Prep101
Math 100/180 Exam Solutions
I
Foundations
Practice Exam Problems
1.1.1
Limits
1.01
(a) Solution:
lim
x 3
( x 3) ( x 1)
x 2 4x 3
x 1
lim
lim
2
2
x 3 ( x 3) ( x 2)
x 3 x 2
x 5x 6
(b) Solution:
lim
x 3
2 ( x 3)
2x 6
2
1
lim
lim
2
x 3 ( x 1) ( x
SOLUTIONS
UBCMath100/180Exam
December2013ExamSolutions
x 2 2 x 15
( x 3) ( x 5)
x3
8
lim
lim
4
x 5
x 5
x 5
2 x 10
2 ( x 5)
2
2
_
1. (a)
lim
1. (b) Let g ( x) 2 x 3 and h( x) x 2 4 x 6 . Since g ( x) f ( x) h( x) for x 1 , and
lim g ( x) lim (2 x 3) 3
x
Mathematics 100 / 180
Formulas
What you must remember
Similar triangles
Two triangles T1 , T2 are similar when
(AAA angle angle angle) The angles of T1 are the same as the angles of T2 .
(SSS side side side) The ratios of the side lengths are the same.
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Math 180 Workshop - Problems #2, Week of January 19, 2015
Basic Skills required to work through the workshop problems:
factoring and simplifying expressions containing ratios and square roots of polynomials;
determining the domain of a function;
Learnin
The University of British Columbia
Final Examination - April 24, 2014
Mathematics 180
Closed book examination
Last Name
Time: 2.5 hours
First
Student Number
Signature
Section Number
Instructor
Special Instructions:
No books, notes, or calculators are allo
Math 180 Workshop - Problems #3, Week of September 22, 2014
Basic skills required to work through the workshop problems:
solving linear and quadratic equations;
nding the equation of a line given two points on the line or one point and the
slope;
nding
Identifying the difference between a quantity and the rate of change
of that quantity 1
In nature often one quantity will inuence the rate of change of another. Note the distinction between a
quantity and how quickly that quantity changes.
The rate of ch
Mathematics 180-102
Page 1 of 10
Student-No.:
Midterm 2
Duration: 45 minutes
This test has 5 questions on 10 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answer
Mathematics 180-101
Page 1 of 9
Student-No.:
Midterm 2
Duration: 45 minutes
This test has 5 questions on 9 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answer i
Mathematics 180-103
Page 1 of 8
Student-No.:
Midterm 2
Duration: 45 minutes
This test has 5 questions on 8 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answer i
MATH 180 Workshop 4 Quiz
Show all your work. Use back of page if necessary.
Last Name:
First Name:
UBC Stud. No.:
1. Consider the function
F (x) = f (xg(x)
obtained from some functions f and g.
(a) Suppose one of your group members claims that F (x) = f (
MATH 180 Workshop 3 Quiz
Show all your work. Use back of page if necessary.
Last Name:
First Name:
UBC Stud. No.:
1. (a) Find the equation of the tangent line to the curve y = 1/x2 at the point
(a, 1/a2 ).
Solution: The derivative is y = 2/x3 . Thus at th
Math 180 Workshop - Problems #4, Week of September 29, 2014
Basic skills required to work through the workshop problems:
identify a composite function and break it down into simpler functions using
products, quotients, function composition;
determining
Math 180 Workshop - Problems #1, Week of January 12, 2015
Basic Skills required to work through the workshop problems:
factoring quadratic and cubic polynomials;
manipulating (factoring, simplifying, razionalizing, etc.) expressions with ratios
and squa