## 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 1: Measurement

##### Term 3 Week 2-4: Euclidean Geometry

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