Differentiation
Differentiation - Past Edexcel Exam Questions
1. (Question 2 - C1 May 2018)
Given
√
y = 3 x − 6x + 4, x>0
(a) (Integration Question)
dy
(b) i. Find dx
.
dy
ii. Hence find the value of x such that dx
= 0.
[4]
2. (Question 10 - C1 May 2018)
Figure 3 shows a sketch of part of the curve C with equation
1 27
y = x+ − 12, x>0
2 x
The point A lies on C and has coordinates 3, − 32 .
(a) Show that the equation of the normal to C at the point A can be written as
10y = 4x − 27. [5]
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, Differentiation
(b) (Simultaneous Equations Question)
3. (Question 2 - C1 May 2017)
Given
√ 4
y= x + √ + 4, x>0
x
dy
√
find the value of dx
when x = 8, writing your answer in the form a 2, where a is a
rational number. [5]
4. (Question 7 - C1 May 2017)
The curve C has equation y = f (x), x > 0, where
6 − 5x2
f 0 (x) = 30 + √ .
x
Given that the point (4, −8) lies on C,
(a) find the equation of the tangent to C at P , giving your answer in the form
y = mx + c, where m and c are constants. [4]
(b) (Integration Question)
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, Differentiation
5. (Question 10 - C1 May 2017)
This figure shows a sketch of part of the curve y = f (x), x ∈ R, where
f (x) = (2x − 5)2 (x + 3).
(a) (Transformations Question)
(b) Show that f 0 (x) = 12x2 − 16x − 35. [3]
Points A and B are distinct points that lie on the curve y = f (x).
The gradient of the curve at A is equal to the gradient of the curve at B.
Given that point A has x-coordinate 3,
(c) find the x-coordinate of point B. [5]
6. (Question 7 - C1 May 2016)
Given that
1 2x3 − 7
y = 3x2 + 6x 3 + √ , x>0
3 x
dy
find dx
. Give each term in your answer in its simplest form. [6]
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Differentiation - Past Edexcel Exam Questions
1. (Question 2 - C1 May 2018)
Given
√
y = 3 x − 6x + 4, x>0
(a) (Integration Question)
dy
(b) i. Find dx
.
dy
ii. Hence find the value of x such that dx
= 0.
[4]
2. (Question 10 - C1 May 2018)
Figure 3 shows a sketch of part of the curve C with equation
1 27
y = x+ − 12, x>0
2 x
The point A lies on C and has coordinates 3, − 32 .
(a) Show that the equation of the normal to C at the point A can be written as
10y = 4x − 27. [5]
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, Differentiation
(b) (Simultaneous Equations Question)
3. (Question 2 - C1 May 2017)
Given
√ 4
y= x + √ + 4, x>0
x
dy
√
find the value of dx
when x = 8, writing your answer in the form a 2, where a is a
rational number. [5]
4. (Question 7 - C1 May 2017)
The curve C has equation y = f (x), x > 0, where
6 − 5x2
f 0 (x) = 30 + √ .
x
Given that the point (4, −8) lies on C,
(a) find the equation of the tangent to C at P , giving your answer in the form
y = mx + c, where m and c are constants. [4]
(b) (Integration Question)
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, Differentiation
5. (Question 10 - C1 May 2017)
This figure shows a sketch of part of the curve y = f (x), x ∈ R, where
f (x) = (2x − 5)2 (x + 3).
(a) (Transformations Question)
(b) Show that f 0 (x) = 12x2 − 16x − 35. [3]
Points A and B are distinct points that lie on the curve y = f (x).
The gradient of the curve at A is equal to the gradient of the curve at B.
Given that point A has x-coordinate 3,
(c) find the x-coordinate of point B. [5]
6. (Question 7 - C1 May 2016)
Given that
1 2x3 − 7
y = 3x2 + 6x 3 + √ , x>0
3 x
dy
find dx
. Give each term in your answer in its simplest form. [6]
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