Non-Linear Graphical Functions

Scheme of work: GCSE Higher: Year 10: Term 5: Non-Linear Graphical Functions

Plot graphs of equations that correspond to straight-line graphs in the coordinate plane
Recognise, sketch and interpret graphs of linear functions

Recognise, plot and interpret graphs of quadratic functions, simple cubic functions and the reciprocal function y = 1/x with x not equal to 0.
Solve quadratic equations by finding approximate solutions using a graph
Plot and interpret graphs exponential graphs
Recognise and use the equation of a circle with centre at the origin
Find the equation of a tangent to a circle at a given point.

To generate the coordinates students need to have a secure understanding of applying the order of operations to substitute and evaluate known values into equations.
Quadratic, Cubic and Reciprocal functions are non-linear and therefore do not have straight lines. All graphs of this nature should be drawn with smooth curves.
When solving equations graphically students should realise solutions are only approximate.
Students need to gain an understanding of the shape of each function in order to identify incorrectly plotted coordinates.
The equation of a circle relates very closely to Pythagoras theorem.
Exponential graphs can be increasing as well as decreasing.
Students need to understand the equivalence between linear graphs in the form y = mx + c and ax + by + c = 0.

Students often have difficulty substituting negative values for complex equations. Encourage the use of mental arithmetic.
Identifying the correct type of function from graphs is often a source of confusion.
By creating the table of results students will be more able to choose a suitable scale for their axes.
Students who complete the table of results correctly often have little difficulty plotting the graph correctly.
Students often have difficulty drawing the equation of a circle correctly in examinations.
Students often have difficulty stating the equation of a linear graph in the form ax + by + c = 0.