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 (10:43)
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1.5.3 The number e (10:25)
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1.6 Simple deductive proofs (8:25)
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1.7.1 More exponents (12:35)
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1.7.2 Laws of logarithms (10:01)
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1.7.3 Change of base law (8:37)
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1.8.1 Sum of an infinite geometric sequence (7:45)
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1.8.2 System of linear equations (3:17)
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1.8.3 Roots of a polynomial (6:03)
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1.9.1 Binomial expansion (intro and full expansion) (20:16)
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1.9.2 Binomial expansion (finding a term) (11:44)
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1.10.1 Counting principles introduction (product and addition principles) (12:20)
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1.10.2 Factorials and arrangements (13:29)
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1.10.3 Algebra of factorials (13:06)
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1.10.4 Combinations and permutations (21:41)
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1.10.5 Keeping objects together or separated (14:49)
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1.10.6 Binomial theorem extension (10:52)
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1.11 Partial fractions (12:36)
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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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1.13.1 Modulus-argument form (20:10)
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1.13.2 Euler form (17:47)
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1.13.3 Complex operations and geometric interpretation (13:26)
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1.13.4 Properties of complex conjugates (11:33)
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1.14.1 Complex solutions to polynomial equations (14:14)
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1.14.2 De Moivre's Theorem (9:37)
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1.14.3 Roots of complex numbers (14:55)
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1.14.4 Roots of unity (6:45)
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1.15.1 Proof by induction (intro and series) (16:05)
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1.15.2 Proof by induction (differentiation) (12:50)
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1.15.3 Proof by induction (divisibility) (11:00)
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1.15.4 Proof by induction (inequalities) (24:00)
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1.15.5 Proof by induction (De Moivre) (11:59)
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1.15.5 Proof by contradiction (intro) (10:28)
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1.15.7 Proof by contradiction (root 2) (5:50)
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1.15.8 Proof by contradiction (infinite primes) (10:00)
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1.15.9 Use of counterexample (6:54)
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1.16.1 System of linear equations (HL only) (16:48)
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1.16.2 System of linear equations part 2 (11:50)
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 Composite functions (11:11)
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2.5.2 Finding inverse functions (9:44)
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2.6.1 Quadratics 3 forms (6:13)
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2.6.2 Factorising quadratics (10:27)
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2.6.3 Vertex form (8:10)
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2.7.1 Solving quadratic equations (10:46)
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2.7.2 Quadratic inequalities (9:54)
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2.7.3 The discriminant (9:53)
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2.8 Rational functions (10:14)
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2.9.1 Exponential modelling (14:33)
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2.9.2 Logarithmic functions (8:27)
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2.10.1 Solving equations using substitution (8:15)
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2.10.2 Solving equations with gdc (9:12)
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2.11.1 Transformations (14:13)
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2.11.2 Composite transformations (12:46)
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2.12.1 Dividing polynomials (6:48)
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2.12.2 Factor and remainder theorems (12:17)
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2.12.3 Graphs of polynomials (16:28)
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2.12.4 Sum and product of roots (14:28)
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2.13.1 Rational functions (quadratic in denominator) (14:00)
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2.13.2 Rational functions (quadratic in numerator) (15:29)
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2.14 Even and odd functions (8:44)
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2.15 Solving inequalities (7:48)
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2.16.1 Graphs of modulus functions combined (10:15)
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2.16.2 Modulus equations and inequalities (9:20)
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2.16.3 Reciprocal transformations (11:39)
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2.16.4 Graphs of y=(f(x))^2 (8:18)
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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3.4.1 Radians (8:14)
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3.4.2 Arcs and sectors (9:12)
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3.5.1 Mr. Flynn's exact triangles (8:06)
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3.5.2 Unit circle (18:37)
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3.5.3 The CAST diagram (15:41)
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3.5.4 Graphs of sin, cos and tan (10:45)
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3.5.5 Sine rule (ambiguous case) (6:00)
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3.6 Trig identities (11:42)
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3.7.1 Sinusoidal graphs (13:04)
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3.7.2 Sinusoidal modelling (11:59)
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3.8.1 Solving trig equations (12:50)
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3.8.2 Solving trig equations with identities (11:28)
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3.9.1 Reciprocal trig identities (11:04)
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3.9.2 Inverse trigonometric functions (25:58)
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3.10 Compound angle identities (14:38)
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3.11 Symmetry in trigonometric functions (4:43)
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3.12.1 Vectors introduction (11:56)
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3.12.2 Operations with vectors (15:47)
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3.12.3 Magnitude and unit vectors (12:38)
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3.13.1 Scalar product and angle between vectors (13:52)
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3.13.2 Properties of the scalar product (11:59)
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3.14.1 Vector equation of a line (17:58)
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3.14.2 Parametric form and cartesian equations of a line (11:15)
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3.14.3 Angle between two lines (6:45)
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3.14.4 Vectors and kinematics (10:40)
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3.15.1 Intersecting lines (11:17)
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3.15.2 Distance between a point and a line (10:15)
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3.16.1 Vector product (9:45)
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3.16.2 Properties of the vector product (5:30)
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3.16.3 Areas using vector product (9:25)
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3.17.1 Vector equation of a plane (12:55)
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3.17.2 Cartesian equation of a plane (14:12)
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3.18.1 Intersection between a line and a plane (5:54)
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3.18.2 Intersection between two planes (11:04)
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3.18.3 Intersection of 3 planes (9:47)
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3.18.4 Angle between a line and a plane (8:54)
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3.18.5 Angle between two planes (8:52)
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 (21:53)
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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 (13:29)
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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 Regression line of x on y (11:01)
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4.11 Testing for independence (8:45)
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4.12 Normal distribution (finding mean and std. dev.) (10:04)
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4.13 Bayes' theorem (11:21)
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4.14.1 Variance and standard deviation (14:46)
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4.14.2 Variance and standard deviation of a discrete random variable (4:50)
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4.14.3 Continuous random variables intro (13:48)
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4.14.4 Mean of a continuous random variable (5:48)
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4.14.5 Median and mode of a discrete random variable (4:00)
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4.14.6 Median and mode of continuous random variable (10:45)
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4.14.7 Variance of a continuous random variable (6:11)
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4.14.8 Linear transformations of X (11:35)
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 (the power rule) (10:27)
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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 (10:07)
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5.5.2 Finding f(x) (5:24)
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5.5.3 Definite integration (8:37)
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5.5.4 Area under the curve (15:03)
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5.5.5 Finding a limit (6:34)
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5.6.1 Derivative of sinx, cosx, lnx, e^x (5:19)
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5.6.2 Chain rule (14:11)
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5.6.3 Product rule (5:47)
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5.6.4 Quotient rule (8:54)
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5.7.1 Relationship between graphs and derivatives (13:27)
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5.7.2 Sketching derivatives (14:23)
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5.7.3 Sketching derivatives with a gdc (6:40)
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5.8.1 Classifying stationary points (13:40)
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5.8.2 Points of inflexion (7:14)
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5.8.3 Optimization (16:10)
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5.9 Kinematics (28:12)
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5.10.1 Integrating e^x and 1/x (5:33)
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5.10.2 Integrating sin and cos (2:57)
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5.10.3 Inverse chain rule (10:18)
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5.10.4 Integration by substitution (19:09)
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5.11 Area between two curves (16:34)
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5.12.1 Continuous functions (6:29)
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5.12.2 Differentiable functions (6:00)
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5.12.3 Differentiation from first principles (13:42)
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5.12.4 Higher derivatives (9:26)
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5.13 l'Hopital's rule (15:34)
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5.14.1 Implicit differentiation (20:50)
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5.14.2 Related rates of change (11:18)
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5.15.1 More derivative rules (14:54)
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5.15.2 More integration rules (14:38)
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5.15.3 Integrating using partial fractions (13:13)
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5.16.1 Integration by substitution (HL only) (22:21)
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5.16.2 Integration by parts (10:20)
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5.16.3 Repeated integration by parts (12:08)
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5.17.1 Area between curve and y-axis (11:37)
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5.17.2 Volume of revolution intro and x-axis (12:26)
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5.17.3 Volume of revolution about y-axis (12:39)
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5.17.4 Volume of revolution between 2 curves (11:09)
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5.18.1 Differential equations introduction (10:08)
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5.18.2 Separation of variables (6:34)
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5.18.3 Euler's method introduction (17:03)
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5.18.4 Euler's method example (16:42)
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5.18.5 Homogenous differential equations (13:54)
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5.18.6 Integrating factor (8:57)
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5.19.1 Maclaurin series introduction (15:14)
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5.19.2 Maclaurin series (8:01)
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5.19.3 Maclaurin series (substitutions and products) (10:19)
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5.19.4 Maclaurin series (binomial series) (10:29)
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5.19.5 Maclaurin series differentiation and integration (15:11)
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5.19.6 Maclaurin series sigma notation (10:58)
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5.19.7 Maclaurin series differential equations (7:19)
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5.19.8 Euler's identity (9:23)
Internal assessment
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1. IA Introduction (10:22)
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2.1 A Presentation (12:45)
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2.2 B Mathematical communication (9:25)
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2.3 C Personal engagement (11:04)
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2.4 D Reflection (5:34)
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2.5 E Use of mathematics (8:42)
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3.1 Choosing a topic 1 (17:52)
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3.2 Choosing a topic 2 (19:57)
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4.1 Quadratic from basketball shot video (8:04)
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4.1.2 Basketball analysis (11:26)
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4.2 Quadratic fit on photo (13:57)
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4.3 Sinusoidal fit on photo (4:33)
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4.4 Data modelling with Excel (7:41)
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4.5 Data modelling with Geogebra (10:34)
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5 Marking an IA (20:14)
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6.1 Ideas part 1 - Modelling (18:20)
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6.2 Ideas part 2 (18:36)
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6.3 Ideas part 3 (14:44)
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Sample Swimming IA Normal Distribution (3:58)
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Sample Gini Coefficient Integration (4:58)
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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 Angry Birds Equation of a Tangent (3:58)
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Sample Volume of Revolution Glasses (3:47)
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Sample Area of a School Integration (2:48)
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Sample India v China Population Modelling (5:09)
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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 Ibuprofen v Paracetamol Calculus (3:46)
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Sample Surface Area of a Chocolate Egg (2:48)
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Sample Polynomial Modelling Caffeine v Performance (5:05)
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Sample Volume of Revoltion HL (3:55)
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Sample Volleyball Serve (6:32)
Specimen Paper 1
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Question 1 (2:46)
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Question 2 (6:49)
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Question 3 (6:47)
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Question 4 (6:10)
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Question 5 (3:48)
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Question 6 (7:36)
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Question 7 (9:28)
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Question 8 (7:04)
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Question 9 a (4:54)
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Question 9 b (9:41)
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Question 10 a (4:15)
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Question 10 b (2:49)
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Question 10 c (2:25)
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Question 10 d (10:30)
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Question 11 a (3:22)
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Question 11 b (7:46)
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Question 11 c (5:46)
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Question 11 d (7:16)
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Question 12 a (3:44)
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Question 12 b (4:59)
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Question 12 c (7:47)
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Question 12 d (3:22)
Specimen Paper 2
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Question 1 (6:54)
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Question 2 (7:21)
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Question 3 (7:25)
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Question 4 (6:12)
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Question 5 (12:35)
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Question 6 (6:37)
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Question 7 (7:13)
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Question 8 (4:53)
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Question 9 (7:41)
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Question 10 a b (9:32)
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Question 10 c d e (11:17)
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Question 11 a (2:29)
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question 11 b (10:04)
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Question 11 c (7:32)
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Question 11 d (5:15)
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Question 11 e (4:24)
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Question 12 a (1:56)
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Question 12 b (5:11)
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Question 12 c (4:37)
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Question 12 d (4:48)
Specimen paper 3
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Question 1 a b (8:38)
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Question 1 c (2:05)
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Question 1 d (4:33)
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Question 1 e (5:49)
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Question 1 f (5:27)
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Question 1 g (6:56)
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Question 1 h (3:17)
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Question 1 i (6:27)
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Question 2 a (4:10)
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Question 2 b (5:29)
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Question 2 c (3:06)
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Question 2 d (3:58)
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Question 2 e (5:36)
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Question 2 f (3:54)
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Question 2 g (3:01)
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Question 2 h (8:27)
May 2021 TZ1 P1
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Question 1 (4:11)
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Question 2 (2:57)
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Question 3 (3:22)
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Question 4 (8:17)
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Question 5 (8:41)
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Question 6 (2:49)
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Question 7 (6:29)
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Question 8 (3:20)
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Question 9 (8:31)
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Question 10ab (2:30)
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Question 10cd (4:55)
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Question 10e (9:14)
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Question 11a (3:52)
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Question 11b (7:33)
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Question 11c (6:16)
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Question 12a (1:53)
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Question 12b (17:29)
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Question 12c (7:57)
2021 May TZ1 P2
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Question 1 (5:32)
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Question 2 (8:47)
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Question 3 (6:49)
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Question 4 (8:21)
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Question 5 (6:59)
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Question 6 (5:44)
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Question 7 (9:22)
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Question 8 (6:35)
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Question 9 (8:34)
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Question 10ab (5:57)
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Question 10c (1:10)
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Question 10d (7:37)
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Question 10e (2:59)
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Question 11ab (2:27)
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Question 11cd (10:47)
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Question 11e (3:51)
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Question 11f (7:23)
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Question 12ab (5:10)
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Question 12c (11:15)
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Question 12de (6:15)
2021 May TZ1 P3
2021 May TZ2 P1
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Question 1 (3:07)
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Question 2 (4:58)
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Question 3 (4:00)
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Question 4 (5:45)
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Question 5 (3:40)
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Question 6 (5:11)
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Question 7 (3:53)
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Question 8 (13:01)
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Question 9 (8:04)
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Question 10ab (4:35)
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Question 10cd (4:59)
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Question 11a (5:57)
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Question 11 b (11:40)
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Question 11c (2:20)
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Question 11d (2:07)
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Question 11e (5:56)
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Question 12a (4:20)
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Question 12b (3:56)
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Question 12c (3:21)
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Question 12d (16:15)
2021 May TZ2 P2
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Question 1 (7:34)
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Question 2 (5:55)
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Question 3 (10:54)
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Question 4 (5:55)
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Question 5 (8:46)
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Question 6 (6:52)
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Question 7 (6:29)
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Question 8 (8:20)
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Question 9ab (7:56)
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Question 9c (5:02)
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Question 10ab (7:20)
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Question 10cde (6:19)
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Question 11a (6:34)
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Question 11bc (6:54)
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Question 11d (6:48)
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Question 12ab (4:23)
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Question 12ci (8:08)
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Question 12cii (2:52)
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Question 12de (8:24)
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Question 12f (4:42)
2021 May TZ2 P3
2021 November P1
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Question 1 (2:08)
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Question 2 (4:04)
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Question 2d (3:08)
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Question 3 (5:14)
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Question 4 (6:05)
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Question 5 (8:19)
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Question 6 (7:55)
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Question 7 (7:46)
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Question 8 (7:55)
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Question 9 (10:25)
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Question 10a (5:48)
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Question 10b (5:16)
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Question 10c (4:04)
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Question 11a (9:50)
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Question 11b (4:44)
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Question 11c (5:29)
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Question 12a (7:45)
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Question 12bc (7:04)
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Question 12d (3:47)
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Question 12e (8:11)
2021 November P2
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Question 1 (5:16)
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Question 1de (3:40)
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Question 2 (5:28)
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Question 3 (5:54)
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Question 4 (6:31)
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Question 5 (10:15)
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Question 6 (9:18)
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Question 7 (7:54)
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Question 8a (5:55)
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Question 8b (4:05)
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Question 9abcd (7:57)
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Question 9ef copy (6:21)
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Question 9g (2:44)
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Question 10ab (2:26)
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Question 10c (3:34)
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Question 10d (6:07)
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Question 10e (8:37)
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Question 11a (4:17)
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Question 11b (3:44)
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Question 11c (2:44)
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Question 11d (13:00)
2021 November P3
2022 May TZ1 P1
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Question 1 (3:02)
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Question 2 (7:11)
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Question 3 (6:21)
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Question 4 (5:07)
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Question 5 (7:23)
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Question 6 (5:53)
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Question 7 (13:18)
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Question 8 (3:54)
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Question 9 (5:26)
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Question 10a (5:25)
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Question 10b (8:27)
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Question 11a (6:20)
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Question 11b (7:00)
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Question 11c (8:05)
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Question 12ab (6:02)
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Question 12c (5:22)
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Question 12d (5:25)
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Question 12e (3:26)
2022 May TZ1 P2
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Question 1 (1:54)
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Question 2 (3:44)
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Question 3 (4:55)
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Question 4 (7:13)
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Question 5 (5:59)
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Question 6 (7:49)
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Question 7 (10:03)
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Question 8 (3:36)
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Question 9 (7:51)
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Question 10ab (4:44)
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Question 10c (4:15)
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Question 10de (7:03)
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Question 11ab (3:03)
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Question 11c (6:40)
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Question 11d (5:41)
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Question 12a (7:24)
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Question 12b (1:56)
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Question 12 ci (14:36)
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Question 12 cii and ciii (4:11)
2022 May TZ1 P3
May 2022 TZ2 P1
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Question 1 (1:24)
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Question 2 (2:53)
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Question 3 (5:51)
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Question 4 (3:37)
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Question 5 (4:30)
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Question 6 (9:58)
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Question 7 (5:37)
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Question 8 (7:41)
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Question 9 (2:28)
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Question 10ab (3:49)
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Question 10c (2:50)
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Question 10de (5:50)
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Question 11a (6:37)
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Question 11b (6:45)
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Question 11c (4:29)
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Question 12ab (5:49)
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Question 12c (7:00)
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Question 12d (3:00)
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Question 12e (11:08)
May 2022 TZ2 P2
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Question 1 (2:57)
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Question 2 (1:36)
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Question 3 (4:15)
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Question 4 (4:53)
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Question 5 (7:13)
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Question 6 (5:47)
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Quesiton 7 (7:57)
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Question 8 (8:45)
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Question 9 (7:03)
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Question 10ab (5:24)
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Question 10c (4:21)
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Question 10d (6:53)
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Question 11abc (7:45)
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Question 11d (4:47)
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Question 11e (5:02)
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Question 12ab (4:35)
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Question 12cd (5:50)
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Question 12e (8:58)
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Question 12f (1:56)
2022 May TZ2 P3
2022 November P1
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Question 1 (1:05)
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Question 2 (3:38)
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Question 3 (4:59)
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Question 4 (3:21)
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Question 5 (3:12)
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Question 6 (4:40)
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Question 7 (7:22)
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Question 8 (8:33)
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Question 9 (8:19)
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Question 10ab (7:26)
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Question 10cd (8:58)
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Question 11a bi (6:46)
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Question 11 b ii-iv (5:43)
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Question 12a (2:25)
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Question 12b (9:03)
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Question 12c (17:11)
2022 November P2
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Question 1 (2:40)
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Question 2 (3:42)
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Question 3 (3:54)
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Question 4 (5:17)
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Question 5 (3:11)
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Question 6 (6:16)
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Question 7 (4:06)
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Question 8 (8:09)
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Question 9 (7:09)
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Question 10abc (7:25)
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Question 10d (4:06)
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Question 11ab (4:47)
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Question 11cd (6:20)
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Question 12abc (11:21)
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Question 12di (3:58)
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Question 12dii (3:32)
2022 November p3
2023 May TZ1 P1
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Question 1 (4:35)
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Question 2 (5:06)
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Question 3 (5:07)
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Question 4 (5:02)
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Question 5 (5:36)
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Question 6 (3:53)
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Question 7 (4:57)
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Question 8 (6:13)
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Question 9 (8:44)
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Question 10 (8:33)
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Question 11ab (7:07)
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Question 11c (7:26)
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Question 11de (5:33)
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Question 12ab (4:25)
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Question 12cd (4:20)
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Question 12e (6:13)
2023 May TZ1 P2
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Question 1 (2:39)
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Question 2 (4:11)
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Question 3 (5:43)
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Question 4 (5:07)
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Question 5 (5:12)
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Question 6 (9:34)
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Question 7 (5:28)
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Question 8 (6:50)
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Question 9 (3:39)
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Question 10ab (6:16)
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Question 10c (4:07)
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Question 11a (5:11)
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Question 11b (1:24)
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Question 11c (4:27)
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Question 11de (2:49)
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Question 11f (6:45)
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Question 12a (5:12)
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Question 12b (3:51)
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Question 12c (3:22)
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Question 12d (4:26)
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Question 12e (4:25)
2023 TZ1 P3
2023 May TZ2 P1
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Question 1 (1:29)
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Question 2 (3:34)
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Question 3 (2:36)
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Question 4 (5:04)
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Question 5 (3:39)
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Question 6 (4:30)
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Question 7 (7:30)
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Question 8 (5:58)
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Question 9ab (12:48)
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Question 9c (6:38)
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Question 10abc (8:06)
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Question 10d (4:20)
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Question 11ab (5:49)
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Question 11c (5:32)
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Question 11d (6:20)
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Question 12a (5:44)
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Question 12bc (13:15)
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Question 12d (2:14)
2023 May TZ2 P2
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Question 1 (2:23)
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Question 2 (3:22)
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Question 3 (4:33)
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Question 4 (4:45)
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Question 5 (4:58)
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Question 6 (5:56)
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Question 7 (4:10)
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Question 8 (7:01)
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Question 9 (5:36)
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Question 10 (9:01)
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Question 11ab (8:37)
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Question 11c (2:29)
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Question 11de (7:21)
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Question 12ab (12:17)
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Question 12cd (4:53)
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Question 12ef (5:25)
2023 May TZ2 P3
2023 November P1
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Question 1 (1:11)
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Question 2 (1:27)
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Question 3 (3:46)
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Question 4 (2:15)
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Question 5 (4:41)
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Question 6 (6:10)
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Question 7 (2:48)
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Question 8 (8:31)
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Question 9 (5:45)
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Question 10ab (5:58)
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Question 10c (2:56)
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Question 11a (4:48)
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Question 11b (4:42)
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Question 11c (4:01)
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Question 11d (6:18)
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Question 11e (2:13)
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Question 12a (4:34)
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Question 12b (4:47)
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Question 12ci (3:57)
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Question 12cii (5:13)
2023 November P2
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Question 1 (3:59)
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Question 2 (4:23)
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Question 3 (6:01)
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Question 4 (4:20)
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Question 5 (5:31)
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Question 6 (2:52)
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Question 7 (3:54)
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Question 8 (6:08)
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Question 9a (3:36)
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Question 9b (5:45)
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Question 10ab (7:37)
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Question 10cd (8:45)
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Question 11abcd (9:27)
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Question 11ef (5:12)
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Question 12a (3:31)
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Question 12b (1:51)
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Question 12c (7:52)
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Question 12d (2:29)
2023 November P3
