Pure 1 course · All short practice · Notes & examples
Maths4U Original · 9709 Pure 1
Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.
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Recall · M4U-P1-QP-INTEGRATION-ACCUMULATION-01
Maths4U Original · Short practice
A flow rate is \(q(t)=2t+3\) litres/minute. How many litres enter from \(t=0\) to \(t=4\) minutes?Enter one number or fraction. Round decimals to at least six decimal places when needed.
Method · M4U-P1-QP-INTEGRATION-ACCUMULATION-02
Maths4U Original · Short practice
An amount starts at 10 units and has rate \(dQ/dt=6t\). Find \(Q(3)\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Apply · M4U-P1-QP-INTEGRATION-ACCUMULATION-03
Maths4U Original · Short practice
A quantity has signed rate \(2t-4\) from \(t=0\) to \(t=4\). Find its net change.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Check understanding · M4U-P1-QP-INTEGRATION-ACCUMULATION-04
Maths4U Original · Short practice
A quantity has rate \(2t-4\) from \(t=0\) to \(t=4\). Find the total variation, the integral of the absolute rate.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-ACCUMULATION-01
Maths4U Original · Short practice
A flow rate is \(q(t)=3t+2\) litres/minute, where t is measured in minutes. Find, in litres, the amount entering from t=0 to t=4.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-ACCUMULATION-02
Maths4U Original · Short practice
An amount starts at 5 units and has rate \(dQ/dt=3t\). Find Q(4).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-ACCUMULATION-03
Maths4U Original · Short practice
A quantity has signed rate \(2t-4\) from t=0 to t=3. Find its net change.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-ACCUMULATION-04
Maths4U Original · Short practice
A quantity has rate \(3t-6\) from t=0 to t=4. Find its total variation.Enter one number or fraction. Round decimals to at least six decimal places when needed.