Date: May 3, 2012 Eta/l; / *1 a; "'14
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Test: Ch 6 Introduction to Vectors 17 13 9 7
Knowledge and Understanding
1. The diagram shows a parallelepiped. Determine a single vector (with head and tail on the parallelep
EXAM REVIEW FOR MCV 4U1
VECTORS AND CALCULUS
Study Tips:
The best way to study for a math exam is to redo all Unit Quizzes and Tests.
Write out all of your formulas and key concepts in one place to help you remember everything since no
formulas will be
Answers to Exam Review for MCV 4U1
Answers:
1.
a)
2. a)
b)
6
13
b)
3
2
1
8
c)
d)
1
48
e)
1
10
Discontinuous at x = 2 with a hole, conditions 1 and 2 fail
Discontinuous at x = 10 with a vertical asymptote, conditions 1, 2 and 3 fail.
Discontinuous at x = 4
Cumulative Review of Calculus,
pp. 267270
1. a. f ( x ) 5 3x2 1 4x 2 5
f (a 1 h) 2 f (a)
m 5 lim
hS0
h
f (2 1 h ) 2 15
5 lim
hS0
h
3 (2 1 h )2 1 4(2 1 h ) 2 5 2 15
5 lim
hS0
h
12 1 12h 1 3h 2 1 8 1 4h 2 20
5 lim
hS0
h
3h 2 1 16h
5 lim
hS0
h
5 lim 3h 1 16
CHAPTER 2
Derivatives
Review of Prerequisite Skills,
pp. 6263
1. a. a5 3 a3 5 a5 1 3
5 a8
b. A 2 2a2 B 3 5 ( 2 2)3 A a2 B 3
5 2 8 A a2 3 3 B
5 2 8a6
7
4p 3 6p9
24p7 1 9
c.
5
12p15
12p15
5 2p16 2 15
5 2p
4 25
26 22
d. A a b B A a b B 5 A a4 2 6 B A b25 2 2
CHAPTER 3
Derivatives and Their Applications
Review of Prerequisite Skills,
pp. 116117
1. a.
3
2
1
y
6
4
2
123
f.
y
x
6 4 2 0
2
4
6
c.
6
4
2
246
y
x
6 4 2 0
2
4
6
d.
6
4
2
6 4 2 0
2
4
6
246
y
x
246
Calculus and Vectors Solutions Manual
12
8
4
y
x
6 4 2 0
CHAPTER 6
Introduction to Vectors
Review of Prerequisite Skills, p. 273
1
"2
e.
2
2
"3
b. 2 "3
d.
f. 1
2
2. Find BC using the Pythagorean theorem,
AC 2 5 AB 2 1 BC 2.
BC 2 5 AC 2 2 AB 2
5 102 2 62
5 64
BC 5 8
opposite
Next, use the ratio tan A 5 adjacent
CHAPTER 7
Applications of Vectors
m 2 5 52 1 122 2 2(5)(12) cos 135
2 !2
5 25 1 144 2 120 a
b
2
5 169 1 84.85
5 253.85
Review of Prerequisite Skills, p. 350
1. The velocity relative to the ground has a
magnitude equivalent to the hypotenuse of a
triangle
CHAPTER 5:
Derivatives of Exponential and
Trigonometric Functions
Review of Prerequisite Skills,
pp. 224225
1
32
1
5
9
2
5
b. 325 5 Q "32 R 2
5 22
54
1
2
c. 2723 5 3
2
Q "27 R
1
52
3
1
5
9
32
2 22
d. a b 5 a b
3
2
9
5
4
2. a. log5 625 5 4
1
b. log4
5 22
1