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ECON 1530 A: Introductory Mathematical Economics I

INSTRUCTIONS.

1. This test has 4 questions. Everyone must answer each question. Ques-tions 1 and 2 are worth 10 marks each. Questions 3 and 4 are worth 5 marks each.

2. Write all of your answers on separate pages. Show all work for all parts of all questions.

3. This is an open book exam. You may consult any information source that is not alive. You may not submit answers that are downloaded from bulletin boards or chat rooms.

4. The test began at 9:30 AM EST. You have 1.0 hour and 15 minutes (75 minutes) to complete and submit your answers to the test questions. After 10:45 AM, submissions will no longer be accepted. Once you submit something, it cannot be changed. To begin the submission process, click the assignment/test title on the eClass course home page where you downloaded the test. If you have last minute concerns, search at: https://lthelp.yorku.ca/submitting-an-assignment.

5. Your submission should include:

i. On your first submitted page, provide your name, student number and signature.

ii. Additional submissions (attachments) will contain your answers to the 4 questions. Please number all pages.

iii. Your attachments can be .jpg (camera) or .pdf (scan) files. Files of type .pdf are strongly preferred.

iv. Please note that picture and scan files can quickly become large. Please set your camera or scanner to the lowest resolution so that your answers are still legible. If submitting pictures, make sure the picture is not too bright or too dark and that you have not accidentally cut off part of your answers.

v. During the submission process, the system will ask you to declare the originality of your work by checking a box.

vi. At the end of the process you will need to press a submission button to finalize you submission. If you don’t, the system will only store you solutions files as drafts.

ANSWER THE FOLLOWING 4 QUESTIONS.

NOTE: Questions 1 and 2 are worth 10 marks each: Questions 3 and 4 are worth 5 marks each.

Question 1. [10 marks]

Define the function Assume c is a positive parameter.

i. Find the roots of this quadratic.

ii. Define the axis of symmetry and explain how it is related to the roots.

iii. Does reach a maximum or a minimum and at which value of x. Do not use calculus.

iv. What is the value of at the maximum or minimum?

v. Graph showing what you discovered in parts i, ii, iii and iv above.

Question 2. [10 marks]

i. Find the equation of the straight line that goes through the points A = (4, −1) and B = (0, 3). Call it Line 1.

ii. Find the equation of the straight line that goes through the points C = (0, 1) and D = (2, 3). Call it Line 2.

iii. Calculate the point where Line 1 intersects Line 2. Show all work.

iv. Graph Line 1, Line 2, points A, B, C and D and the intersection point.

Question 3. [5 marks]

Define the function:

i. Obtain the domain of . Explain how you got your result.

ii. Obtain the range of . Explain how you got your result.

iii. Graph using the information in i and ii (above).

Question 4. [5 marks].

Define the fraction Define the fraction Assume that a, b, c, d are parameters not equal to 0.

i. Simplify

ii. Simplify where e is a parameter not equal to 0.

iii. Simplify a/b/c/d/e.