# Preparing for the Math Placement Exam

In order to achieve placement into MATH 100: Mathematical Sampler or MATH 101: Finite Mathematics, you will need to demonstrate mastery of the following topics

- Arithmetic of Real Numbers
- Add, subtract, multiply, divide (positive and negative whole numbers, fractions, and decimals)

- Linear Equations
- Solving first-degree equations

- Proportions
- Solving proportions using cross-multiplication

- Percents
- Converting percents to decimals and decimals to precents

- Area
- Area formulas for basic shapes

- Algebraic Expressions
- Combining like terms
- Evaluating Algebraic expressions

- Graphs of lines
- Rectangle coordinate system
- x- and y - intercepts
- Slope intercept form

- Rational Expressions
- Simplifying, multiplying, and Dividing rational expressions

In order to achieve placement into MATH 108: Calculus with Review I, you will need to demonstrate mastery of the following topics:

- Everything listed above for MATH 101/MATH 100
- Quadratic equations
- Solving quadratic equations by factoring, square root method, completing the square, and quadratic formula

- Solving equations involving radicals
- Equations involving square roots

- Exponents and radicals
- Properties of exponents
- Negative integers as exponents
- Zero as an exponent
- Change radicals to simplest radical form

- Systems of equations
- The substitution method
- The elimination method

In order to achieve placement into MATH 111: Business Calculus, you will need to demonstrate mastery of the following topics:

- Everything listed above for MATH 100/101 and MATH 108
- Properties of functions
- Add, subtract, multiply, divide two functions
- Determine the domain and range of functions
- Linear functions
- Quadratic functions

- Compositions of functions
- Evaluating composite functions
- Determine the domain and range of composite functions

- Rational functions
- Graphing rational functions

- Logarithms
- Properties of logarithms
- Solving logarithm equations

- Inverse functions
- Determine whether a function is one-to-one
- Verify inverse functions

- Polynomials
- Synthetic division
- Graphing higher-order polynomial functions

In order to achieve placement into MATH 113: Calculus I, you will need to demonstrate mastery of the following topics:

- Everything listed above for MATH 100/101, MATH 108, and MATH 111
- Radiansand degrees
- Convert radians to degrees
- Convert degrees to radians

- Sine, cosine, and tangent of special angles
- Definition of trigonometric functions

- Trigonometric identities
- Reciprocal identities
- Pythagorean Identities
- Quotient Identities
- Sum-Difference Formulas
- Double Angle Formulas

- Graphs of trigonometric functions
- Find period and amplitude

- Solving trigonometric equations
- Find all solutions and solutions on particular intervals

**Review Materials**

Review questions are available at http://act.org/compass/sample/index.html. Students hoping to achieve placement into MATH 100 or 101 will need to be very strong in the Pre-Algebra material and have some competence in Algebra; students hoping to achieve placement into MATH 108 will need to be strong in Algebra (and Pre-Algebra), students hoping to achieve placement into MATH 111 will need to be strong in College Algebra (and Algebra/Pre-Algebra); students hoping to achieve placement into MATH 113 will need to be strong in Trigonometry (and Pre-Algebra, Algebra, and College Algebra).

**MATH 005 and MATH 006**

St. Thomas offers 0 credit Basic Math Skills classes, numbered MATH 005 and MATH 006, for students needing to achieve placement into MATH 100, MATH 101, or MATH 108. MATH 005 and MATH 006 are offered every fall, J-term, and spring. The cost for each course course in 2016-2017 is approximately $300. For more information, see their descriptions in the undergraduate course catalog or contact Olga Lopukhova, the course coordinator, at olopukhova@stthomas.edu.