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