Grade 10 Breakdown:

>Functions

        ◘ Work with relationships between variables in terms of numerical, graphical, verbal and symbolic representations of functions and convert flexibly between these 
          representations (tables, graphs, words and formulae). Include linear and some quadratic polynomial functions, exponential functions, some rational functions and 
          trigonometric functions.

        ◘ Generate as many graphs as necessary, initially by means of point-by-point plotting, supported by available technology, to make and test conjectures and hence 
          generalise the effect of the parameter which results in a vertical shift and that which results in a vertical stretch and/or a reflection about the x-axis.

        ◘ Problem solving and graph work involving the prescribed functions.
       

>Number Patterns, Sequences and Series

        ◘ Investigate number patterns leading to those where there is constant difference between consecutive terms, and the general term is therefore linear.
      

>Finance, Growth and Decay

        ◘ Use simple and compound growth formulae A = P(1 + in) and A = P(1 + i)n to solve problems (including interest, hire purchase, inflation, 
        population growth and other real life problems).
      

>Algebra

        ◘ Understand that real numbers can be irrational or rational.

        ◘ Simplify expressions using the laws of exponents for rational exponents.

        ◘ Establish between which two integers a given simple surd lies.

        ◘ Round real numbers to an appropriate degree of accuracy (to a given number of decimal digits).

        ◘ Manipulate algebraic expressions by:
            (1) Multiplying a binomial by a trinomial;
            (2) Factorising trinomials;factorising the difference and sums of two cubes;
            (3) Factorising by grouping in pairs; and 
            (4) Simplifying, adding and subtracting algebraic fractions with denominators of cubes (limited to sum and difference of cubes).

        ◘ Solve:
            (1) Linear equations
            (2) Quadratic equations
            (3) Literal equations
            (4) Exponential equations
            (5) Linear inequalities
            (6) Systems of linear equations
            (7) Word problems
      

>Probability

        ◘ Compare the relative frequency of an experimental outcome with the theoretical probability of the outcome.

        ◘ Venn diagrams as an aid to solving probability problems.

        ◘ Mutually exclusive events and complementary events.

        ◘ The identity for any two events A and B: P(A or B) = P(A) + (B) - P(A and B)

      

>Euclidean Geometry and Measurement

        ◘ Revise basic results established in earlier grades.

        ◘ Investigate line segments joining the midpoints of two sides of a triangle.

        ◘ Properties of special quadrilaterals.

        ◘ Solve problems involving volume and surface area of solids studied in earlier grades as well as spheres, pyramids and cones and combinations of those objects.
      

>Trigonometry

        ◘ Definitions of the trigonometric ratios sin θ, cos θ and tan θ in a right-angled triangles.
 
        ◘ Extend the definitions of sin θ, cos θ and tan θ to 0° ≤ θ ≤ 360°.

        ◘ Derive and use values of the trigonometric ratios (without using a calculator for the special angles θ ∈ {0°; 30°; 45°; 60°; 90°})

        ◘ Define the reciprocals of trigonometric ratios.

        ◘ Solve problems in two dimensions.
      

>Analytical Geometry

        ◘ Represent geometric figures in a Cartesian coordinate system, and derive and apply, for any two points (x1; y1) and (x2; y2), a formula for calculating:
           (1) The distance between the two points;
           (2) The gradient of the line segment joining the points;
           (3) Conditions for parallel and perpendicular lines
           (4) The co-ordinates of the mid-point of the line segment joining the points.

      

>Statistics

        ◘ Collect, organise and interpret univariate numerical data in order to determine:
           (1) Measures of central tendency
           (2) Five number summary
           (3) Box and whisker diagrams
           (4) Measures of dispersion.