Loyola University Chicago



What topics are included in the Math Placement Assessment?

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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 
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., 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 
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 
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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