MCV 4U1
Unit 3 Review
This worksheet serves as an additional exercise to complement the lesson and the examples given.
Worksheets may take more than one day to complete. If you are stuck, read over the notes taken in class,
see the additional examples from the website, work with fellow students, and come to the tutoring lessons
after school. Complete solutions to all questions are available on the website. When in doubt do more!
In Exercises 1 – 30, find the derivative of the function.
5
1). y  x 
4). y 
3). y  2 sin x cos x
3
7
2). y  3  7 x  3 x
1 2 1
x  x
8
4
2 x 1
2 x 1
5). s  cos(1  2t )
 2
t
6). s  cot  
8). y  x 2 x 1
9). r  sec(1  3 )
2
2
10). r  tan (3   )
2
11). y  x csc 5 x
12). y  ln x
x
13). y  ln(1  e )
14). y  xe
16). y  ln(sin x )
17). y  ln(cos
19). s  log5 (t  7)
20). s  8
1
7). y  x  1 
x
22). y 
(2 x )2 x
x 2 1
25). y  t sec
1
28). y  2 x  1 csc
1
In Exercises 31- 34, find
1
21). y  x

29). y  csc
dy
1
ln x
24). y  sin
26). y  1t 2 cot
x
(1ln x )
2
18). r  log 2 ( )
x)
tan 1 x

1
ln t
2
15). y  e
t
23). y  e
t
x
1
27). y  z cos
2t
(sec x ),
1
1u 2
1
z  1 z 2
 1sin  

 1cos 
30). y  
0  x  2
2
.
dx
4
6
5
32). 5 x  10 y 5  15
31). xy  2 x  3 y  1
33).
xy  1
2
34). y 
x
x 1
In Exercises 35 – 38, find an equation for the (a) tangent and (b) normal to the curve at the indicated point.

35). y  x2 2 x , x  3
36). y  4  cot x  2 csc x , x 
2
2
2
37). x  2 y  9,
(1,2)
38). x  xy  6,
(4,1)
MCV 4U1
Unit 3 Review
39). Free Fall Suppose two balls are falling from rest at a certain height in centimeters above the ground.
2
Use the equation s  490t to answer the following questions.
A). How long does it take the balls to fall the first 160 cm? What is their average velocity for the period?
B). How fast are the balls falling when they reach the 160 cm mark? What is their acceleration then?
40). Filling a Bowl If a hemispherical bowl of radius 10 in. is filed with water to a depth of x in., the

 x  2
 x . Find the rate of increase of volume per inch increase of
 3 
volume of water given by V   10  

depth.
41).The graph of y  sin( x  sin x ) appears to have horizontal tangents at the x –axis. Does it?
200
, where t is the number of days
5t
1 e
since the measles first appeared, and P(t) is the total number of students who have caught the measles to
date.
A). Estimate the initial number of students infected with measles.
B). About how many students in all will get the measles?
C). When will the rate of spread of measles be greatest? What is the rate?
42). The spread of measles in a certain school is given by P (t ) 
2
d y
2
2
43). If x  y  1, find
at the point 2, 3 .
2
dx


MCV 4U1
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Unit 3 Review Solutions
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MCV 4U1
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