Midterm 1 Exam for MATH 100-D200 by R. Pyke, October 3, 2007, Exams of Calculus

The midterm 1 exam for math 100-d200, taught by r. Pyke, at simon fraser university, held on october 3, 2007. The exam covers various topics in mathematics, including solving inequalities, finding points on circles, determining symmetry and intercepts of equations, finding limits, and graphing functions. Students are required to clearly explain their answers and only scientific calculators are allowed.

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2012/2013

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MATH 100-D200 Instructor: R. Pyke
Midterm 1, October 3, 2007
Last Name:
First Name:
SFU Student email : @sfu.ca
1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.
2. Clearly explain your answer. No credit will be given for just
writing down the answer.
3. If the answer space provided is not sufficient, write your answer
on the back of the previous page.
4. Ordinary Scientific Calculators ONLY are allowed.
NO GRAPHING CALCULATORS ALLOWED.
5. Copying someone else’s test, or deliberately expos-
ing written papers to the view of others is forbidden
and will result in a score of zero and disciplinary
action.
Question Score Max
1 5
2 5
3 5
4 6
5 8
6 5
7 5
8 15
Total 54
Page 1 of 7
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MATH 100-D200 Instructor: R. Pyke

Midterm 1, October 3, 2007

Last Name:

First Name:

SFU Student email : @sfu.ca

1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.

2. Clearly explain your answer. No credit will be given for just

writing down the answer.

3. If the answer space provided is not sufficient, write your answer

on the back of the previous page.

4. Ordinary Scientific Calculators ONLY are allowed.

NO GRAPHING CALCULATORS ALLOWED.

5. Copying someone else’s test, or deliberately expos-

ing written papers to the view of others is forbidden

and will result in a score of zero and disciplinary

action.

Question Score Max 1 5 2 5 3 5 4 6 5 8 6 5 7 5 8 15 Total 54

(1) [Marks: 5] Solve the following inequality. Express your answer in interval notation. ∣∣∣ ∣^4 xx −+ 1 1

∣∣∣ ∣ >^2

(4) [Marks: 6] Determine whether the graphs of the following equations possess symmetry with respect to the x-axis, y-axis, or origin, and find any x and y intercepts.

(a) | 3 x^2 y | = 4

(b) 2 x^3 − y = y 2 x+ 1

(5) [Marks: 8] Find the following limits by simplifying the expression first.

(a) lim t→ 1 t −^1

 (t + 3)^12 − 161

 

(b) hlim→ 5

√u + 4 − 3

u − 5

(6) [Marks:5] Find the domain of the following function.

f (x) =

√x 2 − 3 x − 10

x^4 − 16

(c) Make a sketch of the graph.

(d) Find the points of intersection between this parabola and the line y = 3x − 3.

(e) From this, sketch the region in the xy-plane of the points (x, y) that satisfy the inequalities 3 x − 3 ≤ y ≤ − 3 x^2 + 24x − 36