ACT Compass Test Prep made completely easy!

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Our comprehensive lessons on compass test cover help on topics like Trigonometric identities, Linear equations, Exponents, Complex number, Logarithmic functions, Rational expressions, and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest Compass math test problems. Then, strengthen your understanding with tons of Compass test practice.

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Common Questions
I’m preparing for Compass Math. How should I start?

You can first test yourself with this sample Compass test questions to see which areas and topics you need to focus more on. Then, watch our video lessons and work on the practice questions for review and better understanding.

What should I expect when in the Math Compass test?

It is made up with multiple-choice questions. Only calculators with the most basic functions are allowed. You will also be provided a calculator on the screen during the test too.

Any tips on getting a good score in the ACT Compass test?

The test is computer-adaptive. So, the difficulty level of questions given to you changes based on how well you answer the previous ones. Since it is untimed, you should take as much time as you need to best demonstrate your skills.

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ACT Compass Test Prep Topics

We have plenty of free lessons for you to watch

1Numbers and Relations

1.1Place value
1.2Comparing and ordering numbers
1.3Rounding numbers

2Number Theory

2.1Divisibility Rules
2.2Determining Common Factors
2.3Determining Common Multiples

3Operations with Decimals

3.1Adding and subtracting decimals
3.2Multiplying decimals
3.3Dividing decimals
3.4Order of operations (PEMDAS)

4Number System and Radicals

4.1Understanding the number systems (free lessons)
4.2Prime factorization
4.3Greatest Common Factors (GCF)
4.4Least Common Multiple (LCM) (free lessons)
4.5Rational vs. Irrational numbers
4.6Converting repeating decimals to fractions

5Adding and Substracting Fractions

5.1Using models to add and subtract fractions
5.2Adding fractions with like denominators
5.3Subtracting fractions with like denominators
5.4Adding and subtracting fractions with unlike denominators
5.5Adding and subtracting mixed numbers

6Multiplying and Dividing Fractions

6.1Multiplying fractions and whole numbers (free lessons)
6.2Dividing fractions with whole numbers
6.3Multiplying proper fractions
6.4Multiplying improper fractions and mixed numbers
6.5Dividing fractions and mixed numbers
6.6Applications of fraction operations

7Fractions, Decimals, and Percents

7.1Percent of a number
7.2Adding and multiplying percents
7.3Taxes, discounts, tips and more
7.4Simple interest

8Introduction to Variables and Expressions

8.1Evaluating algebraic expressions

9Solving Linear Equations

9.1Solving linear equations using multiplication and division (free lessons)
9.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
9.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
9.4Solving linear equations with variables on both sides
9.5Solving literal equations

10Introduction to Relations and Functions

10.1Relationship between two variables (free lessons)
10.2Understand relations between x- and y-intercepts
10.3Domain and range of a function (free lessons)
10.4Identifying functions
10.5Function notation (free lessons)

11Linear Functions

11.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
11.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
11.3Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
11.4Slope intercept form: y = mx + b (free lessons)
11.5General form: Ax + By + C = 0 (free lessons)
11.6Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
11.7Rate of change
11.8Graphing linear functions using table of values
11.9Graphing linear functions using x- and y-intercepts (free lessons)
11.10Graphing from slope-intercept form y=mx+b
11.11Graphing linear functions using a single point and slope
11.12Word problems of graphing linear functions
11.13Parallel and perpendicular lines in linear functions (free lessons)
11.14Applications of linear relations

12Linear Equations

12.1Introduction to linear equations (free lessons)
12.2Introduction to nonlinear equations
12.3Special case of linear equations: Horizontal lines
12.4Special case of linear equations: Vertical lines
12.5Parallel line equation (free lessons)
12.6Perpendicular line equation
12.7Combination of both parallel and perpendicular line equations
12.8Applications of linear equations

13Solving Systems of Linear Equations

13.1Determining number of solutions to linear equations (free lessons)
13.2Solving systems of linear equations by graphing
13.3Using elimination method to solve systems of equations
13.4Using substitution method to solve systems of equations
13.5Money related questions in linear equations (free lessons)
13.6Unknown number related questions in linear equations
13.7Distance and time related questions in linear equations
13.8Rectangular shape related questions in linear equations

14Exponents

14.1Product rule of exponents (free lessons)
14.2Quotient rule of exponents
14.3Power of a product rule
14.4Power of a quotient rule
14.5Power of a power rule (free lessons)
14.6Negative exponent rule
14.7Combining the exponent rules
14.8Scientific notation
14.9Convert between radicals and rational exponents (free lessons)
14.10Solving for exponents

15Operations with Polynomials

15.1What is a polynomial? (free lessons)
15.2Polynomial components
15.3Multiplying monomial by monomial
15.4Multiplying monomial by binomial
15.5Multiplying binomial by binomial (free lessons)
15.6Multiplying polynomial by polynomial
15.7Applications of polynomials

16Factoring Polynomial Expressions

16.1Common factors of polynomials (free lessons)
16.2Factoring polynomials by grouping
16.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
16.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
16.5Factoring polynomials: x2+bx+cx^2 + bx + c (free lessons)
16.6Applications of polynomials: x2+bx+cx^2 + bx + c
16.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
16.8Factoring polynomials: ax2+bx+cax^2 + bx + c
16.9Factoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
16.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
16.11Evaluating polynomials
16.12Using algebra tiles to solve polynomials
16.13Solving polynomial equations (free lessons)
16.14Word problems of polynomials

17Factoring Trinomials (Advanced)

17.1Factor by taking out the greatest common factor (free lessons)
17.2Factor by grouping
17.3Factoring difference of squares: x2−y2x^2 - y^2
17.4Factoring trinomials
17.5Factoring difference of cubes
17.6Factoring sum of cubes

18Rational Expressions

18.1Simplifying rational expressions and restrictions
18.2Adding and subtracting rational expressions (free lessons)
18.3Multiplying rational expressions
18.4Dividing rational expressions
18.5Solving rational equations
18.6Applications of rational equations
18.7Simplifying complex fractions
18.8Partial fraction decomposition

19Radicals

19.1Square and square roots (free lessons)
19.2Cubic and cube roots
19.3Evaluating and simplifying radicals
19.4Converting radicals to mixed radicals
19.5Converting radicals to entire radicals (free lessons)
19.6Adding and subtracting radicals
19.7Multiplying and dividing radicals
19.8Rationalize the denominator

20Radicals (Advanced)

20.1Operations with radicals (free lessons)
20.2Conversion between entire radicals and mixed radicals
20.3Adding and subtracting radicals (free lessons)
20.4Multiplying radicals
20.5Solving radical equations

21Ratios, Rates, and Proportions

21.1Ratios (free lessons)
21.2Rates
21.3Proportions

22Angles, Lines, and Transversals

22.1Pairs of lines and angles
22.2Parallel lines and transversals
22.3Parallel line proofs
22.4Perpendicular line proofs (free lessons)

23Scale Factors and Similarity

23.1Enlargements and reductions with scale factors (free lessons)
23.2Scale diagrams
23.3Similar triangles
23.4Similar polygons

24Surface Area and Perimeter of Polygons

24.1Classifying Triangles

25Circles

25.1Circles and circumference
25.2Arcs of a circle
25.3Areas and sectors of circles
25.4Angles in a circle (free lessons)
25.5Chord properties in circles
25.6Tangent properties in circles
25.7Central and inscribed angles in circles
25.8Equation of a circle

26Statistics

26.1Median and mode
26.2Mean
26.3Range and outliers
26.4Application of averages

27Sequences and Series

27.1Arithmetic sequences (free lessons)
27.2Arithmetic series (free lessons)
27.3Geometric sequences
27.4Geometric series
27.5Infinite geometric series
27.6Sigma notation
27.7Arithmetic mean vs. Geometric mean

28Functions

28.1Function notation (free lessons)
28.2Operations with functions
28.3Adding functions
28.4Subtracting functions
28.5Multiplying functions
28.6Dividing functions
28.7Composite functions (free lessons)
28.8Inequalities of combined functions
28.9Inverse functions (free lessons)
28.10One to one functions
28.11Difference quotient: applications of functions

29Exponential Functions

29.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
29.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
29.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
29.4Exponents: Negative exponents
29.5Exponents: Zero exponent: a0=1 a^0 = 1
29.6Exponents: Rational exponents
29.7Solving exponential equations using exponent rules
29.8Graphing exponential functions
29.9Graphing transformations of exponential functions
29.10Finding an exponential function given its graph

30Logarithmic Functions

30.1What is a logarithm?
30.2Converting from logarithmic form to exponential form (free lessons)
30.3Evaluating logarithms without a calculator
30.4Common logarithms
30.5Natural log: ln
30.6Evaluating logarithms using change-of-base formula
30.7Converting from exponential form to logarithmic form (free lessons)
30.8Solving exponential equations with logarithms
30.9Product rule of logarithms (free lessons)
30.10Quotient rule of logarithms
30.11Combining product rule and quotient rule in logarithms
30.12Evaluating logarithms using logarithm rules
30.13Solving logarithmic equations (free lessons)
30.14Graphing logarithmic functions
30.15Finding a logarithmic function given its graph

31Applications of Exponential and Logarithmic Functions

31.1Exponential growth and decay by a factor
31.2Exponential decay: Half-life (free lessons)
31.3Exponential growth and decay by percentage
31.4Finance: Compound interest
31.5Continuous growth and decay
31.6Logarithmic scale: Richter scale (earthquake)
31.7Logarithmic scale: pH scale
31.8Logarithmic scale: dB scale
31.9Finance: Future value and present value

32Right Triangle Trigonometry

32.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
32.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
32.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
32.4Combination of SohCahToa questions (free lessons)
32.5Solving expressions using 45-45-90 special right triangles (free lessons)
32.6Solving expressions using 30-60-90 special right triangles
32.7Word problems relating ladder in trigonometry
32.8Word problems relating guy wire in trigonometry
32.9Other word problems relating angles in trigonometry

33Laws of sines and cosines

33.1Law of sines
33.2Law of cosines
33.3Applications of the sine law and cosine law

34Trigonometric Ratios and Angle Measure

34.1Angle in standard position
34.2Coterminal angles (free lessons)
34.3Reference angle
34.4Find the exact value of trigonometric ratios
34.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
34.6Unit circle (free lessons)
34.7Converting between degrees and radians
34.8Trigonometric ratios of angles in radians
34.9Radian measure and arc length

35Graphs of Trigonometric Functions

35.1Sine graph: y = sin x
35.2Cosine graph: y = cos x
35.3Tangent graph: y = tan x
35.4Cotangent graph: y = cot x
35.5Secant graph: y = sec x
35.6Cosecant graph: y = csc x
35.7Graphing transformations of trigonometric functions
35.8Determining trigonometric functions given their graphs

36Trigonometric Identities

36.1Quotient identities and reciprocal identities (free lessons)
36.2Pythagorean identities
36.3Sum and difference identities
36.4Cofunction identities
36.5Double-angle identities (free lessons)

37Solving Trigonometric Equations

37.1Solving first degree trigonometric equations (free lessons)
37.2Determining non-permissible values for trig expressions
37.3Solving second degree trigonometric equations
37.4Solving trigonometric equations involving multiple angles (free lessons)
37.5Solving trigonometric equations using pythagorean identities
37.6Solving trigonometric equations using sum and difference identities
37.7Solving trigonometric equations using double-angle identities

38Imaginary and Complex Numbers

38.1Introduction to imaginary numbers (free lessons)
38.2Complex numbers and complex planes (free lessons)
38.3Adding and subtracting complex numbers
38.4Complex conjugates
38.5Multiplying and dividing complex numbers
38.6Distance and midpoint of complex numbers
38.7Angle and absolute value of complex numbers
38.8Polar form of complex numbers
38.9Operations on complex numbers in polar form

39Introduction to Matrices

39.1Notation of matrices
39.2Adding and subtracting matrices
39.3Scalar multiplication
39.4Matrix multiplication
39.5The three types of matrix row operations
39.6Representing a linear system as a matrix
39.7Solving a linear system with matrices using Gaussian elimination

40Properties of Matrices

40.1Zero matrix
40.2Identity matrix
40.3Properties of matrix addition
40.4Properties of scalar multiplication

41Determinants and Inverses of Matrices

41.1The determinant of a 2 x 2 matrix
41.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
41.3The inverse of a 2 x 2 matrix
41.4The inverse of 3 x 3 matrices with matrix row operations
41.5The inverse of 3 x 3 matrix with determinants and adjugate
41.62 x 2 invertible matrix
41.7Solving linear systems using Cramer's Rule
41.8Solving linear systems using 2 x 2 inverse matrices
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