Grade 12 Core Maths

Theory of Logarithms 15 Topics

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1.1) What is a Logarithm?

1.2) Changing from Logarithmic to exponential form – Examples

1.3) Changing from Exponential to Logarithmic form – Examples

1.4) Log Law 1 – Explanation

1.5) Log Law 1 – Example

1.6) Log Law 2 – Explanation

1.7) Log Law 2 – Examples

1.8) Log Law 3 – Explanation

1.9) Log Law 3 – Examples

1.10) Deduction 1 – Explanation

1.11) Deduction 1 – Examples

1.12) Deduction 2 – Explanation

1.13) Deduction 2 – Example

1.14) Log Law 4 – Explanation

1.15) Log Law 4 – Example

Solving Equations using Logarithms 6 Topics

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2.1 Equations with Logarithms – Situation 1 Explanation

2.2 Equations with Logarithms – Situation 1 Example

2.3 Equation with Logarithms – Situation 2 Explanation

2.4 Equation with Logarithms – Situation 2 Example

2.5 Equation with Logarithms – Situation 3 Explanation

2.6 Equations with Logarithms – Situation 3 Examples

Inverse Functions 6 Topics

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3.1) What is an Inverse Function?

3.2) Inverse of One-to-One Linear Functions – Explanation

3.3) Inverse of One-to-One Linear Functions – Example

3.4) Inverse of Many-to One Quadratic Functions – Explanation

3.5) Inverse of Many-to One Quadratic Functions – Example

3.6) Inverse of the Exponential Function – Example

Financial Mathematics 17 Topics

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4.1) Future Value Annuities – Explanation

4.2) Future Value Annuities – Example 1

4.3) Future Value Annuities – Example 2

4.4) Future Value Annuties – Example 3

4.5) Future Value Annuities – Example 4

4.6) Future Value Annuties – Example 5

4.7) Future Value Annuities – Example 6

4.8) Present Value Annuities – Explanation

4.9) Present Value Annuities – Example 1

4.10) Present Value Annuities – Example 2

4.11) Present Value Annuities – Example 3

4.12) Present Value Annuities – Example 4

4.13) Balance Outstanding on a Loan – Explanation

4.14) Balance Outstanding on a Loan – Example 1

4.15) Balance Outstanding on a Loan – Example 2

4.16) Sinking Funds – Explanation

4.17) Sinking Funds – Example 1

Trigonometry 33 Topics

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5.1) Compound Angle Formulae – Explanation

5.2) Compound Angle Formulae – Example 1

5.3) Compound Angle Formulae – Example 2

5.4) Compound Angle Formulae – Example 3

5.5) Compound Angle Formulae – Example 4

5.6) Compound Angle Formulae – Example 5

5.7) Compound Angle Formulae – Example 6

5.8) Double Angle Formulae – Explanation

5.9) Double Angle Formulae – Example 1

5.10) Double Angle Formulae – Example 2

5.11) Double Angle Formulae – Example 3

5.12) Double Angle Formulae – Example 4

5.13) Double Angle Formulae – Example 5

5.14) Examples involving Diagrams and Pythagoras – Example 1

5.15) Identities Involving Compound and Double Angles – Example 1

5.16) Identities Involving Compound and Double Angles – Example 2

5.17) Identities Involving Compound and Double Angles – Example 3

5.18) Identities Involving Compound and Double Angles – Example 4

5.19) Identities Involving Compound and Double Angles – Example 5

5.20) Identities Involving Compound and Double Angles – Example 6

5.21) Identities Involving Compound and Double Angles – Example 7

5.22) Trigonometric Equations – Explanation

5.23) Trigonometric Equations – Example 1

5.24) Trigonometric Equations – Example 2

5.25) Trigonometric Equations – Example 3

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Algebra 15 Topics

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6.1) Dividing Polynomials using Long Division

6.2) Dividing Polynomials – Other Methods

6.3) Dividing Polynomials – Example 1

6.4) Dividing Polynomials – Example 2

6.5) The Remainder Theorem Explaination

6.6) The Remainder Theorem – Example 1

6.7) The Remainder Theorem – Example 2

6.8) The Remainder Theorem – Example 3

6.9) The Remainder Theorem – Example 4

6.10) The Factor Theorem – Example 1

6.11) The Factor Theorem – Example 2

6.12) The Factor Theorem – Explanation

6.13) Solving Cubic Equations – Explanation

6.14) Solving Cubic Equations – Example 1

6.15) Solving Cubic Equations – Example 2

Differential Calculus 48 Topics

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7.1) The Concept of a Limit – Explanation

7.2) The Concept of a Limit – Example 1

7.3) The Concept of a Limit – Example 2

7.4) The Concept of a Limit – Example 3

7.5) The Concept of a Limit – Example 4

7.6) Average Gradient – Explanation

7.7) Average Gradient – Example 1

7.8) Average Gradient – Example 2

7.9) Average Gradient – Example 3

7.10) Average Gradient – Example 4

7.11) Gradient From First Principles – Explanation

7.12) Gradient from First Principles – Example 1

7.13) Gradient from First Principles – Example 2

7.14) Gradient From First Principles – Example 3

7.15) Rules of Differentiation – Explanation

7.16) Rules of Differentiation – Example 1

7.17) Rules of Differentiation – Example 2

7.18) Rules of Differentiation – Example 3

7.20) The Graph of a Cubic Function – Explanation

7.21) The Graph of a Cubic Function – Example 1

7.22) Sketching a Cubic Function – Example 1

7.23) Sketching Cubic Graphs – Example 2

7.24) Sketching Cubic Functions – Example 3

7.25) Finding the Equation of a Cubic Function – Given 3 x-intercepts

7.26) Finding the Equation of a Cubic Graph – Given 3 x-intercepts Example 1

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Sequences and Series 36 Topics

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8.1) Arithmetic Sequences – Explanation

8.2) Arithmetic Sequences – Example 1

8.3) Arithmetic Sequences – Example 2

8.4) Arithmetic Sequences – Example 3

8.5) Arithmetic Sequences – Example 4

8.6) Arithmetic Sequences – Example 5

8.7) Geometric Sequences – Explanation

8.8) Geometric Sequences – Example 1

8.9) Geometric Sequences – Example 2

8.10) Geometric Sequences – Example 3

8.11) Geometric Sequences – Example 4

8.12) Geometric Sequences – Example 5

8.13) Arithmetic Series – Explanation

8.14) Arithmetic Series – Example 1

8.15) Arithmetic Series – Example 2

8.16) Arithmetic Series – Example 3

8.17) Arithmetic Series – Example 4

8.18) Arithmetic Series – Example 5

8.19) Geometric Series – Explanation

8.20) Geometric Series – Example 1

8.21) Geometric Series – Example 2

8.22) Geometric Series – Example 3

8.23) Sigma Notation – Explanation

8.24) Sigma Notation – Example 1

8.25) Sigma Notation – Example 2

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Analytical Geometry 15 Topics

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9.1) Circle with Centre at the Origin – Explanation

9.2) Circle with Centre at the Origin – Example

9.3) Circles Not Centred at the Origin – Explanation

9.4) Circles Not Centred at the Origin – Example 1

9.5) Circles Not Centred at the Origin – Example 2

9.6) Circles Not Centred at the Origin – Example 3

9.7) Circles Not Centred at the Origin – Example 4

9.8) The Equation of a Tangent to a Circle – Explanation

9.9) The Equation of a Tangent to a Circle – Example 1

9.10) The Equation of a Tangent to a Circle – Example 2

9.11) The Equation of a Tangent to a Circle – Example 3

9.12) The Equation of a Tangent to a Circle – Example 4

9.13) The Equation of a Tangent to a Circle – Example 5

9.14) Analytical Geometry – Mixed Example 1

9.15) Analytical Geometry – Mixed Example 2

Euclidean Geometry 19 Topics

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10.1) Proportionality Theorem – Explanation

10.2) Proportionality Theorem – Example 1

10.3) Proportionality Theorem – Example 2

10.4) Proportionality Theorem – Example 3

10.5) Proportionality Theorem – Example 4

10.6) Proportionality Theorem Converse – Example 1

10.7) Proportionality Theorem Converse – Example 2

10.8) Mid-Point Theorem – Explanation

10.9) Mid-Point Theorem – Example 1

10.10) Mid-Point Theorem – Example 2

10.11) Similarity Theorem – Explanation

10.12) Similarity Theorem – Example 1

10.13) Similarity Theorem – Example 2

10.14) Similarity Theorem – Example 3

10.15) Similarity Theorem – Example 4

10.16) Mixed Example 1

10.17) Mixed Example 3

10.18) Mixed Example 3

10.19) Mixed Example 4

Probability 15 Topics

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11.1) The Fundamental Counting Principle (Rule 1) – Explanation

11.2) Fundamental Counting Principle – Example 1

11.3) Factorial Notation (Rule 2) – Explanation

11.4) Factorial Notation (Rule 2) – Example 1

11.5) Factorial Notation (Rule 3) – Explanation

11.6) Factorial Notation (Rule 3) – Example 1

11.7) Arrangements in a Row – Explanation

11.8) Arrangements in a Row – Example 1

11.9) Arrangements in a Row – Example 2

11.10) Arrangements in a Row – Example 3

11.11) Repeated Letter Arrangements (Rule 4) – Explanation

11.12) Repeated Letter Arrangements (Rule 4) – Example 1

11.13) Repeated Letter Arrangements (Rule 4) – Example 2

11.14) Examples involving Probability 1

11.15) Examples involving Probability 2

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