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ACARA ACMMM121, Families of curves with the same derivative

Year 11-12 · Mathematical Methods

Identify families of curves that share the same derivative function, differing only by the constant of integration.

Below are free printable maths worksheets that support ACMMM121. Print them as PDFs, or generate a fresh one. Every maths answer key is computed in code, so it is never wrong.

Teaching guide

What students learn

Identify families of curves that share the same derivative function, differing only by the constant of integration.

How to teach it

First antidifferentiate to get the family f(x) = F(x) + C, then use the given point: substitute its coordinates to make an equation in C and solve. Emphasise that the point pins down one member of the family of parallel curves.

Worked example
The gradient function of a curve is f'(x) = 2x - 1, and the curve passes through the point (-1, 7). Find f(x).
Answer: f(x) = x^2 - x + 5
Why: Antidifferentiate: f(x) = x^2 - x + C. Substitute (-1, 7): 2 + C = 7, so C = 5. Therefore f(x) = x^2 - x + 5.

Generated and checked in code, so it is correct.

Watch out for

Substituting the point before antidifferentiating, or leaving the answer as F(x) + C without solving for C once a point is given.

Math worksheets

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Year 11-12 Math
Set A · PDF · answer key with Pro

Math worksheets

All math worksheets →
Year 11-12 Math
Set A · PDF · answer key with Pro
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More Year 11-12 Mathematical Methods codes: ACMMM114 · ACMMM116 · ACMMM117 · ACMMM122 · ACMMM125 · ACMMM131 · ACMMM132
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Australian Curriculum content descriptions (c) ACARA, used under CC BY 4.0. Descriptions are paraphrased. See australiancurriculum.edu.au.