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## 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.

PART 1: Elementary Algebra and Logical Reasoning
Prime factorization of an integer
Rounding an integer
Laws of exponents, particularly for integer exponents
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
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., x4 - 7x2 + 12 = 0, or 1 + 2/x - 15/x2 = 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