EXAM REVIEW FOR MCV 4U1 VECTORS AND CALCULUS

EXAM REVIEW FOR MCV
4U1 VECTORS AND
Study Tips: CALCULUS
 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 given on the exam.
 Complete the following extra exercises

Reminders:
 DO NOT COME TO YOUR EXAM WITHOUT BRINGING YOUR TEXTBOOK TO RETURN
 Bring your own calculator, pencil, eraser and ruler to the exam (No sharing allowed)
 There are no formula sheets, questions or dictionaries allowed during the exam.

ADDITIONAL REVIEW EXERCISES
NOTE:
 These review exercises do NOT cover the entire course. Make sure that you look over your old tests and
class notes so that you identify any missing details.

PART A: CALCULUS

Limits, Continuity, and First Principles:
1. Evaluate each limit, if it exists.

1 1
a) lim x2  9 b) lim x 1  3 c) lim 2  x  4
3
x3 x2  7x  30 x2 x2 x2 2x  4
1
d) (x  64)3  4 e) lim x2  x3  2x
lim
x0 x x 5x  x  2x2 

2. Determine all discontinuities and state which conditions of continuity fail for each discontinuity.
3x2 1, x  4
a) f (x) 3x  6 
x2  8x  20 b) f (x)  10, 0  x  4
 5x
 2
3x 10, x  0

3. Find the derivative of each function using FIRST PRINCIPLES.

a) f (x)  3x2  2x 1 3
b) f (x) c) y  4  2x  3
 2x

Derivatives and Basic Applications
4. Find for each curve. (Do not simplify your final
dy answer.)
7 x7 x1  x2 sec x3
dx 2 3x  2
2
4
a) y   5  x b) y y d) y  x e  8 i4
 3 
5x
x 2
c)
4
e4x  4x
5x
3y  8x y  2x  h) y  7x2 cos x2 tan 2x  5
2 2
e) f) 7xy3  2xy  3y 4 g) y  (9 x)5
5 log3

,  
i) y  sin log 5x2   3   cot2 cos ln  6x  4
 