Question 11 b ii-iv | Mr. Flynn IB

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Analysis and Approaches HL

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)
1.10.1 Counting principles introduction (product and addition principles) (12:20)
1.10.2 Factorials and arrangements (13:29)
1.10.3 Algebra of factorials (13:06)
1.10.4 Combinations and permutations (21:41)
1.10.5 Keeping objects together or separated (14:49)
1.10.6 Binomial theorem extension (10:52)
1.11 Partial fractions (12:36)
1.12.1 Complex numbers introduction (10:59)
1.12.2 Operations with complex numbers (10:17)
1.13.1 Modulus-argument form (20:10)
1.13.2 Euler form (17:47)
1.13.3 Complex operations and geometric interpretation (13:26)
1.13.4 Properties of complex conjugates (11:33)
1.14.1 Complex solutions to polynomial equations (14:14)
1.14.2 De Moivre's Theorem (9:37)
1.14.3 Roots of complex numbers (14:55)
1.14.4 Roots of unity (6:45)
1.15.1 Proof by induction (intro and series) (16:05)
1.15.2 Proof by induction (differentiation) (12:50)
1.15.3 Proof by induction (divisibility) (11:00)
1.15.4 Proof by induction (inequalities) (24:00)
1.15.5 Proof by induction (De Moivre) (11:59)
1.15.5 Proof by contradiction (intro) (10:28)
1.15.7 Proof by contradiction (root 2) (5:50)
1.15.8 Proof by contradiction (infinite primes) (10:00)
1.15.9 Use of counterexample (6:54)
1.16.1 System of linear equations (HL only) (16:48)
1.16.2 System of linear equations part 2 (11:50)

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)
2.12.1 Dividing polynomials (6:48)
2.12.2 Factor and remainder theorems (12:17)
2.12.3 Graphs of polynomials (16:28)
2.12.4 Sum and product of roots (14:28)
2.13.1 Rational functions (quadratic in denominator) (14:00)
2.13.2 Rational functions (quadratic in numerator) (15:29)
2.14 Even and odd functions (8:44)
2.15 Solving inequalities (7:48)
2.16.1 Graphs of modulus functions combined (10:15)
2.16.2 Modulus equations and inequalities (9:20)
2.16.3 Reciprocal transformations (11:39)
2.16.4 Graphs of y=(f(x))^2 (8:18)

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)
3.9.1 Reciprocal trig identities (11:04)
3.9.2 Inverse trigonometric functions (25:58)
3.10 Compound angle identities (14:38)
3.11 Symmetry in trigonometric functions (4:43)
3.12.1 Vectors introduction (11:56)
3.12.2 Operations with vectors (15:47)
3.12.3 Magnitude and unit vectors (12:38)
3.13.1 Scalar product and angle between vectors (13:52)
3.13.2 Properties of the scalar product (11:59)
3.14.1 Vector equation of a line (17:58)
3.14.2 Parametric form and cartesian equations of a line (11:15)
3.14.3 Angle between two lines (6:45)
3.14.4 Vectors and kinematics (10:40)
3.15.1 Intersecting lines (11:17)
3.15.2 Distance between a point and a line (10:15)
3.16.1 Vector product (9:45)
3.16.2 Properties of the vector product (5:30)
3.16.3 Areas using vector product (9:25)
3.17.1 Vector equation of a plane (12:55)
3.17.2 Cartesian equation of a plane (14:12)
3.18.1 Intersection between a line and a plane (5:54)
3.18.2 Intersection between two planes (11:04)
3.18.3 Intersection of 3 planes (9:47)
3.18.4 Angle between a line and a plane (8:54)
3.18.5 Angle between two planes (8:52)

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)
4.13 Bayes' theorem (11:21)
4.14.1 Variance and standard deviation (14:46)
4.14.2 Variance and standard deviation of a discrete random variable (4:50)
4.14.3 Continuous random variables intro (13:48)
4.14.4 Mean of a continuous random variable (5:48)
4.14.5 Median and mode of a discrete random variable (4:00)
4.14.6 Median and mode of continuous random variable (10:45)
4.14.7 Variance of a continuous random variable (6:11)
4.14.8 Linear transformations of X (11:35)

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 a 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)
5.12.1 Continuous functions (6:29)
5.12.2 Differentiable functions (6:00)
5.12.3 Differentiation from first principles (13:42)
5.12.4 Higher derivatives (9:26)
5.13 l'Hopital's rule (15:34)
5.14.1 Implicit differentiation (20:50)
5.14.2 Related rates of change (11:18)
5.15.1 More derivative rules (14:54)
5.15.2 More integration rules (14:38)
5.15.3 Integrating using partial fractions (13:13)
5.16.1 Integration by substitution (HL only) (22:21)
5.16.2 Integration by parts (10:20)
5.16.3 Repeated integration by parts (12:08)
5.17.1 Area between curve and y-axis (11:37)
5.17.2 Volume of revolution intro and x-axis (12:26)
5.17.3 Volume of revolution about y-axis (12:39)
5.17.4 Volume of revolution between 2 curves (11:09)
5.18.1 Differential equations introduction (10:08)
5.18.2 Separation of variables (6:34)
5.18.3 Euler's method introduction (17:03)
5.18.4 Euler's method example (16:42)
5.18.5 Homogenous differential equations (13:54)
5.18.6 Integrating factor (8:57)
5.19.1 Maclaurin series introduction (15:14)
5.19.2 Maclaurin series (8:01)
5.19.3 Maclaurin series (substitutions and products) (10:19)
5.19.4 Maclaurin series (binomial series) (10:29)
5.19.5 Maclaurin series differentiation and integration (15:11)
5.19.6 Maclaurin series sigma notation (10:58)
5.19.7 Maclaurin series differential equations (7:19)
5.19.8 Euler's identity (9:23)

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 Swimming IA Normal Distribution (3:58)
Sample Gini Coefficient Integration (4:58)
Sample Optimum Long Jump Distance Calculus (5:34)
Sample Table Tennis Shot Comparison (5:19)
Sample Angry Birds Equation of a Tangent (3:58)
Sample Volume of Revolution Glasses (3:47)
Sample Area of a School Integration (2:48)
Sample India v China Population Modelling (5:09)
Sample Linear Correlation Time v Calories (5:25)
Sample Modelling the Dubai Eye Trig Modelling (4:05)
Sample Ibuprofen v Paracetamol Calculus (3:46)
Sample Surface Area of a Chocolate Egg (2:48)
Sample Polynomial Modelling Caffeine v Performance (5:05)
Sample Volume of Revoltion HL (3:55)
Sample Volleyball Serve (6:32)

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Question 2 (6:49)
Question 3 (6:47)
Question 4 (6:10)
Question 5 (3:48)
Question 6 (7:36)
Question 7 (9:28)
Question 8 (7:04)
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Question 10 a (4:15)
Question 10 b (2:49)
Question 10 c (2:25)
Question 10 d (10:30)
Question 11 a (3:22)
Question 11 b (7:46)
Question 11 c (5:46)
Question 11 d (7:16)
Question 12 a (3:44)
Question 12 b (4:59)
Question 12 c (7:47)
Question 12 d (3:22)

Specimen Paper 2

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Question 2 (7:21)
Question 3 (7:25)
Question 4 (6:12)
Question 5 (12:35)
Question 6 (6:37)
Question 7 (7:13)
Question 8 (4:53)
Question 9 (7:41)
Question 10 a b (9:32)
Question 10 c d e (11:17)
Question 11 a (2:29)
question 11 b (10:04)
Question 11 c (7:32)
Question 11 d (5:15)
Question 11 e (4:24)
Question 12 a (1:56)
Question 12 b (5:11)
Question 12 c (4:37)
Question 12 d (4:48)

Specimen paper 3

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Question 1 c (2:05)
Question 1 d (4:33)
Question 1 e (5:49)
Question 1 f (5:27)
Question 1 g (6:56)
Question 1 h (3:17)
Question 1 i (6:27)
Question 2 a (4:10)
Question 2 b (5:29)
Question 2 c (3:06)
Question 2 d (3:58)
Question 2 e (5:36)
Question 2 f (3:54)
Question 2 g (3:01)
Question 2 h (8:27)

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Question 9 (8:31)
Question 10ab (2:30)
Question 10cd (4:55)
Question 10e (9:14)
Question 11a (3:52)
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Question 11c (6:16)
Question 12a (1:53)
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Question 12c (7:57)

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Question 8 (6:35)
Question 9 (8:34)
Question 10ab (5:57)
Question 10c (1:10)
Question 10d (7:37)
Question 10e (2:59)
Question 11ab (2:27)
Question 11cd (10:47)
Question 11e (3:51)
Question 11f (7:23)
Question 12ab (5:10)
Question 12c (11:15)
Question 12de (6:15)

2021 May TZ1 P3

Question 1ab (6:57)
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Question 1d (4:56)
Question 1e (6:00)
Question 1f (9:48)
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Question 2bc (2:37)
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2021 May TZ2 P1

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Question 10ab (4:35)
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Question 11a (5:57)
Question 11 b (11:40)
Question 11c (2:20)
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2021 May TZ2 P2

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Question 9ab (7:56)
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2021 May TZ2 P3

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Question 10a (5:48)
Question 10b (5:16)
Question 10c (4:04)
Question 11a (9:50)
Question 11b (4:44)
Question 11c (5:29)
Question 12a (7:45)
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2021 November P2

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Question 10c (3:34)
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Question 11a (4:17)
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Question 11c (2:44)
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2021 November P3

Question 1ab (6:55)
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Question 1d (0:45)
Quesiton 1e (3:08)
Question 1f (6:59)
Question 1g (6:21)
Question 2a (6:56)
Quesiton 2b (6:38)
Question 2c (i)(ii) (5:31)
Question 2c(iii) (3:46)

2022 May TZ1 P1

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Question 9 (5:26)
Question 10a (5:25)
Question 10b (8:27)
Question 11a (6:20)
Question 11b (7:00)
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Question 12ab (6:02)
Question 12c (5:22)
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2022 May TZ1 P2

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Question 9 (7:51)
Question 10ab (4:44)
Question 10c (4:15)
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Question 11ab (3:03)
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2022 May TZ1 P3

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Question 10ab (3:49)
Question 10c (2:50)
Question 10de (5:50)
Question 11a (6:37)
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Question 12ab (5:49)
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May 2022 TZ2 P2

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Quesiton 7 (7:57)
Question 8 (8:45)
Question 9 (7:03)
Question 10ab (5:24)
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Question 11abc (7:45)
Question 11d (4:47)
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Question 12ab (4:35)
Question 12cd (5:50)
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2022 May TZ2 P3

Question 1cd (5:43)
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Question 2a (6:19)
Question 2bi (3:23)
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2022 November P1

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Question 7 (7:22)
Question 8 (8:33)
Question 9 (8:19)
Question 10ab (7:26)
Question 10cd (8:58)
Question 11a bi (6:46)
Question 11 b ii-iv (5:43)
Question 12a (2:25)
Question 12b (9:03)
Question 12c (17:11)

2022 November P2

Question 1 (2:40)
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Question 4 (5:17)
Question 5 (3:11)
Question 6 (6:16)
Question 7 (4:06)
Question 8 (8:09)
Question 9 (7:09)
Question 10abc (7:25)
Question 10d (4:06)
Question 11ab (4:47)
Question 11cd (6:20)
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2022 November p3

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Question 1c di (6:02)
Question 1dii (9:44)
Question 1diii e f (6:43)
Question 1 gi gii (6:43)
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Question 2e i ii iii iv (8:31)
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2023 May TZ1 P1

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Question 8 (6:13)
Question 9 (8:44)
Question 10 (8:33)
Question 11ab (7:07)
Question 11c (7:26)
Question 11de (5:33)
Question 12ab (4:25)
Question 12cd (4:20)
Question 12e (6:13)

2023 May TZ1 P2

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Question 7 (5:28)
Question 8 (6:50)
Question 9 (3:39)
Question 10ab (6:16)
Question 10c (4:07)
Question 11a (5:11)
Question 11b (1:24)
Question 11c (4:27)
Question 11de (2:49)
Question 11f (6:45)
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Question 12b (3:51)
Question 12c (3:22)
Question 12d (4:26)
Question 12e (4:25)

2023 TZ1 P3

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