We recommend you revisit your high school notes or books before taking the MPE.  The internet also provides a vast amount of resources on each of the topics below.

I. Algebra

Students should be able to

• Manipulate exponents
• Simplify algebraic expressions
• Perform operations with polynomials, including division with remainders
• Factor polynomials
• Complete the square
• Use Quadratic Formula
• Solve systems of equations
• Solve equations and inequalities
• Solve equations with rational expressions
• Construct algebraic expressions that represent quantities (word problems)

II. Functions

Students should be familiar with

• Domain and range
• Function notation and evaluation
• Function types, including

• absolute value
• polynomial
• rational
• exponential
• logarithmic
• trigonometric

• Composition of functions
• Graphs of functions

III. Trigonometry

Students should be familiar with

• Pythagorean Theorem
• Radian measure
• Unit circle / reference angles
• Sine, cosine, tangent of any angle
• Law of Cosines and Law of Sines

IV. Geometry

Students should be familiar with

• Equations of lines and parabolas
• Similar triangles
• Areas of simple figures, such as triangles, rectangles, trapezoids, and circles
• Volumes of simple solids, such as a box, a cylinder, or sphere