Please Topics in Maths Paper 1 (Pre 2012 Course) (Higher)
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Algebra - Logarithms [HD]
- Index Notation v. Logarithms Notation - Product and Division Laws - Log Power Law
Video Lesson (28 min)
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Algebra - Exponential and Recurrence Equations
- Exponential Equations - Recurrence Equations - Past Exam Questions - Worked Solutions on the above
Video Lesson (22 min)
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Algebraic Fractions and Undetermined Coefficients [HD]
- Algebraic Fractions - Undetermined Co-efficients
Video Lesson (22 min)
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Algebra - Quadratic and Abstract Inequalities [HD]
- Quadratic And Abstract Inequalities - Questions And Example Solutions
Video Lesson (32 min)
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Algebra - Solving Cubic Eqns and the Factor Theorem [HD]
- Solve Cubic Equations - Use the Factor Theorem - Solving Problems Using The Factors Of An Equation - Several Worked Examples
Video Lesson (34 min)
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Algebra - Simultaneous Equations [HD]
- Simultaneous Equations with Three Variables - Simultaneous Equations (With One Linear and One Quadratic Equation) - Modulus and Irrational Equations
Video Lesson (31 min)
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Algebra - Sum & Product of The Roots of Quadratic Eqns [HD]
- Sum and Product of The Roots of a Quadratic Equation - The Roots of a Quadratic Equation
Video Lesson (39 min)
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Binomial Expansion [HD]
- Expanding a Binomial Expression - Finding the Co-efficient of the Expansion - Using the Formula to Calculate the Number of Combinations of a Set - Using Your Calculator to Calculate the Number of Combinations of a Set - Worked Examples
Video Lesson (34 min)
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Calculus - Integration I [HD]
- Basic Integration - Integration by Substitution - Contains Several Worked Examples
Video Lesson (35 min)
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Calculus - Integration II [HD]
- Integrals where solution is in the form Sin (-1) - Integrals where solution is in the form Tan (-1)
Video Lesson (24 min)
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Calculus - Integration III [HD]
- Area bounded by a curve (where y is f(x) and f(x) is a quadratic) - Volume of rotation (by rotating about the x-axis a volume that is bounded by the y-axis)
Video Lesson (32 min)
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Complex Numbers I [HD]
- Introduction to Complex Numbers - Real and Imaginary Parts - Modulus & Conjugate - Addition, Subtraction of Complex Numbers - Argand Diagrams
Video Lesson (27 min)
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Complex Numbers II [HD]
- Complex Roots of Quadratic and Cubic Equations - Formula for Solving Quadratic Equation (Resulting in complex roots) - Using Polar Co-Ordinates - De Moivres Theorem and It's Application - Using the Trigonometric Identities (Contained on page 9 of the tables)
Video Lesson (44 min)
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Calculus - Differentiation I [HD]
- Basic Operation of Differentiation - Product Quotient and Chain Rules - Trigonometric Limits - Differentiation from First Principles (for x Squared, Integral of x and Cosine x) - Implicit Differentiation
Video Lesson (36 min)
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Calculus - Differentiation II [HD]
- Standard Derivatives (including exp and ln) - Using Product and Quotient Rules with The Chain Rule - Working with The Root of Natural Logarithms (e) - Second Derivatives - Parametric Equations of a Curve
Video Lesson (31 min)
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Calculus - Differentiation III [HD]
- Using The Newton-Raphson formula to Find Approximate Roots - The Addition Rule from First Principles - Finding Max, Min and Inflection Points, and their Applications - Graphing a Curve with No Turning Points and Find Its Asympotes
Video Lesson (29 min)
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Matrices [HD]
- What is a Matrix - Dimensions (order) - Addition, Subtraction, Equal and Multiplication - To Multiply A Matrix by a Scaler - Matrices Not Commutative for Multiplication - Identity matrix and inverse matrix - Review of Exam Questions - Several types of recent EXAM questions covered.
Video Lesson (31 min)
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Proof By Induction [HD]
- Proof by Induction - Terminology for Series - Proving Inequalities by Induction
Video Lesson (35 min)
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Sequences and Series I
- Notation - Arithmetic V’s Geometric (a and d) V’s (a and r) - Arithmetic - Geometric - Recurrence Relations
Video Lesson (39 min)
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