CQMS702 - Assignment 3 with Accurate Solutions

Calculus for Business
CQMS702 - Test 1
May 19, 2026

CQMS702 - Assignment 3 with Accurate Solutions

Name: (Print) Last name:

(Print) First name:

Student number:

Section number:

Duration: 90 minutes




PLEASE DO NOT OPEN UNTIL INSTRUCTED TO DO SO.

Please read the instructions below before you begin writing.
1. Please print your name and student number in the space provided above.

2. Please do not remove the staple or detach the pages during the test.

3. The test consists of full-solution questions with the mark for each full solution as
indicated. Answer all questions in the space provided. Clearly explain your methods,
and show all relevant steps in the solution. An answer consisting only of the final
result will be given no credit.




Question 1 2 3 4 5 6 7 Total
Value 7 7 7 7 7 7 8 50
Marks



1

, Question 1. (7 points) Find the center and radius of the circle whose equation is given by
4x 2  4 y 2  12x  20 y  15  0
Show all of your work.

Solution. After we divide both sides by 4, we get

x 2  y 2  3x  5 y  154  0

 (x 2  3x)  ( y 2  5 y)  15
4


 (x 2  3x  9 )  ( y 2  5 y  25
) 15
9 25
4 4 4 4 4


 (x  3 ) 2  ( y  5 ) 2  49
 ( 7 )2
2 2 4 2


So, the center is at ( 3 , 5 ) , and the radius is 7
.
2 2 2




Question 2. (7 points) Find the domain of the function
y  |2 x 1 4x
 3| 5
Express your answer using the interval notations.


Solution The domain of the function is all x that satisfy
1  4x  0

| 2x  3 | 5  0
x  1
 4  x  1 ; x  4
x  4; x  1
4



So, the domain is

(  , 4)  (  4, 14 ]




2