IB DP Maths 4 hours 28 questions
Exam Questions
Differentiation
Introduction to Derivatives / Differentiating Powers of x / Gradients, Tangents &
Normals / Increasing & Decreasing Functions / Local Minimum & Maximum
Points / Modelling with Differentiation
Medium (10 questions) /71 Scan here to return to the course
or visit savemyexams.com
Hard (9 questions) /82
Very Hard (9 questions) /88
Total Marks /241
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,Medium Questions
3
1 (a) The equation of a curve is y = x 2 − 15x + 2
2
dy
Find .
dx
(2 marks)
(b) The gradient of the tangent to the curve at point A is −3 .
Find
(i) the coordinates of A
(ii) the equation of the tangent to the curve at point A Give your answer in the form
y = mx + c .
(4 marks)
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,2 (a) Consider the function f (x ) = 3x 7 − 12x .
Find f ' (x ) .
(1 mark)
(b) Find the gradient of the graph of f at x = 0 .
(2 marks)
(c) Find the coordinates of the points at which the normal to the graph of f has a gradient of 4 .
(3 marks)
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, 4
3 (a) The equation of a curve is y = 4 − .
x
Find the equation of the tangent to the curve at x = 2 .
Give your answer in the form y = mx + c .
(3 marks)
(b) Find the coordinates of the points on the curve where the gradient is 16.
(3 marks)
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Exam Questions
Differentiation
Introduction to Derivatives / Differentiating Powers of x / Gradients, Tangents &
Normals / Increasing & Decreasing Functions / Local Minimum & Maximum
Points / Modelling with Differentiation
Medium (10 questions) /71 Scan here to return to the course
or visit savemyexams.com
Hard (9 questions) /82
Very Hard (9 questions) /88
Total Marks /241
© 2026 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 1
,Medium Questions
3
1 (a) The equation of a curve is y = x 2 − 15x + 2
2
dy
Find .
dx
(2 marks)
(b) The gradient of the tangent to the curve at point A is −3 .
Find
(i) the coordinates of A
(ii) the equation of the tangent to the curve at point A Give your answer in the form
y = mx + c .
(4 marks)
© 2026 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 2
,2 (a) Consider the function f (x ) = 3x 7 − 12x .
Find f ' (x ) .
(1 mark)
(b) Find the gradient of the graph of f at x = 0 .
(2 marks)
(c) Find the coordinates of the points at which the normal to the graph of f has a gradient of 4 .
(3 marks)
© 2026 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 3
, 4
3 (a) The equation of a curve is y = 4 − .
x
Find the equation of the tangent to the curve at x = 2 .
Give your answer in the form y = mx + c .
(3 marks)
(b) Find the coordinates of the points on the curve where the gradient is 16.
(3 marks)
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