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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Maths4U Original · Short practice
A model has \(Q(t)=t^3-3t^2+12\). Find its instantaneous rate at \(t=3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
The signed rate is \(q(t)=3t^2-6t\). Find the net change from \(t=0\) to \(t=3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
For \(Q(t)=t^3-3t^2+12\), find the minimum value on \(0\le t\le3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
A rate is measured in litres per second and integrated with respect to time in seconds. What units does the integral have?Choose one answer.
Maths4U Original · Short practice
A model has \(Q(t)=t^3-4t^2+20\). Find its instantaneous rate at \(\displaystyle t=4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
A model has signed rate \(3t^2-6t\). Find its net change from \(\displaystyle t=0\) to \(\displaystyle t=4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
Find the minimum of \(Q(t)=t^3-6t^2+50\) on \(0\le t\le5\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
A flow is constant at 4 litres/second for 7 seconds. Find the accumulated volume in litres.Enter one number or fraction. Round decimals to at least six decimal places when needed.