# Tips

## What topics are included in the Math Placement Assessment?

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**Preparation**If you have not taken mathematics in your senior year of high school or previous college, we recommend you thoroughly review Algebra I and II, Trigonometry, and Precalculus, if you have taken these courses previously. You may use your high school texts to review. If your course books are not available, then we recommend...

*Online Resources:*

Purple Math, Regents Exam Prep (stay with the math topics on LU's exam), and Khan Academy.

*Print Resources:*

**Part A: Elementary Algebra and Logical Reasoning**

Angel, Allen and Dennis Runde. *Intermediate Algebra for College Students,* 8th ed. Upper Saddle River, NJ: Pearson-Prentice Hall, 2010.

**Part B: Intermediate Algebra**

Angel, Allen and Dennis Runde. *Intermediate Algebra for College Students,* 8th ed. Upper Saddle River, NJ: Pearson-Prentice Hall, 2010.

**Part C: Advanced Algebra**

Axler, Sheldon, *Algebra and Trigonometry,* 1st edition, Hoboken, NJ: Wiley, 2012.

**Part D: Precalculus**

Axler, Sheldon, *Algebra and Trigonometry,* 1st edition, Hoboken, NJ: Wiley, 2012.

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**PART 1: Elementary Algebra and Logical Reasoning**

Prime factorization of an integer

Rounding an integer

Laws of exponents, particularly for integer exponents

Radicals

Simplify expressions

Evaluate an expression

Distance formula (Pythagorean theorem)

Scientific notation

Simple linear equations

Simple story problems: age, area, cost, constant speed, average of a set of numbers, business (tax, profit, discount)

Recognizing the value of a million, a billion, a trillion

Understanding perimeter and area of simple figures

Triangles: number of degrees in the sum of the angles; obtuse and acute angles; Pythagorean theorem; finding area of a right triangle

Circles: finding area and circumference

Percentages

Straight lines: slope, y-intercept, x-intercept

Linear inequalities

Parallel and perpendicular lines **PART 2: Intermediate Algebra**

Factoring polynomials

Division of polynomials

Absolute value

Simple inequalities

Language of functions

Quadratic formula

Meaning of the discriminant: number of real roots, number of complex roots

Finding the vertex of a parabola; finding maximum and minimum values of quadratics

Systems of two equations in two unknowns

Direct and inverse variation

Story problems **PART 3: Advanced Algebra**

Complex numbers, simplifying complex expressions

Factoring sum and difference of two cubes

Inverse functions and composition of functions

Quadratic-like equations (e.g., x^{4} - 7x^{2} + 12 = 0, or 1 + 2/x - 15/x^{2} = 0)

Theory of Equations

Remainder and factor theorems

Descartes' rule of signs

Polynomial division

Finding rational roots of polynomials with integer coefficients

Conjugate pairs theorem

Recognizing the sum and product of roots by looking at coefficients

Equations of circles: recognizing the center and the radius

Linear systems in two unknowns; recognizing inconsistent equations

Rational functions

Analyzing graphs: zeros, singularities, horizontal and vertical asymptotes

Systems of non-linear equations

Formulas for area of basic shapes and surface area and volume of basic solids (for example, cylinders or cubes)

Symmetry of functions (with respect to origin, or with respect to the y-axis)

Story problems revisited

Log and exponential functions

Properties of logs

Exponential growth and decay; doubling time for a growing population, half-life for decay

Compound interest

Limiting behavior of functions: how does y behave as x approaches plus or minus infinity **PART 4: Precalculus**

Recognizing linear functions from a table of data

Piecewise defined functions

Inverse functions

Composition of functions

Average rate of change of a function

Polynomial and Rational functions revisited

Power functions

Graphs of rational functions

Limiting behavior of functions

Understanding rate of growth of functions

Domain and range

Trigonometry

Definition of sine, cosine, tangent, cot, sec, csc

Laws of sines and cosines

Trig identities

Radian vs. degree measure

Periodicity of a function

Inverse trig functions

Logs and exponential functions revisited

Recognizing exponential growth from a table of data

Graphs

Compounding of interest

Properties of the log function; change of base formula

Limiting behavior of functions

Comparison of growth rates of power functions with exponential functions

Transformations of functions

Vertical and horizontal shifts

Reflections and symmetry

Vertical stretches and compressions

Horizontal stretches and compressions

Sequences and Series

Finite geometric series

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