# Learn COMPASS Placement Test Fast

# (from someone who can actually explain it)

# 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.

Start Your Trial! | Sample COMPASS Placement Test Videos |
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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 |