Algebra

This section is going to allow you to learn about:

  1. Functions and their Graphs;
  2. Exponents and Logarithms;
  3. The Remainder and Factor Theorems;
  4. Equations and Inequalities.

Statistics

We will:

  1. Revise symmetric and skewed data;
  2. Use statistical summaries, scatterplots, regression (in particular the least squares regression line) and correlation to analyse and interpret bivariate data.
  3. Use the concepts of interpolation, extrapolation and skewness.

Euclidean Geometry

We will look back at knowledge gained in earlier grades, but add to this as follows:

  1. The necessary and sufficient conditions for polygons to be similar;
  2. Proportionality in triangles;
  3. Equiangular triangles are similar;
  4. Triangles with sides in proportion are similar;
  5. The theorem of Pythagoras.

Probability / Permutations and Combinations

We will revise the work of earlier grades, and add the following:

1.  Solve probability problems using Venn diagrams, tree diagrams and two-way contingency tables;

2.  Apply the fundamental counting principle to solve simple problems relating to permutations and combinations.

Differential Calculus

You will define and apply the following concepts:

  1. Limits;
  2. The derivative of a function;
  3. First principles;
  4. Rules of differentiation;
  5. How to find the equation of the tangent to the graph of a function;
  6. The second derivative, and how it determines the concavity of a function;
  7. How to sketch the graph of a cubic polynomial function;
  8. How to solve practical problems concerning optimisation and rate of change, including the calculus of motion.

Transformational Geometry

Skills to acquire:

  1. How to rotate a point through 90o  — anticlockwise about the origin
  2. How to rotate a point through 90o — clockwise about the origin
  3. How to rotate a point through 180o about the origin
  4. How to translate a point through a units along the x-axis and b units along the y-axis
  5. How to reflect a point in the x-axis
  6. How to reflect a point in the y-axis
  7. How to reflect the graph of a function in the - and -axes
  8. How to find the reflection of a point in the straight line
  9. How to sketch the inverse of a function
  10. How to enlarge or reduce a figure by a scale factor
  11. How to rotate a point through an angle  anticlockwise about the origin

Trigonometry

Here is the menu:

  • We will review the basics;
  • You will see how the sine and cosine functions are formed;
  • Reduction formulae;
  • Compound and double angles;
  • Trigonometrical functions and their graphs;
  • Solving triangles in the context of 2-D and 3-D problems.

Finance, Growth and Decay

You will:

  1. Apply simple and compound growth and decay formulae;
  2. Calculate the effect of different periods of compound growth and decay;
  3. Distinguish between nominal and effective interest rates;
  4. Solve problems involving present value and future value annuities;
  5. Make use of logarithms to calculate the period, n, over which growth or decay takes place;
  6. Compare and decide between investment and loan options.

Analytical Geometry

We will derive and apply the following things:

  1. The equation of a line through two given points;
  2. The equation of a line through one point and parallel or perpendicular to a given line;
  3. The inclination (θ) of a line, where m = tanθ is the gradient of the line (0o ≤ θ ≤ 180o);

 

Also, the equation below defines a circle with centre (a; b) and radius r:

(x – a)2 + (y – b)2 = r2

We will:

  1. Solve problems related to such a circle;
  2. Determine the equation of a tangent to a given circle.

Patterns, Sequences and Series

We will do:

  1. Arithmetic, geometric and quadratic sequences;
  2. Arithmetic and geometric series (progressions);
  3. The infinite geometric sequence and series;
  4. Sigma notation;
  5. How to derive and apply the formulae for the sum of arithmetic and geometric series.