Year 11 - Maths
Signs of a solution
Iteration
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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, pupils continue to explore composite functions and develop understanding of iteration, building on their work on functions and proof.
Lesson Summary
You will learn to deduce why a change of sign may indicate a solution.
Key Notes
- If the value is a solution, then substituting it into the equation should mean the equation evaluates to 0
- Since the solution is an approximation, it is unlikely to be exactly 0
- By substituting the upper and lower bonds of the estimated value into the equation, you can tell if the estimate is good
- If the two values produce one positive and one negative value, this implies the graph would cross the x axis
- The x intercept would be a solution to the equation
Vocabulary To Learn
- Iteration: Iteration is the repeated application of a function or process in which the output of each iteration is used as the input for the next iteration.
- Lower bound: The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded.
- Upper bound: The upper bound for a rounded number is the smallest value that would round up to the next rounded value.
Common Mistakes To Avoid
- A change in sign always indicates a solution. No change in sign means no solution.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
If the value is a solution, then substituting it into the equation should mean the equation evaluates to 0. Since the solution is an approximation, it is unlikely to be exactly 0.
2. Use this key word in a maths sentence and explain it clearly. 'Iteration'
Iteration is the repeated application of a function or process in which the output of each iteration is used as the input for the next iteration. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: A change in sign always indicates a solution. No change in sign means no solution. Correction: A change in sign only indicates a solution if the equation is equal to zero and if the graph of the equation crosses the $$x$$ axis between those points. Where there is a repeated root or two solutions between them there may be no change in sign.
More Lessons In This Unit
Browse all guides in the Year 11 Maths guide library.