Small increments and approximations · Short practice

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Recall

Small increments and approximations — objective 1

Maths4U Original · Short practice

Let \(y=3 x^{3}\). The value of x increases from \(2\) by \(\displaystyle \frac{1}{21}\).

Estimate the increase in y using differentials.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Small increments and approximations — objective 1

Maths4U Original · Short practice

Let \(y=4 x^{4}\). The value of x increases from \(3\) by \(\displaystyle \frac{1}{22}\).

Estimate the increase in y using differentials.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Small increments and approximations — objective 2

Maths4U Original · Short practice

Let \(y=4 x^{4}\). The value of x increases from \(3\) by \(\displaystyle \frac{1}{22}\).

Find the exact increase in y.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Small increments and approximations — objective 2

Maths4U Original · Short practice

Let \(y=2 x^{2}\). The value of x increases from \(4\) by \(\displaystyle \frac{1}{23}\).

Find the exact increase in y.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Small increments and approximations — objective 3

Maths4U Original · Short practice

Let \(y=2 x^{2}\). The value of x increases from \(4\) by \(\displaystyle \frac{1}{23}\).

Estimate the new value of y.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Small increments and approximations — objective 3

Maths4U Original · Short practice

Let \(y=3 x^{3}\). The value of x increases from \(5\) by \(\displaystyle \frac{1}{24}\).

Estimate the new value of y.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Small increments and approximations — objective 4

Maths4U Original · Short practice

Let \(y=3 x^{3}\). The value of x increases from \(5\) by \(\displaystyle \frac{1}{24}\).

Estimate the percentage increase in y.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Small increments and approximations — objective 4

Maths4U Original · Short practice

Let \(y=4 x^{4}\). The value of x increases from \(2\) by \(\displaystyle \frac{1}{20}\).

Estimate the percentage increase in y.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →