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Chris is a Stanford-educated tutor with over 10 years experience tutoring COMPASS Placement Test to students of all abilities, from students struggling to get from a C to a B, to go-getters trying to move an A- up to an A, to struggling students just hoping to pass. In that time he got a lot of experience learning how to explain this stuff in a way it actually makes sense to normal people. Through his videos he has helped countless students, and he can do the same for you.

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COMPASS Math

About the test: The ACT COMPASS math test covers five basic content areas: Pre-Algebra, Algebra, College Algebra, Geometry, and Trigonometry. It is administered on the computer and is untimed. The test is adaptive. This means that the program will start giving you easier questions or harder questions depending on how you answered the previous ones. The routing is shown below. All students start with Algebra and it is very important to do well on this part of the test to make sure you get routed appropriately to the next part of the test.
Pre-Algebra <-Algebra->College Algebra->Geometry->Trigonometry
Calculators: Only basic 4 function calculators involved. See the link below for the list of approved models. There is also a calculator provided on the screen during the test. It will be very similar to what you might have on your phone (not an app, just the basic calculator function) or as the one on your computer
How to Study: Start by taking the official practice test using the link provided below. Since the test itself is untimed, allow yourself as much time as you need on the practice test as well. Use the same calculator as you will use on your test or better yet use the one on your computer to give you practice.
After you take the test, score yourself to see where your weaknesses are and use the table below to find the right video you need to brush up on or re-learn the topic. Of course, if you have unlimited time view them all!
Once you've studied, retake the test to find out where you've made improvement and where you still need work. You can retake the test as often as needed.
General Study Tips: If you haven't found them already, Chris has a great series of videos on HOW to study including how to counter math anxiety prior to a big test and the best ways to prepare. Study Tips
ACT COMPASS Practice Tests and Calculator Guidelines
Pre-Algebra
Content Category Skills Example Lessons
Operations with Integers Order of operations, adding, subtracting, multiplying, and dividing basic integers $72+4÷2+5$ Intro to PEMDAS
Operations with Fractions Adding, subtracting, multiplying, and dividing fractions $2/3+(3/4×1/2)+(3/4-1/3)$ Adding & Subtracting Fractions Multiplying & Dividing Fractions
Operations with Decimals Adding,subtracting,multiplying,and dividing decimals $7.46+1.85+2.5×3$ Decimals
Operations between mixed numbers and improper fractions Adding, subtracting, multiplying,and dividing using mixed numbers and improper fractions $7(1/2)+ 18.85+4(2/3)$ Improper Fractions and Mixed Numbers
Exponents Raising numbers to "a power" (how many times a number is multiplied by itself) $2^4+3^2$ Intro to Exponents Exponent Rules, Like Bases, & Negative Exponents
Square Roots A number that produces a specified quantity when multiplied by itself. $√4+√81$ Simplifying Roots & Radicals
Ratios and Proportions "Part over whole" or fractions that equals a similar fraction $X/2=12/8$ Ratios & Proportions
Percentages "A part" of a certain value which is used in operations. 20% of 100 + 30% of 60 Percents as Ratios Percent Increase & Decrease Percents As Decimals
Averages Another word for the "mean" which is a sum of all numbers in a set of data divided by the amount of numbers Steve tried to compute the average of his 5 test scores. He scored 86 on one, 55 on the next one, then 99, 77, and 90. What is Steve's average test score? Calculating The Mean (Average)
Algebra
Content Category Skills Example Lessons
Substituting values for x Being given a value for x and plugging in What is the value at $(x^2-2)/(x-1)$ Intro to Variables & Expressions
Setting up an Equation Translating an equation from words into numbers and variables A car's distance is determined by the velocity multiplied by the amount of time the car is at that speed.If a car can go at a maximum velocity of 225 meters per second, what equation shows how far the car has travelled at its maximum speed? How to Translate Words Into Equations
Operations with Polynomials Adding,subtracting,multiplying,and dividing equations with multiple variables Simplify: $2a+3b-(-6a+4b)$ Adding Polynomials (a.k.a. Combining Like Terms) Solving Equations With Distribution Basic FOIL on 2-by-2 parentheses
Factoring Undoing a polynomial and simplifying it into its most basic equations as well as using it to find certain input values What is one possible factor of $x^2+4x+3$ ? Factoring Stuff Out (a.k.a. "distrubution in reverse") Easier Factoring Problems Factoring Difference of Squares Hard Factoring Problems
Linear Equations to One Variable An input which leads to an output and using the output to solve for the input Solve for x when $2(x-2)=-10$ Solving Equations With Addition & Subtraction Only Solving Equations With Multiplication & Division Solving Two Step Equations
Exponent Properties Multiplying, dviding, or taking the power of a number or variable to a power $(x^2)((x^5)^2)/ x^9$ =? Basic Exponent Rules & Rational Expressions Negative Exponents Common Algebraic Canceling Mistakes
Irrational functions and multiplying by the Complex Conjugate Simplifying a polynomial over a polynomial and being able to simplify roots in a denominator. $ √x/(3√x- √y)$ Dividing Roots & Rationalizing Denominators Solving Rational Equations (x's in denominators)
Linear Equations in Two Variables Understanding the parts of a function (slope, y-intercept, input, and output) in order to find coordinates and values What is the slope of $4x+3y+2=0$ ? How to Find the Slope of a Line How To Graph Lines (a.k.a. Linear Functions) Horizontal & Vertical Lines Slope-Intercept Form of a Line: y=mx+b Standard Form of a Line: Ax+By=C Point-Slope Form: y-y1=m(x-x1) Equations of Parallel & Perpendicular Lines
College Algebra
Content Category Skills Example Lessons
Complex Functions Plugging in inputs for outputs and understanding their meaning including inequalities, a system of equations (more than one variable), exponential, and absolute value A manufacturer for raw ore has one of two options for refining material: Process A or Process B. Procss A is $A(t)=2t^2+t$ and Process B is $20t$ with t being time in days. If the manufacturer has 7 days to refine ore, what is the maximum output possible? Solving Messy Equations: Combining Like Terms Solving Systems of Simultaneous Equations with Elimination Absolute Value Equations Solving Inequalities with just X Graphing Exponentials Solving Exponential Equations Using Logs
Complex Exponents Raising a number to a rational or irrational number or variable Simplify the following: $(x^(1/2)) (y^(2/3))(z^(5/6))$ Simplifying Roots & Radicals Rational Exponents (a.k.a. fractions upstairs) Basic Exponent Rules & Rational Expressions Common Algebraic Canceling Mistakes
Complex Numbers Numbers which equal the square root of a negative number ($i$) What is $i^24$ equal to? Imaginary Numbers & Square Roots of Negatives Complex Numbers
Arithmatic and Geometric Sequences A function which produces a series of numbers multiplied,divided, added, or subtracted by the previous terms What is the next term in the geometric sequence 64,32,16,8...? Geometric Sequences & Series Arithmetic Sequences & Series
Matrices A set of numbers which can be added, subtracted, multiplied, and divided [2 -6] - [-2 4]=? Basic Matrix Operations Multiplying Matrices The Determinant
Geometry
Content Category Skills Example Lessons
Angles Using the degrees of an angle to solve for other angle values within a set of parallel lines, adjacent to the original angle, or "vertical" angles Solve for x: Parallel Lines & Transversals Theorems Parallel Lines & Transversals Problems
Triangles An isosceles (two sides equal), equalateral (all sides equal), or scalene (no sides equal) 3-sided shape whose angles add up to 180 degrees Solve for x: Obtuse, Acute, and Right Triangles Scalene, Isosceles, and Equilateral Triangles 180Triangle Rule Problems Triangle Exterior Angle Theorem
Congruent Triangles and Pythagorean Theorem Using congruent triangles to solve for the its angles and using the Pythagorean Theorem ($a^2+b^2=c^2$) Solve for x: The Pythagorean Theorem Everything You Need To Know About Congruent Triangles Tips & Tricks For Congruent Triangle Proofs SSS, SAS, ASA, AAS, SSA, H-L/h3>
Circles Using the radius and diameter to find the perimeter (circumference), area, and arc Calculate the arc of the given sector of the circle: Circle Vocab Basic Circle Proofs Circumference & Diameter Basic Circle Area Problems Areas of Circle Sectors
Rectangles A four-sided quadrilateral with two sets of equal sides Solve for x: Areas of Rectangles & Squares Rectangles & Squares
Three-dimensional concepts Taking the volume and surface area of shapes knowing information about the 2-D shape's area Surface Area of 3-D Shapes Volume of Solids
Trigonometry
Content Category Skills Example Lessons
Right-triangle Trigonometry and the Unit Circle Using the degrees of an angle to solve for other angle values within a set of parallel lines, adjacent to the original angle, or "vertical" angles Calculate the missing sides: Intro to SohCahToa Solving Triangles The Unit Circle Introducing Secant, Co-Secant & Co-Tangent Inverse Trig Functions
Special Angles and Trig Identities Special cases and equations involving SohCahToa Simplify the following term: $sin(2x)$ The Pythagorean Identity: sin2X + cos2X = 1 Proofs Using The "Other Two" Pythagorean Identities: tan2X+1 = sec2X & 1+cot2X = csc2X Double-Angle, Half-Angle, and Sum/Difference Formulas
Trigonometry Functions Graphing and understanding basic trigonometric functions on a graph Graph the following equation: Graphing Sine & Cosine Graphing Tangent, Cotangent, Secant & Co-Secant
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