Analysis and Approaches (AA) SL
Course Curriculum
Topic 1: Number and algebra
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- 1.1 Scientific notation (10:44)
- 1.2.1 Arithmetic sequences and series (12:13)
- 1.2.2 Sigma notation (5:05)
- 1.3 Geometric sequences and series (13:52)
- 1.4.1 Compound interest (11:51)
- 1.4.2 Depreciation (6:21)
- 1.4.3 Inflation (5:28)
- 1.5.1 Laws of exponents (4:04)
- 1.5.2 Introduction to logs (10:43)
- 1.5.3 The number e (10:25)
- 1.6 Simple deductive proofs (8:25)
- 1.7.1 More exponents (12:35)
- 1.7.2 Laws of logarithms (10:01)
- 1.7.3 Change of base law (8:37)
- 1.8.1 Sum of an infinite geometric sequence (7:45)
- 1.8.2 System of linear equations (3:17)
- 1.8.3 Roots of a polynomial (6:03)
- 1.9.1 Binomial expansion (intro and full expansion) (20:16)
- 1.9.2 Binomial expansion (finding a term) (11:44)
Topic 2: Functions
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- 2.1.1 Gradient of a line (8:34)
- 2.1.2 Equation of a straight line (5:58)
- 2.1.3 Parallel and perpendicular lines (8:25)
- 2.2.1 Functions introduction (13:26)
- 2.2.2 Evaluating functions (6:08)
- 2.2.3 Inverse functions (11:21)
- 2.3 Sketching functions (9:07)
- 2.4.1 Features of graphs (12:22)
- 2.4.2 Asymptotes (9:01)
- 2.5.1 Composite functions (11:11)
- 2.5.2 Finding inverse functions (9:44)
- 2.6.1 Quadratics 3 forms (6:13)
- 2.6.2 Factorising quadratics (10:27)
- 2.6.3 Vertex form (8:10)
- 2.7.1 Solving quadratic equations (10:46)
- 2.7.2 Quadratic inequalities (9:54)
- 2.7.3 The discriminant (9:53)
- 2.8 Rational functions (10:14)
- 2.9.1 Exponential modelling (14:33)
- 2.9.2 Logarithmic functions (8:27)
- 2.10.1 Solving equations using substitution (8:15)
- 2.10.2 Solving equations with gdc (9:12)
- 2.11.1 Transformations (14:13)
- 2.11.2 Composite transformations (12:46)
Topic 3: Geometry and trigonometry
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- 3.1.1 Midpoint of a line segment (4:54)
- 3.1.2 Distance between 2 points (5:37)
- 3.1.3 Volume and surface area (14:44)
- 3.1.4 Trigonometry in 3d (15:12)
- 3.2.1 Pythagoras' theorem (3:00)
- 3.2.2 Soh cah toa (8:21)
- 3.2.3 Sine rule (6:16)
- 3.2.4 Cosine rule (6:59)
- 3.2.5 Area of a triangle (2:58)
- 3.3.1 Bearings (10:46)
- 3.3.2 Angles of elevation and depression (8:22)
- 3.4.1 Radians (8:14)
- 3.4.2 Arcs and sectors (9:12)
- 3.5.1 Mr. Flynn's exact triangles (8:06)
- 3.5.2 Unit circle (18:37)
- 3.5.3 The CAST diagram (15:41)
- 3.5.4 Graphs of sin, cos and tan (10:45)
- 3.5.5 Sine rule (ambiguous case) (6:00)
- 3.6 Trig identities (11:42)
- 3.7.1 Sinusoidal graphs (13:04)
- 3.7.2 Sinusoidal modelling (11:59)
- 3.8.1 Solving trig equations (12:50)
- 3.8.2 Solving trig equations with identities (11:28)
Topic 4: Statistics and probability
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- 4.1.1 Discrete v continuous data (7:28)
- 4.1.2 Sampling techniques (10:44)
- 4.2.1 Histograms and cumulative frequency curves (21:04)
- 4.2.2 Box and whisker diagram (6:37)
- 4.2.3 Interpreting box plots (8:23)
- 4.2.4 Outliers (9:30)
- 4.3.1 Averages and spread (11:22)
- 4.3.2 Frequency tables (14:10)
- 4.3.3 Constant changes to data (8:42)
- 4.3.4 Variance and Standard Deviation by hand (8:12)
- 4.4 Linear regression and correlation (21:53)
- 4.5 Probability formulae (9:47)
- 4.6.1 Venn diagrams (19:15)
- 4.6.2 Tree diagrams (13:29)
- 4.7 Discrete random variables (13:41)
- 4.8 Binomial distribution (17:18)
- 4.9 Normal distribution (28:45)
- 4.10 Regression line of x on y (11:01)
- 4.11 Testing for independence (8:45)
- 4.12 Normal distribution (finding mean and std. dev.) (10:04)
Topic 5: Calculus
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- 5.1.1 Introduction to differentiation (13:20)
- 5.1.2 Introduction to limits (16:17)
- 5.2.1 Increasing and decreasing functions (12:49)
- 5.3.1 Differentiation (the power rule) (10:27)
- 5.3.2 Derivative at a point (6:03)
- 5.4 Tangents and normals (9:49)
- 5.5.1 Integration power rule (10:07)
- 5.5.2 Finding f(x) (5:24)
- 5.5.3 Definite integration (8:37)
- 5.5.4 Area under the curve (15:03)
- 5.5.5 Finding a limit (6:34)
- 5.6.1 Derivative of sinx, cosx, lnx, e^x (5:19)
- 5.6.2 Chain rule (14:11)
- 5.6.3 Product rule (5:47)
- 5.6.4 Quotient rule (8:54)
- 5.7.1 Relationship between graphs and derivatives (13:27)
- 5.7.2 Sketching derivatives (14:23)
- 5.7.3 Sketching derivatives with gdc (6:40)
- 5.8.1 Classifying stationary points (13:40)
- 5.8.2 Points of inflexion (7:14)
- 5.8.3 Optimization (16:10)
- 5.9 Kinematics (28:12)
- 5.10.1 Integrating e^x and 1/x (5:33)
- 5.10.2 Integrating sin and cos (2:57)
- 5.10.3 Inverse chain rule (10:18)
- 5.10.4 Integration by substitution (19:09)
- 5.11 Area between two curves (16:34)
Internal assessment
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- 1. IA Introduction (10:22)
- 2.1 A Presentation (12:45)
- 2.2 B Mathematical communication (9:25)
- 2.3 C Personal engagement (11:04)
- 2.4 D Reflection (5:34)
- 2.5 E Use of mathematics (8:42)
- 3.1 Choosing a topic 1 (17:52)
- 3.2 Choosing a topic 2 (19:57)
- 4.1 Quadratic from basketball shot video (8:04)
- 4.1.2 Basketball analysis (11:26)
- 4.2 Quadratic fit on photo (13:57)
- 4.3 Sinusoidal fit on photo (4:33)
- 4.4 Data modelling with Excel (7:41)
- 4.5 Data modelling with Geogebra (10:34)
- 5 Marking an IA (20:14)
- 6.1 Ideas part 1 - Modelling (18:20)
- 6.2 Ideas part 2 (18:36)
- 6.3 Ideas part 3 (14:44)
- Sample Optimum Long Jump Distance Calculus (5:34)
- Sample Volume of Revolution Glasses (3:47)
- Sample Angry Birds Equation of a Tangent (3:58)
- Sample Gini Coefficient Integration (4:58)
- Sample Table Tennis Shot Comparison (5:19)
- Sample Swimming IA Normal Distribution (3:58)
- Sample Surface Area of a Chocolate Egg (2:48)
- Sample Polynomial Modelling Caffeine v Performance (5:05)
- Sample Area of a School Integration (2:48)
- Sample Linear Correlation Time v Calories (5:25)
- Sample Volume of Revoltion HL (3:55)
- Sample Modelling the Dubai Eye Trig Modelling (4:05)
- Sample Ibuprofen v Paracetamol Calculus (3:46)
- Sample India v China Population Modelling (5:09)
- Sample Volleyball Serve (6:32)
Specimen paper 1
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Specimen paper 2
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2021 May TZ2 Paper 1
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2021 May TZ2 P2
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2021 May TZ1 P1
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- Question 1 (3:28)
- Question 2 (5:32)
- Question 3 (8:47)
- Question 4 (6:49)
- Question 5 (8:21)
- Question 6 (6:59)
- Question 7a (5:51)
- Question 7b (4:48)
- Question 7c (7:05)
- Question 8ab (6:54)
- Question 8cd (6:05)
- Question 8e (8:03)
- Question 9ab (5:57)
- Question 9c (1:10)
- Question 9d (7:37)
- Question 9e (2:59)
2021 November P1
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2022 May TZ1 P1
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2022 May TZ1 P2
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2022 May TZ2 P1
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2022 November P1
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2023 May TZ1 P1
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2023 November P1
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