Year 10 - Maths
Advanced 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.
- Sketching the graph can help when solving problems.
- Problem solving requires you to draw on any useful knowledge.
Vocabulary To Learn
- 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
- Exponential: The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.
- Asymptote: An asymptote is a line that a curve approaches but never touches.
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. Sketching the graph can help when solving problems.
2. Use this key word in a maths sentence and explain it clearly. 'Quadratic'
A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2. 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
- 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
- Problem solving with non-linear graphs Study Guide
Browse all guides in the Year 10 Maths guide library.