Signs of a solution
I can deduce why a change of sign may indicate a solution.
Signs of a solution
I can deduce why a change of sign may indicate a solution.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- 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
Keywords
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 misconception
A change in sign always indicates a solution. No change in sign means no solution.
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.
To help you plan your year 11 maths lesson on: Signs of a solution, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Signs of a solution, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Iteration unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Starter quiz
6 Questions

A -
$$y=x^2$$
B -
$$y=x^3$$
C -
$$y=-x^2$$
D -
$$y=\frac{1}{x}$$
Exit quiz
6 Questions

