1.7.2 Annuities | Mr. Flynn IB

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Applications and Interpretation 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 (7:55)
1.5.3 The number e (10:25)
1.6.1 Rounding (10:05)
1.6.2 Upper and lower bounds (8:09)
1.6.3 Percentage error (5:51)
1.7.1 Loans (8:35)
1.7.2 Annuities (10:16)
1.7.3 Change of base (8:37)
1.8.1 System of linear equations (3:17)
1.8.2 Roots of a polynomial (6:03)
1.9.1 Laws of logs (10:01)
1.9.2 Change of base (8:37)
1.10 More exponents (12:35)
1.11 Sum of an infinite geometric sequence (7:45)
1.12.1 Complex numbers introduction (10:59)
1.12.2 Operations with complex numbers (10:17)
1.12.3 Complex solutions to polynomial equations (14:14)
1.13.1 Modulus-argument form (20:10)
1.13.2 Euler form (17:47)
1.13.3 Adding sinusoidal functions (12:21)
1.13.4 Operations and geometric interpretation (13:26)
1.14.1 Introduction to matrices (3:39)
1.14.2 Algebra of matrices (3:33)
1.14.3 Multiplication of matrices (6:58)
1.14.4 Identity matrix (3:40)
1.14.5 Properties of matrices (2:47)
1.14.6 Determinant and inverse of a matrix (8:15)
1.14.7 System of linear equations (6:00)
1.15.1 Eigenvalues and eigenvectors combined (18:09)
1.15.2 Powers of matrices (11:04)

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 Linear modelling (10:39)
2.5.2 Quadratic functions (6:34)
2.5.3 Quadratic modelling (10:14)
2.5.4 Exponential modelling (14:33)
2.5.5 Direct and inverse variation (14:55)
2.5.6 Cubic modelling (11:29)
2.5.7 Sinusoidal graphs (13:13)
2.5.8 Creating a sinusoidal model (8:56)
2.6 Finding the parameters of a model (6:22)
2.7.1 Composite functions (11:11)
2.7.2 Finding inverse functions (9:44)
2.8.1 Transformations (14:13)
2.8.2 Composite transformations (12:46)
2.9.1 Half life (12:56)
2.9.2 Logarithmic functions (8:27)
2.9.3 Logistic modelling (12:52)
2.9.4 Piecewise functions (8:40)
2.10.1 Scaling with logs (13:16)
2.10.2 Log log graphs (10:24)

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 Arcs and Sectors (5:10)
3.5 Perpendicular bisectors (15:59)
3.6.1 Voronoi diagrams intro (11:09)
3.6.2 Voronoi examples (14:53)
3.7.1 Radians (8:14)
3.7.2 Arcs and sectors (9:12)
3.8.1 Mr. Flynn's exact triangles (8:06)
3.8.2 Unit circle (18:37)
3.8.3 The CAST diagram (15:41)
3.8.4 Graphs of sin, cos and tan (10:45)
3.8.5 Sine rule (ambiguous case) (6:00)
3.8.6 Trig identities (5:11)
3.8.7 Solving Trigonometric Equations (12:50)
3.9.1 Matrix transformations (intro and stretches) (7:33)
3.9.2 Translations (3:35)
3.9.3 Enlargements (4:53)
3.9.4 Rotations (9:58)
3.9.5 Reflections (14:56)
3.9.6 Composite matrix transformations (6:32)
3.9.7 Determinant of a transformation matrix (9:58)
3.10.1 Vectors introduction (11:56)
3.10.2 Operations with vectors (15:47)
3.10.3 Magnitude and unit vectors (12:38)
3.11 Vector equation of a line (17:58)
3.12.1 Vectors and kinematics (10:40)
3.12.2 Motion with variable velocity (9:53)
3.13.1 Scalar product and angle between vectors (13:52)
3.13.2 Angle between two lines (6:45)
3.13.3 Vector product (9:45)
3.13.4 Areas using vector product (9:25)
3.13.5 Components of vectors (10:07)
3.14 Introduction to graph theory (16:02)
3.15.1 Adjacency matrices (9:33)
3.15.2 Weighted adjacency tables (5:12)
3.15.3 Walks (20:13)
3.16.1 Graph routes (5:32)
3.16.2 Kruskal's algorithm (8:07)
3.16.3 Prim's algorithm (5:05)
3.16.4 Prim's algorithm with adjacency table (5:00)
3.16.5 Eulerian graphs (5:45)
3.16.6 Chinese postman problem (17:20)
3.16.7 Hamiltonian graphs (3:02)
3.16.8 Travelling salesman problem (7:10)
3.16.9 TSP practical problems (5:52)
3.16.10 Nearest neighbour algorithm (5:32)
3.16.11 Deleted vertex algorithm (5:28)

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 (16:15)
4.7 Discrete random variables (13:41)
4.8 Binomial distribution (17:18)
4.9 Normal distribution (28:45)
4.10 Spearman's rank correlation coefficient (17:09)
4.11.1 Chi squared intro (10:34)
4.11.2 Chi squared test for independence (16:57)
4.11.3 Chi squared goodness of fit (11:45)
4.11.4 t test (19:21)
4.12.1 Surveys and questionnaires (4:20)
4.12.2 Reliability v validity (6:25)
4.12.3 Chi squared (categorising data) (12:13)
4.12.4 Chi squared (degrees of freedom) (16:54)
4.13.1 Non linear regression (6:08)
4.13.2 Sum of square residuals (10:30)
4.13.3 The coefficient of determination (14:20)
4.14.1 Linear transformations of X (11:35)
4.14.2 Linear combinations of n random variables (10:29)
4.14.3 Unbiased estimates for the mean and variance (11:42)
4.14.4 Unbiased estimates example questions (8:29)
4.15.1 Linear combination of n independent normal random variables (19:28)
4.15.2 Normal distribution sampling (11:39)
4.15.3 The central limit theorem (12:56)
4.16.1 Confidence intervals (known variance) (9:06)
4.16.2 Confidence intervals (unknown variance) (5:04)
4.17 Poisson distribution (14:59)
4.18.1 Z-test one tailed (9:28)
4.18.2 Z-test two tailed (8:58)
4.18.3 T-test (4:45)
4.18.4 Matched pairs (5:52)
4.18.5 Testing for population proportion (6:02)
4.18.6 Test for mean using Poisson distribution (8:19)
4.18.7 Testing for correlation (7:25)
4.18.8 Type I an II errors Intro (9:14)
4.18.9 Normal errors (9:51)
4.18.10 Poisson errors (11:50)
4.18.11 Binomial errors (9:02)
4.19.1 Markov chains introduction (12:02)
4.19.2 Transition matrices (13:17)
4.19.3 Steady state and long term probabilities (15:11)

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 power rule (9:37)
5.3.2 Derivative at a point (6:03)
5.4 Tangents and normals (9:49)
5.5.1 Integration (power rule) (11:50)
5.5.2 Finding f(x) (5:24)
5.5.3 Area under the curve (6:44)
5.6 Stationary points (11:27)
5.7 Optimization (16:10)
5.8 Trapezoidal rule (14:16)
5.9.1 Derivative of sinx,cosx,lnx,e^x (5:19)
5.9.2 Differentiation (rational exponents) (10:27)
5.9.3 Chain rule (14:11)
5.9.4 Product rule (5:47)
5.9.5 Quotient rule (8:54)
5.9.6 Related rates of change (11:18)
5.10.1 Relationship between graphs and derivatives (13:27)
5.10.2 Sketching derivatives (14:23)
5.10.3 Classifying stationary points (13:40)
5.10.4 Points of inflexion (7:14)
5.11.1 Integration power rule (rational power) (10:07)
5.11.2 Integrating sin and cos (2:57)
5.11.3 Integrating e^x and 1/x (5:33)
5.11.4 Inverse chain rule (10:18)
5.11.5 Integration by substitution (19:09)
5.12.1 Area under the curve (15:03)
5.12.2 Area between curve and y-axis (11:37)
5.12.3 Volume of revolution intro and x-axis (12:26)
5.12.4 Volume of revolution about y-axis (12:39)
5.13.1 Kinematics (28:12)
5.13.2 Kinematics 2 (6:14)
5.14.1 Setting up a differential equation (5:04)
5.14.2 Separation of variables (6:34)
5.15 Slope fields (11:40)
5.16.1 Euler's method (17:03)
5.16.2 Euler's method example (16:42)
5.16.3 Euler's method for coupled systems (13:36)
5.17.1 Phase portraits intro (11:48)
5.17.2 Solutions of coupled differential equations (p1) (12:27)
5.17.3 Solutions of coupled differential equations (p2) (11:07)
5.17.4 Sketching phase portraits introduction (5:33)
5.17.5 Sketching phase portraits (source) (6:01)
5.17.6 Sketching phase portraits (sink) (3:58)
5.17.7 Sketching phase portraits (spiral sink) (3:58)
5.17.8 Sketching phase portraits (spiral source) (7:47)
5.17.9 Sketching phase portraits (centre) (5:04)
5.18.1 Second order DE (Euler's method) (10:10)
5.18.2 Second order DE (exact solution) (11:01)

Internal assessment

1.1 IA Introduction (10:22)
1.2 A Presentation (12:45)
1.3 B Mathematical communication (9:25)
1.4 C Personal engagement (11:04)
1.5 D Reflection (5:34)
1.6 E Use of mathematics (8:42)
1.7 Choosing a topic 1 (17:52)
1.8 Choosing a topic 2 (19:57)
2.1 Quadratic from basketball video (8:04)
2.2 basketball analysis (11:26)
2.3 Quadratic fit on photo (13:57)
2.4 Sinusoidal fit on photo (4:33)
2.5 Data modelling with Excel (7:41)
2.6 Data modelling with Geogebra (10:34)
2.7 Modelling a skateboard ramp (15:38)
2.8 Modelling the price of bitcoin (15:41)
2.9 Volume of revolution (9:21)
2.10 Running IA (16:28)
2.11 Voronoi IA (21:36)
2.12 Modelling Ain Dubai (14:56)
3.1 Ideas 1 - Modelling data (18:20)
3.2 Ideas 2 (18:36)
3.3 Ideas 3 (14:44)
4.1 Marking an IA (20:14)
Sample Swimming IA Normal Distribution (3:58)
Sample Surface Area of a Chocolate Egg (2:48)
Sample Angry Birds Equation of a Tangent (3:58)
Sample Volume of Revoltion HL (3:55)
Sample Linear Correlation Time v Calories (5:25)
Sample Modelling the Dubai Eye Trig Modelling (4:05)
Sample Volume of Revolution Glasses (3:47)
Sample Optimum Long Jump Distance Calculus (5:34)
Sample Table Tennis Shot Comparison (5:19)
Sample Ibuprofen v Paracetamol Calculus (3:46)
Sample Gini Coefficient Integration (4:58)
Sample India v China Population Modelling (5:09)
Sample Polynomial Modelling Caffeine v Performance (5:05)
Sample Area of a School Integration (2:48)
Sample Volleyball Serve (6:32)

Specimen P1

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Specimen P2

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Specimen P3

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2021 May TZ1 P1

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2021 May TZ1 P2

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2021 May TZ1 P3

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2021 May TZ2 P1

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2021 May TZ2 P2

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2021 May TZ2 P3

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2021 November P1

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2021 November P2

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2021 November P3

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2022 May TZ1 P1

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2022 May TZ1 P2

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2022 May TZ1 P3

Question 1a (3:49)
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2022 May TZ2 P1

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2022 May TZ2 P2

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2022 May TZ2 P3

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2022 November P1

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2022 November P2

Question 1ab (2:16)
Question 1cd (5:36)
Question 2 (10:44)
Question 3ab (5:50)
Question 3cd (6:46)
Question 4abc (3:23)
Question 4def (6:29)
Question 5 (10:56)
Question 6ab (5:51)
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Question 7ab (7:55)
Question 7c (6:10)
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2022 November P3

Question 1abc (4:54)
Question 1de (5:21)
Question 1f (4:17)
Question 1g (12:10)
Question 1h (5:49)
Question 2ab (5:30)
Question 2cd (5:48)
Question 2e (4:19)
Question 2fi complete (3:03)
Question 2fii (3:08)
Question 2g (2:01)
Question 2hi (5:24)

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1.7.2 Annuities

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