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## Math 103

**Math 134 - Intermediate Algebra**
**Final Exam Review**
**The following equations may be useful on the review.**
**The following equations may be useful while taking this exam.**
**Slope-Intercept Form: **y =

*mx *+

*b*
**Slope Formula: **
**Point-Slope Form: **y − 1

**Special Products:**
**Special Forms:**
*a *−

*b *= (

*a *+

*b*) (

*a *−

*b*)

*a *+ 2

*ab *+

*b *= (

*a *+

*b*) 2

*a *− 2

*ab *+

*b *= (

*a *−

*b*) 2

**Volume of a rectangular prism: **l w
**1.** *(4pt)* Complete the table of values. Then plot the solution points on the rectangular coordinate system.

**Determine whether the ordered pair is a solution of the equation.**
**2.** *(3pt)* 3

*y *+ 2

*x *= 12 , ( 4,2)

**3.** *(3pt)* −2

*x *+

*y *= 1 , ( 3

**Algebraically, find the x- and y-intercepts. **

Use the x- and y-intercepts to sketch the graph of the line.

All work (algebra) must be shown. DO NOT USE A TABLE OF VALUES.
**4.** *(3pt)* 2

*x *+ 4

*y *= 20

**Consider the relation. **
**5. ***g *:{ ( −3, )

**a. ***(1pt) *List the domain: __________________________________

**b. ***(1pt) *List the range: ___________________________________

**c.) ***(2pt)* Is the set a function? If yes,explain. If no, explain.

**Evaluate the following function at the given values. Show the substitution correctly. **

No Decimal Answer.
**6. ***(3pt) * *f *(

*x*) =

**Use the slope formula to find the slope of the line passing through the points.**
**7. ***(3pt) *( −2,5) , ( 3, − )

**Write the equation in slope-intercept form for the line containing the given pair of points. **
**8. ***(4pt) *( −2,3) and ( 2,5)

**Application Problems**
**9.** In 2002, Medicaid long-term care expenses totaled $92 billion. This figure had risen to $109 billion

by 2006. Let

*M *represent Medicaid long-term care expenses, in billions of dollars, and

*t *the number of years since 2000. Let

*t *= 0

* *represent 2000.

**a.) ***(2pt)* Represent the given information as two ordered pairs of the form (

*t*,

*M *) .

**b.) ***(3pt)* Write a linear equation in slope-intercept form that relates the long-term expenses

*M *to

**c.) ***(1pt)* What will the estimated Medicaid long-term expenses be in 2013?

Write a well-structured sentence with the units correctly stated.

**Use the rules of exponents to simplify the following expression. Write your answer using only positive **

exponents.
** 10.** *(3pt)* (

*a b * **11.** *(3pt)*

**12.** *(3pt)*
**13.** *(3pt)*

**Perform the indicated operation(s) and simplify the following algebraic expression:**
** 14.** *(3pt)*
+ −

*a *+ 5

*a *+ 3

*a *−

**15.** *(3pt)* ( 3

*y *−8) ( 9

*y *+ 3)

*(3pt)* (

*t *− 0.3

*t *− 20) −(

*t *−1.5

*t *+ 0.3

*t *− )

**17***. **(3pt)*
(

*x *+ 4)(

*x *− 2

*x *+1)

**Application Problems**
**18.** An electronics company is marketing a new kind of camera. Total revenue is the total amount of

money taken in. The company determines that when it sells

*x *cameras, its total revenue is given by

*R *= 175

*x *− 0.4

*x *.
Total cost is the total cost of producing

*x *cameras. The company determines that the total cost of
The total profit

*P * is the difference between revenue and cost.

**a.) ***(2pt)* Find the polynomial representing total profit

*P*.

**b.) ***(2pt)* Using the polynomial, calculate the total profit on the production and sale of 75 cameras.

**c.) ***(1pt)* Write a well-structured sentence(s) with the units correctly stated.

**Evaluate the expression.**
**a. ***(2pt)* Write the answer in decimal notation. _______________________________

**b ***(2pt)* Write the answer in scientific notation. _____________________________

**Evaluate the expression.**
**20. *** *
**a. ***(2pt)* Write the answer in decimal notation rounded to 2 decimal places. ______________________

**b ***(2pt)* Write the answer in scientific notation rounded to 2 decimal places. ____________________

**21.** Every day about 12.4 billion spam e-mails are sent. If each spam e-mail wastes 4 seconds, how many

**a.)** *(3pt)* Write the answer in scientific notation._________________________________

**b.)** *(3pt)* Write the answer in decimal form._____________________________________

**c.) ***(1pt)* Write a well-structured sentence(s) with the units correctly stated.

**Use Long Division to divide the polynomials. Show all your work.**
2

*t *− 9

*t *+11

*t *− 3

** No credit unless long division is shown.**
**Use Synthetic Division to divide the polynomials. Show all your work.**
** No credit unless synthetic division is shown.**
**Completely factor the following algebraic expressions.**
**24.** *(3pt)* 2

**25.** *(3pt)*
**26.** *(3pt)*
−8

*x *−8

*x *+ 30

**27. ***(3pt) *3

**Solve the following polynomial equations by factoring and using the zero-factor property.**
** 28.** *(4pt)* 2

**29.** *(4pt)*
** 30.** *(4pt)*
**Application Problems**
**31.** A photograph is 3inches longer than it is wide. Its area is 40 square inches. What is the length and

**a.) ***(2pt)* Write a quadratic equation to find the dimensions.

**b.) ***(2pt)* Solve the quadratic equation.

**c.) ***(1pt)* Write a well-structured sentence(s) with the units correctly stated.

**Application Problems**
**32.** Many people suffering from constricted bronchial muscles are prescribed the drug Albuterol. The

number of micrograms

*A *of Albuterol in a person’s bloodstream

*t *minutes after 200 micrograms have been inhaled can be approximated by:

**a.) ***(3pt)* Calculate how long after an inhalation will there be about 150 micrograms of Albuterol

**b.) ***(1pt)* Write a well-structured sentence(s) with the units correctly stated.

Source: http://www.olc.edu/~jdudek/webfolder/MST-Math-Final/MATH134-FINAL-EXAM-REVIEW.pdf

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