# Non-Linear Graphical Functions

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

#### Prerequisite Knowledge

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

#### Success Criteria

• 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.

#### Key Concepts

• 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.

#### Common Misconceptions

• 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.

## Non-Linear Graphical Functions Resources

### Mr Mathematics Blog

#### Interpreting Cumulative Frequency Graphs

Linking cumulative frequency graphs to ratio, percentages and financial mathematics.

#### Higher GCSE Maths Revision Lesson

In this lesson there are five grade 8 and 9 maths problems for higher ability students.