9 Sections
150 Lessons
31 Days
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Algebra
24 Items
1.1
Simplifying exponents
1.2
Exponents: solve for x when x is in the base
1.3
Exponents: solve for x when x is in the exponent
1.4
Simplifying surds
1.5
Writing an infinite recurring decimal as a fraction
1.6
Finding the product
1.7
Factorising
1.8
Algebraic fractions
1.9
Algebraic expressions: adding and subtracting fractions
1.10
Solve for x: linear equations
1.11
Solve for x: quadratic equations by factorising
1.12
Solve for x: quadratic equations by completing the square
1.13
Solve for x: surd and linear equations
1.14
Solve for x: linear and surd equations
1.15
Solve for x: quadratic and surd equations
1.16
Solve for x: surd and quadratic equations by factorising
1.17
Solve for x: quadratic, linear, exponential and surd equations
1.18
Simultaneous equations
1.19
Simultaneous linear equations: substitution method
1.20
Simultaneous linear equations: elimination method
1.21
Simultaneous linear equations: equating method
1.22
Exam question : 2016 November Paper 1, Question 1 – Algebra
1.23
Exam question: 2018 November Paper 1, Question 1 – Algebra
1.24
Exam question: 2018 November Paper 1, Question 2 – Algebra
Analytical Geometry
20 Items
2.1
Straight lines: finding the gradient (Example 1)
2.2
Straight lines: finding the gradient (Example 2)
2.3
Straight lines: distance between two points (Example 1)
2.4
Straight lines: distance between two points (Example 2)
2.5
Distances (Example 3)
2.6
Straight lines: coordinates of the midpoint (Example 1)
2.7
Straight lines: coordinates of the midpoint (Example 2)
2.8
Midpoints (Example 3)
2.9
Midpoints: finding a point given the midpoint and another point
2.10
Straight lines: Finding equation of a line that passes through two points (Example 1)
2.11
Straight lines: Finding equation of a line that passes through two points (Example 2)
2.12
Parallel straight lines: finding the equation (Example 1)
2.13
Parallel straight lines: finding the equation (Example 2)
2.14
Straight lines: angle of inclination (Example 1)
2.15
Straight lines: angle of inclination (Example 2)
2.16
Circles with any centre
2.17
Finding the equation of a circle with any centre
2.18
Finding the equation of a circle with any centre (second worked example)
2.19
Exam question: November 2021, Question 3
2.20
Exam questions: November papers, analytical geometry
Differential Calculus
24 Items
3.1
First principles (Example 1)
3.2
First principles (Example 2)
3.3
Derivatives: using the power rule (Example 1)
3.4
Derivatives: using the power rule (Example 2)
3.5
Determining dx
3.6
Cubic functions: finding intercepts
3.7
Cubic functions: finding turning points
3.8
Cubic functions: point of inflection and concavity
3.9
Cubic functions: drawing the graphs
3.10
Cubic functions: finding values of x, long division vs synthetic division (Example 1)
3.11
Cubic functions: finding values of x, long division vs synthetic division (Example 2)
3.12
Cubic functions: finding the equation given the turning point (Example 1)
3.13
Cubic functions: finding the equation given the turning point (Example 2)
3.14
Exam question: November 2017, Question 7.1, derivative from first principles
3.15
Exam question: November 2017, Question 7.2, derivatives
3.16
Exam question: November 2018, Question 8.1, derivative from first principles
3.17
Exam question: November 2018, Question 8.2, derivatives
3.18
Exam question: November 2020, Question 7.1, derivative from first principles
3.19
Exam question: November 2020, Question 7.2, derivatives
3.20
Exam question: November 2021, Question 9.1, derivative from first principles
3.21
Exam question: November 2021, Question 9.2, derivatives
3.22
Exam question: November 2021, Question 10, cubic functions
3.23
Exam question: November 2022, Question 7.1, derivative from first principles
3.24
Exam question: November 2022, Question 7.2, derivatives
Finance , Growth & Decay
11 Items
4.1
Quick intro: simple interest and compound interest
4.2
Simple interest: calculating interest on a deposit, the future value
4.3
Simple interest: calculating the interest rate
4.4
Simple interest: calculating the period or number of years
4.5
Simple interest: hire purchase
4.6
Compound interest: calculating the compound interest rate
4.7
Simple interest vs compound interest: which investment account is better
4.8
Simple depreciation: the straight line method
4.9
Compound depreciation: the reducing balance method
4.10
Exam question: November 2016, Question 7
4.11
Exam question: November 2017, Question 6
Graphs and Functions
32 Items
5.1
Linear graphs: finding intercepts and drawing the graph (Example 1)
5.2
Linear graphs: finding intercepts and drawing the graph (Example 2)
5.3
Linear graphs: finding the equation from two points (Example 1)
5.4
Linear graphs: finding the equation from two points (Example 2)
5.5
Parabolic functions: intercepts, turning point and drawing the graph (Example 1)
5.6
Parabolic functions: intercepts, turning point and drawing the graph (Example 2)
5.7
Parabolic functions: finding the equation from the turning point and one point (Example 1)
5.8
Parabolic functions: finding the equation from the turning point and one point (Example 2)
5.9
Hyperbolic functions: intercepts, asymptotes and drawing the graph (Example 1)
5.10
Hyperbolic functions: intercepts, asymptotes and drawing the graph (Example 2)
5.11
Hyperbolic functions: finding the equation from asymptotes and a point (Example 1)
5.12
Hyperbolic functions: finding the equation from asymptotes and a point (Example 2)
5.13
Exponential graphs: intercepts, asymptotes and drawing the graph (Example 1)
5.14
Exponential graphs: intercepts, asymptotes and drawing the graph (Example 2)
5.15
Exponential graphs: inverse functions
5.16
Linear and parabolic functions: points of intersection
5.17
Exam question: 2011 November Paper 1, Question 5 (hyperbolic)
5.18
Exam question: 2011 November Paper 1, Question 6 (parabolic)
5.19
Exam question: 2012 November Paper 1, Question 4 (exponential)
5.20
Exam question: 2012 November Paper 1, Question 4 (parabolic)
5.21
Exam question: 2014 November Paper 1, Question 5 (exponential)
5.22
Exam question: 2014 November Paper 1, Question 6 (parabolic)
5.23
Exam question: 2018 November Paper 1, Question 5 (hyperbolic)
5.24
Exam question: 2018 November Paper 1, Question 6 (parabolic)
5.25
Exam question: 2020 November Paper 1, Question 4 (hyperbolic)
5.26
Exam question: 2020 November Paper 1, Question 5 (exponential)
5.27
Exam question: 2021 November Paper 1, Question 5 (hyperbolic)
5.28
Exam question: 2021 November Paper 1, Question 6 (exponential)
5.29
Exam question: 2021 November Paper 1, Question 7 (parabolic)
5.30
Exam question: 2022 November Paper 1, Question 4 (hyperbolic)
5.31
Exam question: 2022 November Paper 1, Question 5 (linear)
5.32
Exam question: 2022 November Paper 1, Question 4 (parabolic & exponential)
Probability
3 Items
6.1
Exam question: 2018 November Paper 1, Question 8 – Probability
6.2
Exam question: 2018 November Paper 1, Question 9 – Probability
6.3
Exam question: 2018 November Paper 1, Question 12 – Probability
NUMBER PATTERNS, SEQUENCES AND SERIES
19 Items
7.1
Quadratic pattern: finding the next term
7.2
Quadratic pattern: finding the general formula Tn
7.3
Quadratic pattern: given the last term, find the number of terms n
7.4
Arithmetic sequence: finding the next term and the general formula
7.5
Arithmetic sequence: given the last term, find the number of terms n
7.6
Arithmetic sequence in terms of x: finding x
7.7
Arithmetic series: calculating the sum of the first n terms
7.8
Arithmetic series: calculating the sum of the series
7.9
Arithmetic series: given the sum, calculate the number of terms
7.10
Geometric sequence: finding the next term and the general formula
7.11
Geometric sequence: given the last term, find the number of terms n
7.12
Geometric sequence: exam examples
7.13
Geometric series: calculating the sum to infinity
7.14
Geometric series: showing whether a series converges or diverges
7.15
Exam question: 2018 November Paper 1, Question 3, arithmetic patterns
7.16
Exam question: 2018 November Paper 1, Question 4, quadratic patterns
7.17
Exam question: 2021 November Paper 1, Question 2, geometric patterns
7.18
Exam question: 2021 November Paper 1, Question 3, quadratic number patterns
7.19
Exam question: 2021 November Paper 1, Question 4, arithmetic patterns
Statistics
5 Items
8.1
Ungrouped data: mean, mode and median
8.2
Ungrouped data: range and quartiles, box and whisker diagram
8.3
Grouped data: median, lower and upper quartiles
8.4
Finding variance and standard deviation – Simple Method
8.5
Finding variance and standard deviation using a table
Trigonometry Part 2 - sin cos and area rule
12 Items
9.1
Trigonometric identities
9.2
Proving trigonometric identities (LHS = RHS)
9.3
Finding general solutions
9.4
Solving right-angled triangles without a calculator, using Pythagoras
9.5
Sine, cosine and area rule: identifying which rule to use
9.6
Using the sine rule
9.7
Using the cosine rule
9.8
Using the area rule
9.9
Exam question: November 2021, Question 5.1, trigonometric ratios
9.10
Exam question: November 2021, Question 5.1, trigonometric identities
9.11
Exam question: November 2021, Question 5.1, solving a right-angled triangle without a calculator
9.12
Exam question: November 2021, Question 8, sine, cosine and area rule
Grade 12
Curriculum
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