramp (15:38)
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2.8 Modelling the price of bitcoin (15:41)
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2.9 Volume of revolution (9:21)
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2.10 Running IA (16:28)
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2.11 Voronoi IA (21:36)
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2.12 Modelling Ain Dubai (14:56)
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3.1 Ideas 1 - Modelling data (18:20)
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3.2 Ideas 2 (18:36)
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3.3 Ideas 3 (14:44)
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4.1 Marking an IA (20:14)
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Sample Swimming IA Normal Distribution (3:58)
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Sample Surface Area of a Chocolate Egg (2:48)
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Sample Angry Birds Equation of a Tangent (3:58)
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Sample Volume of Revoltion HL (3:55)
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Sample Linear Correlation Time v Calories (5:25)
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Sample Modelling the Dubai Eye Trig Modelling (4:05)
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Sample Volume of Revolution Glasses (3:47)
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Sample Optimum Long Jump Distance Calculus (5:34)
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Sample Table Tennis Shot Comparison (5:19)
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Sample Ibuprofen v Paracetamol Calculus (3:46)
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Sample Gini Coefficient Integration (4:58)
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Sample India v China Population Modelling (5:09)
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Sample Polynomial Modelling Caffeine v Performance (5:05)
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Sample Area of a School Integration (2:48)
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Sample Volleyball Serve (6:32)
Specimen P1
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Question 1 (5:48)
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Question 2 (4:59)
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Question 3 (7:52)
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Question 4 (7:59)
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Question 5 (4:38)
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Question 6 (6:47)
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Question 7 (3:17)
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Question 8 (11:03)
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Question 9 (5:26)
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Question 10 (5:14)
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Question 11 (4:28)
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Question 12 (9:33)
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Question 13 (6:43)
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Question 14 (9:20)
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Question 15 (8:53)
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Question 16 (6:14)
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Question 17 (10:27)
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Question 18 (9:52)
Specimen P2
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Question 1ab (7:42)
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Question 1cd (7:33)
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Question 1e (7:15)
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Question 2a (3:15)
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Question 2bc (5:14)
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Question 2def (6:08)
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Question 3a (6:16)
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Question 3bc (10:08)
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Question 3d (5:19)
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Question 4ab (5:39)
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Question 4c (4:20)
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Question 4d (3:19)
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Question 5ab (4:04)
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Question 5cd (3:46)
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Question 5ef (4:29)
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Question 5g (3:19)
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Question 6ab (6:16)
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Question 6c (1:21)
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Question 6de (9:04)
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Question 7a (7:52)
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Question 7bc (2:21)
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Question 7d (7:46)
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Question 7efg (6:11)
Specimen P3
2021 May TZ1 P1
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Question 1 (2:30)
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Question 2 (5:34)
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Question 3 (8:58)
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Question 4 (9:40)
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Question 5 (6:24)
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Question 6 (5:39)
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Question 7 (11:58)
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Question 8 (8:28)
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Question 9 (9:18)
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Question 10 (7:24)
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Question 11 (7:40)
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Question 12 (5:53)
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Question 13 (5:27)
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Question 14 (4:59)
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Question 15 (5:16)
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Question 16 (6:11)
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Question 17 (5:32)
2021 May TZ1 P2
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Question 1ab (8:26)
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Question 1cd (7:20)
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Question 1ef (6:06)
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Question 2ab (6:44)
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Question 2cde (6:50)
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Question 3a (5:27)
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Question 3b (1:01)
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Question 3cd (6:10)
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Question 4ab (6:16)
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Question 4c (6:50)
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Question 4d (5:08)
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Question 5ab (9:27)
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Question 5cd (8:35)
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Question 6a (4:36)
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Question 6b (4:50)
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Question 6c (4:10)
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Question 6d (1:41)
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Question 6e (8:54)
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Question 7a (4:44)
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Question 7b (7:17)
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Question 7d (6:59)
2021 May TZ1 P3
2021 May TZ2 P1
2021 May TZ2 P2
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Question 1ab (4:55)
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Question 1cd (6:30)
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Question 2ab (9:49)
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Question 2d (5:10)
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Question 2e (7:24)
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Question 3ab (9:49)
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Question 3cde (6:16)
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Question 3fg (2:44)
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Question 4ab (4:47)
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Question 4c (8:06)
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Question 4d (5:46)
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Question 4e (3:43)
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Question 5ab (6:29)
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Question 5c (2:40)
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Question 5d (7:49)
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Question 6abc (7:12)
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Question 6def (4:12)
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Question 7a (5:51)
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Question 7bc (3:11)
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Question 7d (1:43)
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Question 7e (5:14)
2021 May TZ2 P3
2021 November P1
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Question 1 (4:17)
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Question 2 (4:37)
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Question 3 (6:13)
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Question 4 (8:06)
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Question 5 (7:18)
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Question 6 (4:48)
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Question 7 (7:06)
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Question 8 (6:06)
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Question 9 (3:45)
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Question 10 (4:44)
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Question 11 (4:49)
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Question 12 (4:34)
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Question 13 (4:31)
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Question 14 (5:15)
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Question 15 (9:06)
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Question 16 (11:13)
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Question 17 (6:55)
2021 November P2
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Question 1ab (7:39)
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Question 1cd (6:35)
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Question 2ab (3:26)
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Question 2cd (6:06)
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Question 2e (3:15)
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Question 2f (3:31)
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Question 3abc (4:02)
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Question 3d (4:49)
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Question 4a (9:40)
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Question 4b (4:08)
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Question 4c (5:03)
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Question 5ab (8:33)
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Question 5c (5:35)
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Question 6ab (3:55)
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Question 6c (4:51)
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Question 6d (5:36)
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Question 7a (5:40)
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Question 7b (5:59)
2021 November P3
2022 May TZ1 P1
2022 May TZ1 P2
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Question 1abc (4:41)
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Question 1def (4:52)
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Question 2a (6:00)
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Question 2bcd (7:46)
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Question 3abcd (8:19)
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Question 3e (2:15)
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Question 4a (6:52)
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Question 4b (9:29)
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Question 5ab (4:19)
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Question 5c (9:58)
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Question 6a (2:48)
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Question 6bc (10:07)
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Question 6d (6:53)
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Question 7a (5:51)
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Question 7bc (4:52)
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Question 7d (4:56)
2022 May TZ1 P3
2022 May TZ2 P1
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Question 1 (2:55)
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Question 2 (5:52)
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Question 3 (4:23)
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Question 4 (3:23)
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Question 5 (9:59)
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Question 6 (5:47)
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Question 7 (4:20)
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Question 8 (9:04)
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Question 9 (5:07)
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Question 10 (3:22)
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Question 11 (7:13)
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Question 12 (6:35)
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Question 13 (5:39)
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Question 14 (5:44)
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Question 15 (6:50)
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Question 16 (9:57)
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Question 17 (15:03)
2022 May TZ2 P2
2022 May TZ2 P3
2022 November P1
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Question 1 (3:55)
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Question 2 (3:46)
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Question 3 (5:00)
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Question 4 (7:31)
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Question 5 (5:31)
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Question 6 (6:11)
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Question 7 (6:36)
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Question 8 (7:01)
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Question 9 (7:17)
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Question 10 (7:15)
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Question 11 (6:11)
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Question 12 (7:36)
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Question 13 (6:01)
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Question 14 (10:19)
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Question 15 (7:21)
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Question 16 (5:06)
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Question 17 (13:08)
2022 November P2
2022 November P3
