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-DIFFERENTIATION-TANGENTS-NORMALS-01
Maths4U Original · Short practice
Find the gradient of the tangent to \(y=x^2+1\) at \(x=3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Method · M4U-P1-QP-DIFFERENTIATION-TANGENTS-NORMALS-02
Maths4U Original · Short practice
Find the gradient of the normal to \(y=x^2+1\) at \(x=3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Apply · M4U-P1-QP-DIFFERENTIATION-TANGENTS-NORMALS-03
Maths4U Original · Short practice
The tangent to \(y=x^2\) at \(x=2\) has equation \(y=4x+c\). Find \(c\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Check understanding · M4U-P1-QP-DIFFERENTIATION-TANGENTS-NORMALS-04
Maths4U Original · Short practice
What is the normal to \(y=x^2\) at its vertex?Choose one answer.
Fresh review variant · M4U-P1-QP-VAR-DIFFERENTIATION-TANGENTS-NORMALS-01
Maths4U Original · Short practice
Find the tangent gradient to \(y=x^2+3\) at x=5.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-DIFFERENTIATION-TANGENTS-NORMALS-02
Maths4U Original · Short practice
Find the normal gradient to \(y=x^2+1\) at x=2.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-DIFFERENTIATION-TANGENTS-NORMALS-03
Maths4U Original · Short practice
The tangent to \(y=x^2\) at x=3 is \(y=6x+c\). Find c.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-DIFFERENTIATION-TANGENTS-NORMALS-04
Maths4U Original · Short practice
The normal at the vertex of \(y=(x-4)^2+2\) is \(x=k\). Find k.Enter one number or fraction. Round decimals to at least six decimal places when needed.