Di erentiation - Past Edexcel Exam Questions
Differentiation
Differentiation - Past Edexcel Exam Questions
1. Given
y = 3 x - 6x + 4,
(Question 2 - C1 May 2018) x>0
(a) (Integration Question)
(b)
i.
Find
dy dx
.
ii.
Hence find
the
value
of
x
such
that
dy dx
= 0.
[4]
2.
(Question 10 - C1 May 2018)
Figure 3 shows a sketch of part of the curve C with equation
y
=
1 2
x
+
27 x
-
12,
x>0
The point A lies on C and has coordinates
3,
-
3 2
.
(a) Show that the equation of the normal to C at the point A can be written as
10y = 4x - 27.
[5]
c StudyWell Publications Ltd. 2020
(b) (Simultaneous Equations Question)
Differentiation
3.
(Question 2 - C1 May 2017)
Given
y
=
x
+
4 x
+
4,
x>0
find
the
value
of
dy 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
f
(x)
=
30
+
6
-5x2 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)
c StudyWell Publications Ltd. 2020
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 (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
y
=
3x2
+
6x
1 3
+
2x3- 3x
7
,
x>0
find
dy dx
.
Give
each
term
in
your
answer
in
its
simplest
form.
[6]
c StudyWell Publications Ltd. 2020
Differentiation
7.
(Question 11 - C1 May 2016)
The curve C has equation y = 2x3 + kx2 + 5x + 6, where k is a constant.
(a)
Find
dy dx
.
[2]
The point P , where x = -2, lies on C. The tangent to C at the point P is parallel to the line with equation 2y - 17x - 1 = 0. Find
(b) the value of k,
[4]
(c) the value of the y-coordinate of P ,
[2]
(d) the equation of the tangent to C at P , giving your answer in the form
ax + by + c = 0, where a, b and c are integers.
[2]
8.
(Question 3 - C1 May 2015)
Given
that
y
=
4x3
-
5 x2
,
x
=
0,
find
in
their
simplest
form
(a)
dy dx
[3]
(b) (Integration Question)
9. The curve C has equation
(Question 6 - C1 May 2015)
y = (x2 + 4)(x - 3) , 2x
x=0
(a)
Find
dy dx
in
its
simplest
form.
[5]
(b) Find an equation of the tangent to C at the point where x = -1.
Give your answer in the form ax + by + c = 0 where a, b and c are integers. [5]
c StudyWell Publications Ltd. 2020
Differentiation
10.
(Question 10 - C1 May 2015)
A curve with equation y = f (x) passes through the point (4, 9).
Given that
f
(x)
=
3x 2
-
9 4x
+
2,
x>0
(a) (Integration Question)
Point P lies on the curve. The normal to the curve at P is parallel to the line 2y + x = 0.
(b) Find the x-coordinate of P .
[5]
11.
(Question 7 - C1 May 2014)
Differentiate with respect to x, giving each answer in its simplest form.
(a) (1 - 2x)2
[3]
(b)
x5+6x 2x2
[4]
12.
(Question 6 - C1 May 2015)
A curve with equation y = f (x) passes through the point (4, 25).
Given that
f
(x)
=
3 8
x2
-
10x-
1 2
+
1,
x>0
(a) (Integration Question)
(b) Find an equation of the normal to the curve at the point (4, 25).
Give your answer in the form ax + by + c = 0, where A, b and c are integers to be
found.
[5]
c StudyWell Publications Ltd. 2020
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