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VCE Specialist Mathematics

Reviewing linear equations

Solving equations (26:27)
Solving equations 2 (37:19)
Literal equations (23:28)
Review of worded question (19:12)
Solving worded problems (18:13)
Elimination method (27:59)
Substitution method (18:54)
Real-world simultaneous equations (31:08)
Inequality (20:28)
Solving inequalities - Multiply or divide by a negative number (15:59)
Changing the subject of a formula (27:54)
Review of worded question (writing simultaneous equations and solve) (19:12)
Solving equations (26:27)
Solving equations 2 (37:19)
Literal equations (23:28)
Review of worded question (19:12)
Solving worded problems (18:13)
Elimination method (27:59)
Substitution method (18:54)
Real-world simultaneous equations (31:08)
Inequality (20:28)
Solving inequalities - Multiply or divide by a negative number (15:59)
Changing the subject of a formula (27:54)
Review of worded question (writing simultaneous equations and solve) (19:12)

Unit1&2 Reviewing algebra

Indices (19:31)
Scientific notation (25:24)
Solving linear equations (26:27)
Solving problems with simultaneous linear equations (31:08)
Changing the subject of a formula (27:54)
Adding and subtracting algebraic fractions (27:30)
Adding and subtracting algebraic fractions 2 (16:48)
Adding and subtracting algebraic fractions 3 (29:58)
Multiplication and division of algebraic fractions (15:31)
Algebraic fractions and rational indices (23:46)
Literal equation (23:28)

Unit1&2 Number systems and sets

Intersection and Union Compliment in the Venn diagram (20:23)
Rational and irrational numbers (14:10)
Recurring Decimals to Fractions (17:02)
Interval notation (9:41)
Simplify surds (26:30)
Like surds (19:41)
Multiplying and Dividing Surds (18:27)
Rationalising the denominator (18:22)
GCD, LCM (23:16)

Unit1&2 Sequences and series

Arithmetic series (20:44)
Geometric Series (21:33)
Compound interest (19:09)
Finding the nth term of the sequence (23:37)
Infinite Geometric Series (16:16)

Unit1&2 Additional algebra

Polynomial identities (16:31)
Quadratic equation (15:22)
Partial fraction 1 (33:28)
Partial fraction 2 (33:35)
Simultaneous equations (19:11)

Unit1&2 Proof

Direct proof (39:22)
Proof by contrapositive (35:16)
Proof by contradiction (25:24)
Equivalent statements (21:45)
Disproving statements (23:23)
Mathematical induction 1 (24:28)
Mathematical induction 2 (24:51)
Mathematical induction 3 (24:09)

Unit1&2 Algorithms

Karatsuba’s algorithm (11:12)

Unit1&2 Combinatorics

Factorial notation (17:34)
Permutation and Combination (38:48)
Permutations with restrictions (14:50)
Permutations of like objects (24:15)
Combinations with restrictions (19:25)
Pascal’s triangle (24:34)

Unit1&2 Matrices

Matrix notation (18:00)
Addition subtraction and multiplication by a real number (matrix) (16:21)

Unit1&2 Simulation, sampling and sampling distributions

Expected value and variance for discrete random variables (30:56)
Distribution of sums of random variables (31:39)
Populations and samples (44:11)

Unit1&2 Trigonometric ratios and applications

Reviewing trigonometry (21:05)
The sine rule (11:37)
The cosine rule (15:02)
The area of a triangle (17:47)
Circle mensuration (23:03)
Angles of elevation, angles of depression (16:34)
Applying Trigonometry elevation depression (15:48)
True bearings (20:56)
Drawing true bearings on a map (26:53)

Unit1&2 Trigonometric identities

Reciprocal circular functions (36:14)
The Pythagorean identity (16:26)
Compound and double angle formulas (25:55)
Simplifying acosx+bsinx (29:25)
Sums and products of sines and cosines (23:05)

Unit1&2 Graphing functions and relations

The inverse circular functions (32:17)
Graphing Rational Functions (63:54)
Reciprocal circular functions (36:14)
The modulus function (47:06)
Equation of a circle (22:56)
Locus of a circle and ellipse (20:08)
Cartesian equations of ellipses (29:11)
Parametric equations for circle ellipse hyperbola (38:55)
Polar coordinates (20:31)

Unit1&2 Complex numbers

The set of complex numbers (27:24)
Operations with Complex numbers (28:14)
Solving equations over the complex numbers (47:32)
Polar form of a complex number (35:07)
Sketching subsets of the complex plane (41:09)

Unit1&2 Vectors in the plane

Introduction to Vector (34:17)
Components of vectors (39:13)
Scalar product of vectors (9:27)
Vector projections (34:31)
Geometric proofs (62:00)
Applications of vectors: displacement and velocity (20:24)
Vectors in three dimensions (26:04)

Unit3&4 Preliminary topics

Circular function (part1)
Circular function (part2)
Sketch graphs of sine and cosine using transformation (44:16)
Pyhagorean identities (16:26)
The sine rule (11:37)
The cosine rule (15:02)
Arithmetic series (20:44)
Geometric series (21:33)
Recurrence relations (Finding the nth term of the sequence) (23:37)
The modulus function (47:06)
The circle equation (22:56)
Hyperbola (28:49)
Ellipse (29:11)
Parametric equations for circle ellipse hyperbola (38:55)
Algorithms and pseudocode

Unit3&4 Logic and proof

Direct proof (39:22)
Negations and Proof by contrapositive (35:16)
Proof by contradiction (25:24)
Equivalent statements (21:45)
Disproving statements (23:23)
Mathematical induction (part1) (24:28)
Mathematical induction (part2) (24:51)
Mathematical induction (part3) (24:09)
Telescoping series (38:42)
Proving inequalities(Logic and proof) (19:12)

Unit3&4 Circular functions

Reciprocal circular functions (36:14)
Compound and double angle formula (25:55)
The inverse circular function (32:17)
General solution of trigonometric equations (27:30)
Sums and products of sines and cosines (23:05)

Unit3&4 Vectors

Introduction to Vector (34:17)
Vectors in three dimenstions (26:04)
Scalar product of vectors (9:27)
Vector projections (34:31)
Collinearity (33:57)
Geometric proofs (62:00)

Unit3&4 Vector equations of lines and planes

Vector equations of lines (29:12)
Intersection of lines and skew lines (32:50)
Scalar product and Vector product (40:16)
Finding the plane determined by a point and a normal vector (37:41)
Distance from a point to a line (27:06)
Distance between two parallel planes
Distances angles and intersections (36:41)
Distance between two skew lines (15:30)

Unit3&4 Complex number

The set of complex numbers (27:24)
Operations with Complex numbers (28:14)
Complex conjugate (24:00)
Polar form of a complex number (35:07)
Solving equations over the complex numbers (28:14)
Geometric interpretation of multiplication and division of Polar form (25:17)
Using De moivre`s theorem to solve equations (35:42)
Sketching subsets of the complex plane (41:09)

Review of Calculus

Power rule (25:12)
Calculus of circular function (20:33)
Calculus of e^x (25:02)
Product rule (27:24)
Calculus of tan (14:26)
Quotient rule (18:54)
Calculus of natural logarithm function (28:57)
Chain rule (18:56)

Unit3&4 Differentiation and rational functions

Derivative of inverse circular function (23:58)
Rate of change of any combination of two variables (27:45)
Stationary points (46:01)
Exponential and Logarithmic Functions (21:03)
Concavity and second derivative test (38:08)
Derivatives of x=f(y) and Implicit differentiation (49:35)
Parametric equation and related rates (39:33)
Rational Functions (Addition of ordinates) (32:57)
Graphing Rational Functions (63:54)

Unit3&4 Techiques of integration

Integration by substitution pt1 (35:31)
Integration by substitution pt2 (42:24)
Partial fractions pt1 (33:28)
Partial fractions pt2 (33:35)
Integration by parts - methods (17:48)
Antiderivatives involving inverse circular functions (23:58)
Integration by parts - special math pt1 (23:50)
Integration by parts - special math pt2
Products to sums (23:05)

Unit3&4 Applications of integration

Finding the area of a region (38:35)
Volume of solid of revolution (26:54)
Arc length (28:07)
Area of surface of revolution (21:38)

Unit3&4 Differential equations

Differential equation 1 – Filp over and integration (33:59)
Eulers method (20:41)

Unit3&4 Kinematics

Position velocity and acceleration (30:18)
Other expressions for acceleration (27:53)
Velocity time graph (27:28)
Displacement(velocity) and Distance(speed) (20:24)

Unit3&4 Linear combinations of random variables and the sample mean

Mean variance and standard deviation pt1 (30:56)
Mean variance and standard deviation pt2 (31:39)
Mean variance and standard deviation pt3 (43:27)
Mean variance and standard deviation pt4 (44:11)

Unit3&4 Confidence intervals and hypothesis testing for the mean

Confidence intervals for the population mean (28:45)
Hypothesis testing for the mean (One tailed test) (29:40)
Hypothesis testing for the mean (Two tailed test) (21:07)
Errors in hypothesis testing

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