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# Mathematics

## Grade 10

Functions and graphs

- Asymptotes
- Axes of symmetry
- Finding the equation of the exponential function
- Finding the equation of the hyperbola
- Finding the equation of the parabola
- Finding the equation of the straight line
- Function notation
- Graphs - Domain and range
- Graphs - Intercepts
- Graphs - Introduction
- Graphs - Turning points
- Increasing and decreasing functions
- Parameters of the exponential function
- Parameters of the hyperbola
- Parameters of the parabola
- Parameters of the straight line
- Problem solving and graph work
- Representing functions
- Shifting straight lines, parabolas, hyperbolas and exponential functions
- Shifting trig graphs
- Sketching the exponential function
- Sketching the hyperbola
- Sketching the parabola
- Sketching the straight line
- Stretching and compressing straight lines, parabolas, hyperbolas and exponential functions
- Stretching and compressing trig graphs
- The cos graph
- The sin graph
- The tan graph

Algebra

- Adding and subtracting algebraic fractions
- Changing the subject of equations
- Exponents
- Factorisation - Common factors
- Factorisation - Difference of two squares
- Factorisation - Grouping in pairs
- Factorisation - Sum and difference of two cubes
- Factorisation of trinomials
- Factorising a binomial
- Factorising by grouping in pairs
- How to establish between which two integers a simple surd lies
- Introduction to the laws of exponents
- Multiplying a binomial by a trinomial
- Multiplying and dividing algebraic fractions
- Simplifying algebraic expressions using factorisation
- Simplifying expressions using the laws of exponents
- Solving equations by factorisation (1)
- Solving equations by factorisation (2)
- Solving equations by factorisation (3)
- Solving inequalities
- Solving linear equations with brackets
- Solving linear equations with fractions
- Solving linear equations without brackets
- Solving quadratic equations by factorisation
- Solving simultaneous equations
- Working with the laws of exponents

Trigonometry

- An introduction to trig ratios
- Angles of elevation and depression
- Determining the sides of a triangle using the trig ratios
- Determining angles using trig ratios
- Finding angles in more than one triangle
- Finding sides in more than one triangle
- Plotting the cos function
- Plotting the sin function
- Plotting the tan function
- Reciprocal ratios
- Solving trig equations (1)
- Solving trig equations (2)
- Special angles
- The link between trig ratios and the Cartesian plane
- Trig ratios and similar triangles
- Using trigonometric concepts to solve problems involving quadrilaterals