Year 10 - Maths
Problem solving with non-linear graphs
Non-linear graphs
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit graphical representations of non-linear graphs are introduced and explored, and their key features identified.
Lesson Summary
You will learn to use your knowledge of non-linear graphs to solve problems.
Key Notes
- The shape of the graph can be used to identify the form of its equation.
- If the graph has a context, then the solutions should be given in context.
Vocabulary To Learn
- Linear: The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.
- Quadratic: A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2
- Cubic: A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3
Common Mistakes To Avoid
- A graph drawn on axes with no scale shown means nothing is known about the graph.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The shape of the graph can be used to identify the form of its equation. If the graph has a context, then the solutions should be given in context.
2. Use this key word in a maths sentence and explain it clearly. 'Linear'
The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: A graph drawn on axes with no scale shown means nothing is known about the graph. Correction: Understanding the shape of a parabola, cubic curve, and reciprocal graph and then applying key features like positive/negative coefficients and $$y$$-intercepts enables pupils to infer much about the equation without needing actual coordinate values.
More Lessons In This Unit
- Advanced problem solving with non-linear graphs Study Guide
- Checking and securing understanding of drawing quadratic graphs Study Guide
- Drawing cubic graphs Study Guide
- Drawing exponential graphs Study Guide
- Drawing reciprocal graphs Study Guide
- Drawing the graph for the equation of a circle Study Guide
- Key features of a cubic graph Study Guide
- Key features of a quadratic graph Study Guide
- Key features of a reciprocal graph Study Guide
- Key features of an exponential graph Study Guide
Browse all guides in the Year 10 Maths guide library.