Non-Linear Graphical Functions

August 23, 2016

Students learn how to  plot quadratic, cubic, reciprocal and exponential graphs.  As learning progresses they use these graphs to model a range of scenerios and estimate solutions to equations.

This unit takes place in Term 5 of Year 10 and follows straight line graphs.

Non-Linear Graphical Functions Lessons
Algebra: Free Resources
Plotting Cubic Functions
4 Part Lesson
Plotting Cubic Functions
How to plot cubic functions by completing a table of results.
Algebra: Interactive Lessons
Solving Cubic and Reciprocal Equations Graphically
4 Part Lesson
Solving Cubic and Reciprocal Equations Graphically
How to solve cubic and reciprocal equations using graphical methods.
Algebra: Interactive Lessons
Solving Quadratic Equations Graphically
4 Part Lesson
Solving Quadratic Equations Graphically
How to estimate the solutions to a quadratic equation using graphs.
Algebra: Interactive Lessons
Plotting Exponential Graphs
4 Part Lesson
Plotting Exponential Graphs
How to plot exponential graphs from a table of results.
Algebra: Interactive Lessons
Deriving the Equation of Tangents
4 Part Lesson
Deriving the Equation of Tangents
How to find the equation of a tangent to a curve and circle.
Algebra: Interactive Lessons
Equation of Circles
4 Part Lesson
Equation of Circles
How to derive the equation of circles on Cartesian axes.
Algebra: Interactive Lessons
Plotting Reciprocal Functions
4 Part Lesson
Plotting Reciprocal Functions
How to plot reciprocal graphs from a table of results.
Algebra: Interactive Lessons
Plotting Quadratic Functions
4 Part Lesson
Plotting Quadratic Functions
Students learn how to plot a quadratic graph using a table of results.
Additional Resources
Algebra: Interactive Lessons
Plotting Quadratic Graphs
Extended Learning
Plotting Quadratic Graphs
Students gain additional practice plotting quadratic graphs.
Algebra: Interactive Lessons
Plotting Nonlinear Graphs
Revision
Plotting Curved Graphs
Students revise how to plot curved graphs including quadratic, cubic and reciprocal functions using a table of r...
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 ≠ 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 coordinate’s 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 in negative values to 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.

Mr Mathematics Blog

Geometric and Negative Binomial Distributions

August 5, 2022

Year 13 Further Mathematics: Statistics 1: Geometric and Negative Binomial Distributions

Conditional Probability

July 26, 2022

Scheme of Work: A-Level Applied Mathematics: Statistics 2: Conditional Probability

The Normal Distribution

July 26, 2022

A-Level Applied Mathematics Scheme of Work: Normal Distribution