Precalculus - A Complete Course

Students will describe in general terms what the graph of a function represents and why it might be useful.

Students will learn the general shape and key features of common functions.

Students will make an approximate sketch of the graph of a function from its equation.

Students will sketch the graph of a function from its equation using key points on the graph.

Students will describe the behaviour of functions based on the functions graph.

Check how much you've learnt about Graphs of Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will confidently find the inverse of a function and composite of two functions. Students will also describe the relationship between these two operations and sketch the graph of a function and its inverse.

Students will sketch the graph of the inverse of a function.

Students will determine the domain & range of an inverse function.

Students will determine the composite of two functions.

Students will determine the domain & range of a composite function.

Students will work with composing a function with its inverse.

Check how much you've learnt about Composite & Inverse Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what a linear equation is and state the key features of a linear equation.

Students will solve linear equations using a standard technique.

Students will solve equations with parentheses (brackets) in them.

Students will solve equations which have fractions in them.

Check how much you've learnt about Linear & Quadratic Equations by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what a general polynomial expressions is and give examples of polynomial expressions.

Students will describe what it means to factorise a polynomial expression and why it’s useful.

Students will factorise polynomial expressions using synthetic division where one factor is already known.

Students will factorise polynomial expressions using a combination of inspection and synthetic division.

Students will describe what a polynomial equation is and understand the general approach to solving polynomial equations.

Students will solve polynomial equations which have already been factorised.

Students will solve polynomial equations by factorising.

Check how much you've learnt about Polynomials by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe exponential functions and their key features.

Students will describe the key features of the graph of exponential functions and sketch exponential functions from their equation.

Students will describe logarithmic functions and their key features.

Students will describe the key features of graphs of logarithmic functions and sketch logarithmic functions from the equation.

Students will confidently rewrite exponential expressions as logarithmic expressions and vice versa.

Students will use the laws of logarithms to combine, separate and rewrite logarithmic expressions.

Check how much you've learnt about Exponential and Logarithmic Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what a radian measure is and where it comes from, and to write radian measures in different formats.

Students will confidently convert radians to degrees and degrees to radians using key ratios.

Students will describe what the trig functions are from the unit circle definition and how it relates to the geometry of triangles.

Students will state key points on the graph of the Sine function and to sketch the graph.

Students will state key points on the graph of the Cosine function and to sketch the graph.

Students state key points on the graph of the Tangent function and to sketch the graph.

After this class students will be able to use the CAST diagram to gain information about the value of the trigonometric functions Sin, Cos and Tan.

After this class students will be able to use the CAST diagram presented in radians to gain information about the trigonometric functions.

Check how much you've learnt about Trigonometric Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will state and use the Trigonometric double angle formulas.

Students will state and use the Trigonometric addition formulas.

Students will apply the Trigonometric addition formulas to rewrite Trigonometric expressions.

Check how much you've learnt about Trigonometric Identities by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what polar co-ordinates are and how they differ from Cartesian coordinates.

Students will convert Cartesian co-ordinates to Polar co-ordinates and vice versa.

Students will state formulas for common curve shapes in polar form.

Students will sketch curves given in polar form by plotting key points.

Check how much you've learnt about Polar Co-ordinates by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what the binomial expansion is and why it’s useful.

Students will describe and use Pascal’s triangle in relation to the binomial expansion.

Students will describe how factorials can be used to count objects from a set under certain conditions.

Students will use combinatoric factorial notation to determine the coefficients of terms in a binomial expansion.

Students will use the binomial expansion to expand the form (1 + x)^n.

Check how much you've learnt about The Binomial Expansion by trying these practice questions. Remember to check your work against the step by step solutions provided.