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Guided Self-Placement

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Mathematics Courses

The Arizona Western College math course placement process aims to help students determine the appropriate math course to register for. Please take some time to explore the course placements listed below. To ensure a successful placement, we urge students to engage in honest self-reflection regarding their past math experiences and academic goals. __ This is not a test__. This is a guide to help gauge your level of mathematics skills while you determine the math course to enroll in. Please answer the questions to the best of your ability and take your time.

*Note that not all programs require the same course placements. If you are unsure which course(s) may be needed for your program, please contact an advisor. If students believe that a higher level of math (MAT 220 and higher) is appropriate for their current skill set, they are encouraged to contact the Associate Dean of Mathematics, Science, Engineering, Wellness & Physical Education.*

**To access all the MAT courses for self-placement, please toggle the links below.**

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MAT 071 Guided Self Placement

**Course Description:** Introduction to algebra with an accelerated review of arithmetic skills.

You should consider enrolling in MAT 071 if most of the following statements describe you:

- I rely on the calculator to add, subtract, multiply, and divide whole numbers and decimals.
- I forgot (or did not learn) how to add, subtract, multiply, and divide fractions.
- I am not sure how to solve problems with percents and proportions.
- I have difficulty understanding how to solve a word problem.
- I have never liked math.
- I have always struggled in math classes, and I need extra support.
- I don’t know how to solve problems that have variables like
*x*or*y*.

**Course Description:** Overview of the techniques and skills of beginning algebra.

You should consider enrolling in MAT 081 if most of the following statements describe you:

- I know how to add, subtract, multiply, and divide whole numbers without a calculator.
- I know how to add, subtract, multiply, and divide decimals without a calculator.
- I know how to add, subtract, multiply, and divide fractions and mixed fractions.
- I feel comfortable solving problems involving percents without using a calculator.
- I feel comfortable solving basic word problems if the formulas are given in the problem.
- I can solve simple equations like
*5x -12 = 50*

**Course Description:** Logical development of the laws of algebra, factoring linear equations, simultaneous equations, functions and graph, exponents and radicals, quadratic equations.

Student should demonstrate satisfactory ability and understanding of the following MAT 081 Learning Outcomes (prior course in the MAT sequence):

- Use associative, commutative, and distributive properties.
- Simplify and evaluate algebraic expressions.
- Solve equations and inequalities in one variable.
- Distinguish between, and define, both relations and functions.
- Graph and use linear equations in two variables.
- Solve systems of linear equations in two variables.
- Use exponent rules.
- Perform algebraic operations with polynomials.
- Solve basic word problems.
- Solve and use formulas.
- Perform operations using scientific notation.

If you are familiar with and able to answer at least 7 of the following questions, then this class should be an appropriate placement.

- Divide: (30x
^{8 }+ 60x^{5 }+ 12x^{2}) ÷ 6x^{2} - Multiply: (x - 9y)(5x - 4y)
- Combine like terms: (7x
^{5 }- 14x^{3 }+ 21) - (9x^{5 }- 6x^{3 }+ 11) - Simplify: $\frac{-28{x}^{8}{y}^{3}}{35{x}^{5}{y}^{13}}$
- For the function ƒ(x) = x
^{3}-5x + 7, find ƒ(-2). - Write the equation for a line passing through (-3, 5) and has a slope of m= $\frac{4}{3}$.
- Solve: four less than ten times a number is the same as twelve times the number. Find the number.
- Solve: 3(2x - 4) = 5(x + 3)
- Simplify: 5 ⋅ 3 - 8(3)
^{2}÷ (-2) - Convert 65 miles per hour to kilometers per hour if 1 mile equals 1.61 kilometers.

**Course Description:** Applications in statistics, probability, finance, discrete mathematics, and other selected topics of interest in management science, voting systems, and geometry.

If you agree with or think you may be able to correctly answer at least 9 of the following questions without a calculator, then MAT 142 should be an appropriate placement.

- My home and work obligations allow me to spend 6 hours or more a week working on math outside of class. An online course may require at least 10 hours a week.
- I have the self-discipline to complete homework assignments and study outside of class.
- I will seek tutoring outside of class if I am having problems with the material.
- Reduce $\frac{36}{81}$ to its simplest form.
- Rewrite $7\frac{1}{6}$ as an improper fraction.
- Rewrite 0.23 as a percent.
- Rewrite $\frac{3}{5}$ as a percent.
- Evaluate and reduce your answer to lowest terms: $\frac{15}{8}\times \frac{64}{27}$
- Solve for x : 4x - 13 = 23
- Evaluate and write your answer in lowest terms: $\frac{3}{4}-\frac{4}{7}$
- Evaluate the expression x
^{2 }- 3y for x = 5 and y = 3 - For the function ƒ
*(x)*= 5(2)^{x}, find the value of ƒ*(x)*when x = 3.

**Course Descriptions:**

**MAT 150, 151:** Extension and further development of algebra, with an emphasis on functions – including linear, quadratic, rational, radical, exponential and logarithmic. Other topics include function transformations, regression analysis, inequalities, absolute values, systems of equations, matrices, sequences, and series.

**MAT 187:** Development of algebra with a concentration on functions and a study of exponentials, logarithms, sequences, and series. It also includes a study of trigonometric functions and identities.

Student should demonstrate satisfactory ability and understanding of the following MAT 121 Learning Outcomes (prior course in the MAT sequence):

- Factor polynomials.
- Assess and solve absolute value equations and inequalities in one variable.
- Identify, solve, and find domains and ranges of functions.
- Simplify and perform algebraic operations on rational expressions.
- Solve equations containing rational expressions.
- Simplify expressions containing radicals and rational exponents.
- Solve equations comprised of radical and rational exponents.
- Find real and complex roots of quadratic equations.

If you are familiar with and able to answer at least 7 of the following questions correctly, then MAT 150 should be an appropriate placement. If you are able to answer at least 9 questions correctly, then MAT 151 may be an appropriate class for you to enroll in. If you are able to answer at least 11 questions correctly, then MAT 187 may be an appropriate placement.

- Evaluate: (9 - 13)
^{2}+ 15 ÷ (-3) - Multiply using the distributive property and collect like terms, if possible: 4x(5x - 2) - 2(x
^{2 }- 3x). - For the function ƒ(x) = x
^{3 }-5x + 7, find ƒ(-2). - Solve for x. Express your answer in lowest terms: $\frac{x}{2}-\frac{x}{8}=\frac{3}{4}$
- Evaluate the expression:

- Solve: 3(x + 6) = -2 (4x - 1) + x
- Libby’s four quiz grades in her math class are 89, 87, 80, and 81. What score does Libby need to obtain on her next quiz to get an average of 85 on her quizzes?
- Solve and graph the solution on a number line: 2x + 7 < 4x + 27
- Factor: 3x
^{2 }- 5x - 2 - Factor completely: 5x
^{2}-45 - Simplify:

- A 13-foot ladder rests against a wall. The base of the ladder is 5 feet from the wall. How far is the top of the ladder from the ground?
- What is the maximum value of f(x) = -3(x + 5)
^{2 }- 4? - Solve x
^{2 }= x + 1

#### MAT 121

**Answer key:** (Note: These should be hidden by default and only visible if students click on “Answer key”)

**1.)** 5x^{6 }+ 10x^{3 }+ 2 ; **2.)** 5x^{2 }-49xy + 36y^{2 }; **3.)** -2x^{5 }-8x^{3 }+ 10; **4.) $\frac{-4{x}^{3}}{5{y}^{10}}$ 5.)** ƒ(-2) = 9 ;

**6.)** y = $\frac{4}{3}x+9$ ; **5.)** ƒ(-2) = 9; **7.)** The number is -2 ; **8.)** x = 27 ; **9.)** 51; **10.)** 104.65 kilometers per hour. ** **

#### MAT 142

**Answer key:**

**4.)** $\frac{4}{9}$ ; **5.)** $\frac{43}{6}$ ; **6.)** 23% ; **7.)** 60% ; **8.)** $\frac{40}{9}$ ; **9.)** x = 9; **10.)** $\frac{5}{28}$; **11.)** 16; **12.)** ƒ(3)=40

#### MAT 150, 151, and 187

**Answer key:**

**1.)** 11; **2.)** 18x^{2 }- 2x ; **3.)** 9; **4.)** x = 2; **5.)** $-\frac{8}{27}$; **6.)** x = $-\frac{16}{10}$ or $-\frac{8}{5}$ ; **7.)** Libby needs an 88 on her next quiz; **8.)** x > -10; **9.)** (3x + 1)(x - 2) ; **10.)** 5(x - 3)(x + 3); **11.)** $\frac{64{a}^{6}{b}^{9}}{27{c}^{3}}$ ; **12.)** The top of the ladder is 12 feet from the ground; **13.)** The maximum value is -4 ; **14.)** x= $\frac{1\pm \sqrt{5}}{2}$