Question 4 | Mr. Flynn IB

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Analysis and Approaches SL

Topic 1: Number and algebra

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

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

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

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 (21:52)
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

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

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

Question 1 (4:17)
Question 2 (2:46)
question 3 (6:49)
Question 4 (6:47)
Question 5 (3:48)
Question 6 (7:36)
Question 7 (9:51)
Question 8 a b c (7:25)
Question 8 d e (6:20)
Question 9 a (4:15)
Question 9 b (2:49)
Question 9 c (2:25)
Question 9 d (10:30)

Specimen paper 2

Question 1 (5:59)
Question 2 (6:54)
Question 3 (7:21)
Question 4 (7:25)
Question 5 (6:12)
Question 6 (12:35)
Question 7 a b (10:43)
Question 7 c d e (9:13)
Question 8 a b (9:32)
Question 8 c d e (11:17)
Question 9 a b (5:43)
Question 9 c (6:31)
Question 9 d (8:14)

2021 May TZ2 Paper 1

Question 1 (2:57)
Question 2 (3:07)
Question 3 (6:23)
Question 4 (4:00)
Question 5 (5:45)
Question 6 (5:11)
Question 7 a b (3:43)
Question 7 c d (5:10)
Question 7 e (2:38)
Question 8 a b (4:35)
Question 8 c d (4:59)
Question 9 a b (5:43)
Question 9 c d (3:22)
Question 9 e (9:13)

2021 May TZ2 P2

Question 1 (7:34)
Question 2 (4:47)
Question 3 (5:55)
Question 4 (10:54)
Question 5 (4:30)
Question 6 (8:46)
Question 7 a b c (6:31)
Question 7 d e (8:22)
Question 8 a b (7:20)
Question 8 c d e (6:19)
Question 9 a b (5:44)
Question 9 c d (7:48)

2021 May TZ1 P1

Question 1 (4:11)
Question 2 (2:47)
Question 3 (2:57)
Question 4 (3:22)
Question 5 (8:17)
Question 6 (8:41)
Question 7a (4:31)
Question 7bc (3:42)
Question 7d (3:28)
Question 8ab (4:38)
Question 8cd (4:44)
Question 8e (5:20)
Question 9ab (2:30)
Question 9cd (4:55)
Question 9e (9:14)

2021 May TZ1 P2

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

Question 1 (3:37)
Question 2 (2:08)
Question 3 (4:04)
Question 4 (6:05)
Question 5 (8:19)
Question 6 (7:55)
Question 7a (5:48)
Question 7b (5:16)
Question 7c (4:04)
Question 8abc (4:43)
Question 8d (7:15)
Question 9abc (9:35)
Question 9d (6:03)

2021 November P2

Question 1 (5:16)
Question 2 (3:43)
Question 3 (5:28)
Question 4 (5:54)
Question 5 (6:31)
Question 6 (10:15)
Question 7a (4:29)
Question 7b (6:37)
Question 7c (3:19)
Question 8abcd (7:57)
Question 8ef (6:21)
Question 9a (3:43)
Question 9b (8:27)
Question 9c (3:06)
Question 9d (5:32)

2022 May TZ1 P1

Question 1 (2:40)
Question 2 (2:25)
Question 3 (7:11)
Question 4 (6:21)
Question 5 (5:07)
Question 6 (7:23)
Question 7abc (3:56)
Question 7de (3:37)
Question 8a (3:18)
Question 8b (8:24)
Question 9a (4:33)
Question 9b (9:55)

2022 May TZ1 P2

Question 1 (4:10)
Question 2 (1:54)
Question 3 (3:44)
Question 4 (4:55)
Question 5 (7:13)
Question 6 (5:59)
Question 7abc (6:40)
Question 7d (5:26)
Question 8ab (7:01)
Question 8c (5:03)
Question 9ab (3:03)
Question 9c (6:40)
Question 9d (5:41)

2022 May TZ2 P1

Question 1 (1:08)
Question 2 (1:24)
Question 3 (2:53)
Question 4 (4:42)
Question 5 (3:37)
Question 6 (4:30)
Question 7abc (4:19)
Question 7de (4:16)
Question 8a (3:10)
Question 8b (6:52)
Question 9ab (3:49)
Question 9c (2:50)
Question 9de (5:50)

2022 May TZ2 P2

Question 1 (2:57)
Question 2 (1:36)
Question 3 (4:20)
Question 4 (4:15)
Question 5 (4:53)
Question 6 (7:13)
Question 7abc (4:43)
Question 7d (3:33)
Question 8ab (5:24)
Question 8c (6:53)
Question 9abc (6:57)
Question 9d (4:07)
Question 9e (3:04)

2022 November P1

Question 1 (2:31)
Question 2 (1:05)
Question 3 (3:38)
Question 4 (4:59)
Question 5 (3:21)
Question 6 (4:40)
Question 7ab (6:36)
Question 7c (4:32)
Question 8a (2:38)
Question 8b (5:31)
Question 9ab (7:26)
Question 9cd (8:58)

2022 November P2

Question 1 (2:40)
Question 2 (3:57)
Question 3 (3:42)
Question 4 (3:54)
Question 5 (5:17)
Question 6 (3:11)
Question 7 (13:47)
Question 8 (7:14)
Question 9abc (7:25)
Question 9d (4:06)

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