Daily Tutoring Online course
This online course is designed to provide students with a comprehensive understanding of specialist math, focusing on Unit 1 & 2 content. Topics covered include functions, calculus, algebra, and more. Through a combination of video lectures, interactive quizzes, and practical exercises, students will develop the skills necessary to solve mathematical problems effectively.
Curriculum
Reviewing linear equations
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- 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
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- 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
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- 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
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Unit1&2 Additional algebra
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Unit1&2 Proof
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Unit1&2 Algorithms
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Unit1&2 Combinatorics
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Unit1&2 Matrices
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Unit1&2 Simulation, sampling and sampling distributions
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Unit1&2 Trigonometric ratios and applications
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Unit1&2 Trigonometric identities
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Unit1&2 Graphing functions and relations
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- 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
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Unit1&2 Vectors in the plane
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Unit3&4 Preliminary topics
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- 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
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- 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
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Unit3&4 Vectors
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Unit3&4 Vector equations of lines and planes
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- 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
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- 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
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Unit3&4 Differentiation and rational functions
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days
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- 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
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days
days
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- 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
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Unit3&4 Differential equations
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Unit3&4 Kinematics
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Unit3&4 Linear combinations of random variables and the sample mean
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Unit3&4 Confidence intervals and hypothesis testing for the mean
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