Grade 11 Topics
Term 1
Week 1-3: Exponents and surds
Week 4-6: Equations and Inequalities
Week 7-8: Number Patterns
Week 9-11 Analytical Geometry
Term 2
Week 1-4: Functions
Week 5-8: Trigonometry
Term 3
Week 1: Measurement
Week 2-4: Euclidean Geometry
Week 5-6: Trigonometry
Week 7-8: Finance
Week 9-10: Probability
Term 4
Week 1-2: Statistics
Term 1 Week 1-3: Exponents and surds
Simplify expressions and solve equations using the laws of exponents for rational exponents
- Textbook
- Video
Add, subtract, multiply and divide simple surds
- Textbook
- Video
Solve simple equations involving surds
- Textbook
- Video
Term 1 Week 4-6: Equations and Inequalities
Revision
- Textbook
Complete the square
- Textbook
- Video
- Basics
- Examples
Quadratic equations (by factorisation and by using the quadratic formula)
Quadratic inequalities in one unknown (Interpret solutions graphically)
- Textbook
- Examples
- Video
Equations in two unknowns, one of which is linear and the other quadratic
- Textbook
- Video
Nature of roots
- Textbook
- Video
- Video: Discriminant and graphs
Term 1 Week 7-8: Number Patterns
Term 1 Week 9-11: Analytical Geometry
The equation of a line through two given points
- Textbook
- Video
The equation of a line through one point and parallel or perpendicular to a given line
- Video
- Examples
The inclination of a line, where is the gradient of the line
- Textbook
- Video
Term 2 Week 1-4: Functions
Term 2 Week 5-8: Trigonometry
Investigate the influence of p in the parabola: y = a(x+p)^2 + q
- Textbook
- Interactive graphing to see the influence of a, p and q: y = ax^2 + bx + c
- How to find the equation of a parabola
- Explore the influence of a, b and c in
- Video
- Real world examples of the parabola
The hyperbola: y = a / (x+p) + q
- Textbook
- Interactive graphing to see the influence of a, p and q
- Interactive: Find the equation
- Analyse the data (fun project)
The exponential graph: y = a.b^(x+p) + q
- Textbook
- Interactive graphing to see the influence of a, p and q
- Examples
- Match graphs and their equations
Investigate the influence of k and p in trig graphs:
y = a sin (kx+p) + q
- Textbook
- Interactive graphing to see the influence of a, p and q
- Online exercise to find the properties
y = a cos (kx+p) + q
- Textbook
- Interactive graphing to see the influence of a, p and q
- Video
y = a tan (kx+p) + q
- Textbook
- Interactive graphing to see the influence of a, p and q
- Why the asymptotes of a tan graph
Trigonometric Identities
- Textbook
- Video
- Maths is fun (ignore those not in CAPS)
Reduction formula
- Textbook
- Summary
Trigonometric equations
- Textbook
Term 3 Week 2-4: Euclidean Geometry
Term 3 Week 1: Measurement
Accept results established in earlier grades as axioms and also that a tangent to a circle is perpendicular to the radius, drawn to the point of contact.
Then investigate and prove the theorems of the geometry of circles:
- The line drawn from the centre of a circle perpendicular to a chord bisects the chord;
- The perpendicular bisector of a chord passes through the centre of the circle;
- Angles subtended by a chord of the circle, on the same side of the chord, are equal;
- The opposite angles of a cyclic quadrilateral are supplementary;
- Two tangents drawn to a circle from the same point outside the circle are equal in length;
- The angle between the tangent to a circle;
- and the chord drawn from the point of contact is equal to the angle in the alternate segment.
Use the above theorems and their converses, where they exist, to solve riders
- Textbook
- Here you can download a pdf book
- How to proof a cyclic quad example 1
- How to proof a cyclic quad example 2
Term 3 Week 5-6: Trigonometry
Sine, cosine and area rules
- Textbook
- How to decide which law to use
- Trigonometry for solving problems
Term 3 Week 7-8: Finance
Simple and compound decay formulae: A = P(1 - in) and A = P(1 - i)^n
(including straight line depreciation and depreciation on a reducing balance)
- Textbook
- Graphical difference between simple and compound
Effect of different periods of compound growth and decay
(including nominal and effective interest rates)
- Definitions, Meaning, and Example Calculations
- Real live meaning of nominal rates
Term 3 Week 9-10: Probability
Revise the addition rule for mutually exclusive events: 𝑃(𝐴 𝑜𝑟 𝐵)=𝑃𝐴 +𝑃(𝐵) and P(A) = 1 – P(A')
Dependant and Independent events
- Textbook
- Video
- Rules
Venn diagrams
- Textbook
- Examples
Tree diagrams
- Textbook
Contingincy Tables
- Textbook
- Examples
Term 4 Week 1-2: Statistics
Histograms
- Textbook
- Video 1
- Video 2
Frequency polygon and Ogives (cumulative frequency curves)
- Textbook
- Example
- Video
Variance and standard deviation of ungrouped data
- Textbook
- Conceptual Difference Between Standard Deviation & Variance
Symmetric and skewed data
- Textbook
- Sketches
Identification of outliers
- Textbook
- Video