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
For \(y=x^3-4x\), find \(\displaystyle \frac{dy}{dx}\) at \(x=2\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
For \(y=\sqrt{x}+x^{-1}\), find \(\displaystyle \frac{dy}{dx}\) at \(x=4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
For \(y=(3x-2)^4\), find \(\displaystyle \frac{dy}{dx}\) at \(x=1\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
On \(y=x^2\), the chord from \(x=3\) to \(x=3+h\) has gradient \(6+h\). What value does this approach as \(h\to0\)?Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
For \(y=2x^3-5x\), find \(\displaystyle \frac{dy}{dx}\) at \(\displaystyle x=2\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
For \(y=\sqrt{x}+x^{-1}\), find \(\displaystyle \frac{dy}{dx}\) at \(\displaystyle x=1\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
For \(y=(2x+1)^3\), find \(\displaystyle \frac{dy}{dx}\) at \(\displaystyle x=1\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Maths4U Original · Short practice
On \(y=x^2\), the chord from \(\displaystyle x=-2\) to \(\displaystyle x=-2+h\) has gradient -4+h. Find the limiting gradient as h tends to zero.Enter one number or fraction. Round decimals to at least six decimal places when needed.