Grade 11
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ByArinaoKhangale
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Grade 11 is where most learners lose Mathematics. The work stops rewarding memorised methods and starts needing you to understand why they work.
This course covers every Grade 11 CAPS topic and the topics that follow straight on from them, in the order they build on each other. Each one starts from first principles and ends on the kind of question the November paper actually asks.
Every line is written down
Marks are given for method, not only for the answer. A learner who writes the right answer with three steps missing loses most of the marks for that question. Nothing is skipped here.
What you will cover
- Algebra — exponents, surds, algebraic fractions, quadratic equations by factorising and by completing the square, simultaneous equations
- Graphs and functions — linear, parabolic, hyperbolic and exponential, both drawing the graph and finding the equation from it
- Analytical geometry — distance, midpoint, gradient, angle of inclination, equations of straight lines, and the equation of a circle
- Trigonometry — ratios, identities, general solutions, and the sine, cosine and area rules
- Number patterns, sequences and series — quadratic patterns, arithmetic and geometric sequences and series, sum to infinity, and testing for convergence
- Finance, growth and decay — simple and compound interest, depreciation, hire purchase
- Differential calculus — derivatives from first principles, the power rule, cubic functions, turning points and points of inflection, and drawing cubic graphs
- Probability — the addition rule, independent and dependent events
- Statistics — mean, median, quartiles, box and whisker diagrams, variance and standard deviation
Past paper questions, worked in full
Real November Paper 1 questions, from reading the question to the final line of the memo, so you can see how a topic turns into marks.
What you need
- A scientific calculator and paper. You will be writing, not watching.
- A phone or laptop. The lessons stream on mobile data.
- Grade 10 Mathematics. Grade 11 is built straight on top of it.
This is Mathematics, not Mathematical Literacy.
- Grade 11
- 9 Sections
- 151 Lessons
- 31 Days
- Algebra24 Items
- 1.1Simplifying exponents
- 1.2Exponents: solve for x when x is in the base
- 1.3Exponents: solve for x when x is in the exponent
- 1.4Simplifying surds
- 1.5Writing an infinite recurring decimal as a fraction
- 1.6Finding the product
- 1.7Factorising
- 1.8Algebraic fractions
- 1.9Algebraic expressions: adding and subtracting fractions
- 1.10Solve for x: linear equations
- 1.11Solve for x: quadratic equations by factorising
- 1.12Solve for x: quadratic equations by completing the square
- 1.13Solve for x: surd and linear equations
- 1.14Solve for x: linear and surd equations
- 1.15Solve for x: quadratic and surd equations
- 1.16Solve for x: surd and quadratic equations by factorising
- 1.17Solve for x: quadratic, linear, exponential and surd equations
- 1.18Simultaneous equations
- 1.19Simultaneous linear equations: substitution method
- 1.20Simultaneous linear equations: elimination method
- 1.21Simultaneous linear equations: equating method
- 1.22Exam question : 2016 November Paper 1, Question 1 – Algebra
- 1.23Exam question: 2018 November Paper 1, Question 1 – Algebra
- 1.24Exam question: 2018 November Paper 1, Question 2 – Algebra
- Analytical Geometry20 Items
- 2.1Straight lines: finding the gradient (Example 1)
- 2.2Straight lines: finding the gradient (Example 2)
- 2.3Straight lines: distance between two points (Example 1)
- 2.4Straight lines: distance between two points (Example 2)
- 2.5Distances (Example 3)
- 2.6Straight lines: coordinates of the midpoint (Example 1)
- 2.7Straight lines: coordinates of the midpoint (Example 2)
- 2.8Midpoints (Example 3)
- 2.9Midpoints: finding a point given the midpoint and another point
- 2.10Straight lines: Finding equation of a line that passes through two points (Example 1)
- 2.11Straight lines: Finding equation of a line that passes through two points (Example 2)
- 2.12Parallel straight lines: finding the equation (Example 1)
- 2.13Parallel straight lines: finding the equation (Example 2)
- 2.14Straight lines: angle of inclination (Example 1)
- 2.15Straight lines: angle of inclination (Example 2)
- 2.16Circles with any centre
- 2.17Finding the equation of a circle with any centre
- 2.18Finding the equation of a circle with any centre (second worked example)
- 2.19Exam question: November 2021, Question 3
- 2.20Exam questions: November papers, analytical geometry
- Differential Calculus24 Items
- 3.1First principles (Example 1)
- 3.2First principles (Example 2)
- 3.3Derivatives: using the power rule (Example 1)
- 3.4Derivatives: using the power rule (Example 2)
- 3.5Determining dx
- 3.6Cubic functions: finding intercepts
- 3.7Cubic functions: finding turning points
- 3.8Cubic functions: point of inflection and concavity
- 3.9Cubic functions: drawing the graphs
- 3.10Cubic functions: finding values of x, long division vs synthetic division (Example 1)
- 3.11Cubic functions: finding values of x, long division vs synthetic division (Example 2)
- 3.12Cubic functions: finding the equation given the turning point (Example 1)
- 3.13Cubic functions: finding the equation given the turning point (Example 2)
- 3.14Exam question: November 2017, Question 7.1, derivative from first principles
- 3.15Exam question: November 2017, Question 7.2, derivatives
- 3.16Exam question: November 2018, Question 8.1, derivative from first principles
- 3.17Exam question: November 2018, Question 8.2, derivatives
- 3.18Exam question: November 2020, Question 7.1, derivative from first principles
- 3.19Exam question: November 2020, Question 7.2, derivatives
- 3.20Exam question: November 2021, Question 9.1, derivative from first principles
- 3.21Exam question: November 2021, Question 9.2, derivatives
- 3.22Exam question: November 2021, Question 10, cubic functions
- 3.23Exam question: November 2022, Question 7.1, derivative from first principles
- 3.24Exam question: November 2022, Question 7.2, derivatives
- Finance , Growth & Decay11 Items
- 4.1Quick intro: simple interest and compound interest
- 4.2Simple interest: calculating interest on a deposit, the future value
- 4.3Simple interest: calculating the interest rate
- 4.4Simple interest: calculating the period or number of years
- 4.5Simple interest: hire purchase
- 4.6Compound interest: calculating the compound interest rate
- 4.7Simple interest vs compound interest: which investment account is better
- 4.8Simple depreciation: the straight line method
- 4.9Compound depreciation: the reducing balance method
- 4.10Exam question: November 2016, Question 7
- 4.11Exam question: November 2017, Question 6
- Graphs and Functions33 Items
- 5.1Linear graphs: finding intercepts and drawing the graph (Example 1)
- 5.2Linear graphs: finding intercepts and drawing the graph (Example 2)
- 5.3Linear graphs: finding the equation from two points (Example 1)
- 5.4Linear graphs: finding the equation from two points (Example 2)
- 5.5Parabolic functions: intercepts, turning point and drawing the graph (Example 1)
- 5.6Parabolic functions: intercepts, turning point and drawing the graph (Example 2)
- 5.7Parabolic functions: finding the equation from the turning point and one point (Example 1)
- 5.8Parabolic functions: finding the equation from the turning point and one point (Example 2)
- 5.9Hyperbolic functions: intercepts, asymptotes and drawing the graph (Example 1)
- 5.10Hyperbolic functions: intercepts, asymptotes and drawing the graph (Example 2)
- 5.11Hyperbolic functions: finding the equation from asymptotes and a point (Example 1)
- 5.12Hyperbolic functions: finding the equation from asymptotes and a point (Example 2)
- 5.13Exponential graphs: intercepts, asymptotes and drawing the graph (Example 1)
- 5.14Exponential graphs: intercepts, asymptotes and drawing the graph (Example 2)
- 5.15Exponential graphs: inverse functions
- 5.16Linear and parabolic functions: points of intersection
- 5.17Exam question: 2011 November Paper 1, Question 5 (hyperbolic)
- 5.18Exam question: 2011 November Paper 1, Question 6 (parabolic)
- 5.19Exam question: 2012 November Paper 1, Question 4 (exponential)
- 5.20Exam question: 2012 November Paper 1, Question 4 (parabolic)
- 5.21Exam question: 2014 November Paper 1, Question 5 (exponential)
- 5.22Exam question: 2014 November Paper 1, Question 6 (parabolic)
- 5.23Exam question: 2018 November Paper 1, Question 5 (hyperbolic)
- 5.24Exam question: 2018 November Paper 1, Question 6 (parabolic)
- 5.25Exam question: 2020 November Paper 1, Question 4 (hyperbolic)
- 5.26Exam question: 2020 November Paper 1, Question 5 (exponential)
- 5.27Exam question: 2021 November Paper 1, Question 5 (hyperbolic)
- 5.28Exam question: 2021 November Paper 1, Question 6 (exponential)
- 5.29Exam question: 2021 November Paper 1, Question 7 (parabolic)
- 5.30Exam question: 2022 November Paper 1, Question 4 (hyperbolic)
- 5.31Exam question: 2022 November Paper 1, Question 5 (linear)
- 5.32Exam question: 2022 November Paper 1, Question 4 (exponential)
- 5.33Exam question: 2022 November Paper 1, Question 4 (parabolic)
- Probability3 Items
- NUMBER PATTERNS, SEQUENCES AND SERIES19 Items
- 7.1Quadratic pattern: finding the next term
- 7.2Quadratic pattern: finding the general formula Tn
- 7.3Quadratic pattern: given the last term, find the number of terms n
- 7.4Arithmetic sequence: finding the next term and the general formula
- 7.5Arithmetic sequence: given the last term, find the number of terms n
- 7.6Arithmetic sequence in terms of x: finding x
- 7.7Arithmetic series: calculating the sum of the first n terms
- 7.8Arithmetic series: calculating the sum of the series
- 7.9Arithmetic series: given the sum, calculate the number of terms
- 7.10Geometric sequence: finding the next term and the general formula
- 7.11Geometric sequence: given the last term, find the number of terms n
- 7.12Geometric sequence: exam examples
- 7.13Geometric series: calculating the sum to infinity
- 7.14Geometric series: showing whether a series converges or diverges
- 7.15Exam question: 2018 November Paper 1, Question 3, arithmetic patterns
- 7.16Exam question: 2018 November Paper 1, Question 4, quadratic patterns
- 7.17Exam question: 2021 November Paper 1, Question 2, geometric patterns
- 7.18Exam question: 2021 November Paper 1, Question 3, quadratic number patterns
- 7.19Exam question: 2021 November Paper 1, Question 4, arithmetic patterns
- Statistics5 Items
- Trigonometry Part 2 - sin cos and area rule12 Items
- 9.1Trigonometric identities
- 9.2Proving trigonometric identities (LHS = RHS)
- 9.3Finding general solutions
- 9.4Solving right-angled triangles without a calculator, using Pythagoras
- 9.5Sine, cosine and area rule: identifying which rule to use
- 9.6Using the sine rule
- 9.7Using the cosine rule
- 9.8Using the area rule
- 9.9Exam question: November 2021, Question 5.1, trigonometric ratios
- 9.10Exam question: November 2021, Question 5.1, trigonometric identities
- 9.11Exam question: November 2021, Question 5.1, solving a right-angled triangle without a calculator
- 9.12Exam question: November 2021, Question 8, sine, cosine and area rule