St Andrew’s Academy
Mathematics Department
Higher Mathematics
REL 1.3 (Differentiation 1)
ASSESSMENT PREPARATION
DIFFERENTIATION 1 PRACTICE
RELATIONSHIPS 1.3
PRACTICE A
1.
Given y 
dy
1  x4
, find
.
2
dx
x
(4)
2.
The diagram shows a sketch of the curve
with equation y  x 2  6 x  8 with a tangent
drawn at the point (5,3).
y
.
Find the equation of this tangent.
(b) Explain why a tangent to the curve
at (3,2) is parallel to the x-axis.
o
(5,3)
x
(4)
3.
(a)
Differentiate  6 cos x with respect to x.
(1)
(b)
Given y 
1
sin x ,
3
find
dy
.
dx
(1)
PRACTICE B
x4  2
dy
, find
.
3
x
dx
1.
Given y 
2.
The diagram shows a sketch of the curve
with equation y  x 2  10 x  24 with a tangent
drawn at the point (7,3).
(a)
Find the equation of this tangent.
(b)
Explain why a tangent to the curve
at (5,2) is parallel to the x-axis.
St Andrew’s Academy Maths Department 2016-17 (HIGHER)
(4)
y
y  x 2  10 x  24
.
o
(7,3)
x
(4)
2
3.
(a)
Differentiate 2 cos x with respect to x.
(1)
(b)
Given y  5 sin x , find
dy
.
dx
(1)
PRACTICE C
3  x6
dy
, find
.
4
x
dx
1.
Given y 
2.
y
The diagram shows a sketch of the curve
with equation y  x 2  12 x  35 with a tangent
drawn at the point (4,3).
(4)
(a)
Find the equation of this tangent.
(b)
Explain why a tangent to the curve
at (6,-3) is parallel to the x-axis.
o
(4,3)
.
x
(4)
3.
(a)
Differentiate  12 sin x with respect to x.
(1)
(b)
Given y  2 cos x , find
dy
.
dx
(1)
St Andrew’s Academy Maths Department 2016-17 (HIGHER)
3
MARKING SCHEME
PRACTICE A
dy
1.
 2 x  3  2 x
dx
4 x  y  17  0
2.
dy
 0 and so the tangent is parallel to the x-axis
2b.
When x = 3,
dx
3.
(a) 6 sin x
(b)
dy 1
 cos x
dx 3
PRACTICE B
1.
2.
2b.
3.
dy
 1  6x4
dx
4 x  y  25  0
dy
 0 and so the tangent is parallel to the x-axis
When x = 5,
dx
(a)  2 sin x
(b)
dy
 5 cos x
dx
PRACTICE C
1.
2.
2b.
3.
dy
 12 x  5  2 x
dx
4 x  y  19  0
dy
 0 and so the tangent is parallel to the x-axis
When x = 6,
dx
(a)  12 cos x
(b)
dy
 2 sin x
dx
St Andrew’s Academy Maths Department 2016-17 (HIGHER)
4