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Simon Fraser University
Math 100
Final Exam Date: April 17, 2007
Instructor: Sue Haberger Time: 8:30 – 11:30 am
Last Name (print):____________________________ First Name:_____________________
Signature:___________________________________ SFU Email ID:___________________
Instructions:
- Do not open this exam until instructed to do so.
- Ensure that you have 12 pages of questions numbered page 2 to page 13.
- No calculators, notes or books are allowed.
- Give all final numerical answers exactly, simplify all final expressions.
- For full marks, show all steps leading to your final answer. Clearly indicate your final
answer.
- Answer each question in the space provided. Use the back of the previous page if necessary
- if you do this, clearly instruct the marker “continued on back of previous page”.
Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total
Mark
Maximum 16 10 10 10 6 3 7 5 5 6 2 2 5 3 90
Final Exam
- (2 marks each) Give the exact simplified numerical value of each expression. Write
your final answer on the line provided
(Remember that expressions such as 5 , 4
! , e^3 , and ln 6 are exact numerical
values)
a) The value of
o 80 in radians = a) ___________
b)^3
4 7 8
0!
c) log 5! log ( )= 25
1 5 5 c) ___________
d) =
log 25 2
1 10 d) ___________
Final Exam
- Given two functions: 1
x
f x and ( ) 1
2 g x = x!
a) (3 marks) Evaluate exact and simplified:
!!(^6 )
f
g = (^) ( gf )( 0 )= ( g o f )( 0 )=
b) (2 marks) Give a simplified expression for ( f o g )( x )
c) (2 marks) Give a simplified expression for h
g ( 3 + h )! g ( 3 ) , (assume h! 0 )
d) (3 marks) Determine a formula for ( )
1 f x
! , the inverse of f ( x ).
State the range of
! 1 f.
1 f x
! = ____________________
Range of
! 1 f : ______________________
Final Exam
- (10 marks) Use the graph of f ( x ) shown to answer the questions:
a) f ( 0 )=_______________
b) f (! 5 )=_______________
c) For what values of x is f ( x )= 0?
_____________________________
d) As x "! , f ( x )!_________
e) As
(^) x! 3 , f ( x )!_________
f) Give the interval where f ( x ) is
decreasing: ___________________
g) Give the range of f ( x ) in interval
notation: _______________________
h) State the numbers (if any) at which
f ( x ) has a relative maximum:
_____________________________
i) Solve: f ( x )! 0 (answer in interval
notation):
______________________________
Final Exam
- (6 marks) For the graph of the quadratic function: ( ) 10 18
2 f x = x! x +
a) Give the y - intercept
b) Give the co-ordinates of the vertex
c) Give the exact value(s) of the x - intercepts.
d) Give the range in interval notation.
- (3 marks) Use sign analysis on the number line to solve the inequality:
4 3 2 x > x + 6 x
Final Exam
- For the polynomial function: ( ) 3 15 5
3 2 f x = x! x! x +
a) (3 marks) State the quotient and remainder when f ( x ) is divided by ( x + 2 )
b) (3 marks) Given that 3
1 is a zero of f ( x ) determine all the real zeros.
c) (1 mark) Which of the following could be the graph of f ( x )?
Write the letter of your choice: ________
Final Exam
- Solve each equation. Give all solutions in exact simplified form
a) (2 marks) 3 + log 2 ( x! 3 )=log 2 ( x + 11 )
b) (2 marks) 3 10
( 1 2 )
! x e
c) (2 marks) 2
ln( 10! 7 x )=^1
Final Exam
- (2 marks) If $20,000 is invested at an annual rate of 2
41 % compounded
continuously, how long (in years) would it take to grow to $25,000? (Give your answer
as an exact “calculator ready” expression)
- (2 marks) Simplify: cos( ) sin( ) 2
x +" + "! x =
Final Exam
- (3 marks) A track and field area is to be constructed in the shape of a rectangle with
semicircles at each end. The inside perimeter of the track is to be 400 metres. Find the
dimensions (length and width) of the rectangle that maximizes the area of the rectangular
portion of the field. Give exact answers.
Note: For a circle of radius r : Circumference: C = 2! r Area:
2 A =! r
