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We got you covered with our complete help for Compass math test including all five subject areas: Pre-algebra, Algebra, College Algebra, Geometry, and Trigonometry.

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
2.2Prime factorization
2.3Determining common factors
2.4Determining 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

9Introduction to Equations

9.1Ratios (free lessons)
9.2Rates

10Solving Linear Equations

10.1Solving linear equations using multiplication and division (free lessons)
10.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
10.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
10.4Solving linear equations with variables on both sides
10.5Solving literal equations

11Introduction to Relations and Functions

11.1Relationship between two variables (free lessons)
11.2Understand relations between x- and y-intercepts
11.3Domain and range of a function (free lessons)
11.4Identifying functions
11.5Function notation (free lessons)

12Linear Functions

12.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
12.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
12.3Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
12.4Slope intercept form: y = mx + b (free lessons)
12.5General form: Ax + By + C = 0 (free lessons)
12.6Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
12.7Rate of change
12.8Graphing linear functions using table of values
12.9Graphing linear functions using x- and y-intercepts (free lessons)
12.10Graphing from slope-intercept form y=mx+b
12.11Graphing linear functions using a single point and slope
12.12Word problems of graphing linear functions
12.13Parallel and perpendicular lines in linear functions (free lessons)
12.14Applications of linear relations

13Linear Equations

13.1Introduction to linear equations (free lessons)
13.2Introduction to nonlinear equations
13.3Special case of linear equations: Horizontal lines
13.4Special case of linear equations: Vertical lines
13.5Parallel line equation (free lessons)
13.6Perpendicular line equation
13.7Combination of both parallel and perpendicular line equations
13.8Applications of linear equations

14Solving Systems of Linear Equations

14.1Determining number of solutions to linear equations (free lessons)
14.2Solving systems of linear equations by graphing
14.3Solving systems of linear equations by elimination
14.4Solving systems of linear equations by substitution
14.5Money related questions in linear equations (free lessons)
14.6Unknown number related questions in linear equations
14.7Distance and time related questions in linear equations
14.8Rectangular shape related questions in linear equations

15Exponents

15.1Product rule of exponents (free lessons)
15.2Quotient rule of exponents
15.3Power of a product rule
15.4Power of a quotient rule
15.5Power of a power rule (free lessons)
15.6Negative exponent rule
15.7Combining the exponent rules
15.8Scientific notation
15.9Convert between radicals and rational exponents (free lessons)
15.10Solving for exponents

16Operations with Polynomials

16.1What is a polynomial? (free lessons)
16.2Polynomial components
16.3Multiplying monomial by monomial
16.4Multiplying monomial by binomial
16.5Multiplying binomial by binomial (free lessons)
16.6Multiplying polynomial by polynomial
16.7Applications of polynomials

17Factoring Polynomial Expressions

17.1Common factors of polynomials (free lessons)
17.2Factoring polynomials by grouping
17.3Solving polynomials with unknown coefficients
17.4Solving polynomials with unknown constant terms
17.5Factoring polynomials: x2+bx+cx^2 + bx + c (free lessons)
17.6Applications of polynomials: x2+bx+cx^2 + bx + c
17.7Solving polynomials with the unknown "b" from ax2+bx+c{ax^2+bx+c}
17.8Factoring polynomials: ax2+bx+cax^2 + bx + c
17.9Factoring 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)
17.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
17.11Evaluating polynomials
17.12Using algebra tiles to solve polynomials
17.13Solving polynomial equations (free lessons)
17.14Word problems of polynomials

18Factoring Trinomials (Advanced)

18.1Factor by taking out the greatest common factor (free lessons)
18.2Factor by grouping
18.3Factoring difference of squares: x2−y2x^2 - y^2
18.4Factoring trinomials
18.5Factoring difference of cubes
18.6Factoring sum of cubes

19Rational Expressions

19.1Simplifying rational expressions and restrictions
19.2Adding and subtracting rational expressions (free lessons)
19.3Multiplying rational expressions
19.4Dividing rational expressions
19.5Solving rational equations
19.6Applications of rational equations
19.7Simplifying complex fractions
19.8Partial fraction decomposition

20Radicals

20.1Square and square roots (free lessons)
20.2Cubic and cube roots
20.3Evaluating and simplifying radicals
20.4Converting radicals to mixed radicals
20.5Converting radicals to entire radicals (free lessons)
20.6Adding and subtracting radicals
20.7Multiplying and dividing radicals
20.8Rationalize the denominator

21Radicals (Advanced)

21.1Operations with radicals (free lessons)
21.2Conversion between entire radicals and mixed radicals
21.3Adding and subtracting radicals (free lessons)
21.4Multiplying radicals
21.5Solving radical equations

22Ratios, Rates, and Proportions

22.1Ratios (free lessons)
22.2Rates
22.3Proportions

23Angles, Lines, and Transversals

23.1Pairs of lines and angles
23.2Parallel lines and transversals
23.3Parallel line proofs
23.4Perpendicular line proofs (free lessons)

24Scale Factors and Similarity

24.1Enlargements and reductions with scale factors (free lessons)
24.2Scale diagrams
24.3Similar triangles
24.4Similar polygons

25Surface Area and Perimeter of Polygons

25.1Classifying triangles
25.2Pairs of lines and angles

26Circles

26.1Circles and circumference
26.2Arcs of a circle
26.3Areas and sectors of circles
26.4Angles in a circle (free lessons)
26.5Chord properties
26.6Tangent properties
26.7Central and inscribed angles in circles
26.8Conics - Circle

27Statistics

27.1Median and mode
27.2Mean
27.3Range and outliers
27.4Application of averages

28Sequences and Series

28.1Arithmetic sequences (free lessons)
28.2Arithmetic series (free lessons)
28.3Geometric sequences
28.4Geometric series
28.5Infinite geometric series
28.6Sigma notation
28.7Arithmetic mean vs. Geometric mean

29Functions

29.1Function notation (advanced) (free lessons)
29.2Operations with functions
29.3Adding functions
29.4Subtracting functions
29.5Multiplying functions
29.6Dividing functions
29.7Composite functions (free lessons)
29.8Inequalities of combined functions
29.9Inverse functions (free lessons)
29.10One to one functions
29.11Difference quotient: applications of functions

30Exponential Functions

30.1Exponents: Product rule (ax)(ay)=a(x+y)(a^x)(a^y)=a^{(x+y)} (free lessons)
30.2Exponents: division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
30.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x \cdot y)} (free lessons)
30.4Exponents: Negative exponents
30.5Exponents: Zero exponent: a0=1 a^0 = 1
30.6Exponents: Rational exponents
30.7Solving exponential equations using exponent rules
30.8Graphing exponential functions
30.9Graphing transformations of exponential functions
30.10Finding an exponential function given its graph

31Logarithmic Functions

31.1What is a logarithm?
31.2Converting from logarithmic form to exponential form (free lessons)
31.3Evaluating logarithms without a calculator
31.4Common logarithms
31.5Natural log: ln
31.6Evaluating logarithms using change-of-base formula
31.7Converting from exponential form to logarithmic form (free lessons)
31.8Solving exponential equations with logarithms
31.9Product rule of logarithms (free lessons)
31.10Quotient rule of logarithms
31.11Combining product rule and quotient rule in logarithms
31.12Evaluating logarithms using logarithm rules
31.13Solving logarithmic equations (free lessons)
31.14Graphing logarithmic functions
31.15Finding a logarithmic function given its graph

32Applications of Exponential and Logarithmic Functions

32.1Exponential growth and decay by a factor
32.2Exponential decay: Half-life (free lessons)
32.3Exponential growth and decay by percentage
32.4Finance: Compound interest
32.5Continuous growth and decay
32.6Logarithmic scale: Richter scale (earthquake)
32.7Logarithmic scale: pH scale
32.8Logarithmic scale: dB scale
32.9Finance: Future value and present value

33Right Triangle Trigonometry

33.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
33.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
33.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
33.4Combination of SohCahToa questions (free lessons)
33.5Solving expressions using 45-45-90 special right triangles (free lessons)
33.6Solving expressions using 30-60-90 special right triangles
33.7Word problems relating ladder in trigonometry
33.8Word problems relating guy wire in trigonometry
33.9Other word problems relating angles in trigonometry

34Laws of sines and cosines

34.1Law of sines
34.2Law of cosines
34.3Applications of the sine law and cosine law

35Trigonometric Ratios and Angle Measure

35.1Angle in standard position
35.2Coterminal angles (free lessons)
35.3Reference angle
35.4Find the exact value of trigonometric ratios
35.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
35.6Unit circle (free lessons)
35.7Converting between degrees and radians
35.8Trigonometric ratios of angles in radians
35.9Radian measure and arc length

36Graphs of Trigonometric Functions

36.1Sine graph: y = sin x
36.2Cosine graph: y = cos x
36.3Tangent graph: y = tan x
36.4Cotangent graph: y = cot x
36.5Secant graph: y = sec x
36.6Cosecant graph: y = csc x
36.7Graphing transformations of trigonometric functions
36.8Determining trigonometric functions given their graphs

37Trigonometric Identities

37.1Quotient identities and reciprocal identities (free lessons)
37.2Pythagorean identities
37.3Sum and difference identities
37.4Cofunction identities
37.5Double-angle identities (free lessons)

38Solving Trigonometric Equations

38.1Solving first degree trigonometric equations (free lessons)
38.2Determining non-permissible values for trig expressions
38.3Solving second degree trigonometric equations
38.4Solving trigonometric equations involving multiple angles (free lessons)
38.5Solving trigonometric equations using pythagorean identities
38.6Solving trigonometric equations using sum and difference identities
38.7Solving trigonometric equations using double-angle identities

39Imaginary and Complex Numbers

39.1Introduction to imaginary numbers (free lessons)
39.2Complex numbers and complex planes (free lessons)
39.3Adding and subtracting complex numbers
39.4Complex conjugates
39.5Multiplying and dividing complex numbers
39.6Distance and midpoint of complex numbers
39.7Angle and absolute value of complex numbers
39.8Polar form of complex numbers
39.9Operations on complex numbers in polar form

40Introduction to Matrices

40.1Notation of matrices
40.2Adding and subtracting matrices
40.3Scalar multiplication of matrices
40.4Matrix multiplication
40.5The three types of matrix row operations
40.6Representing a linear system as a matrix
40.7Solving a linear system with matrices using Gaussian elimination

41Properties of Matrices

41.1Zero matrix
41.2Identity matrix
41.3Properties of matrix addition
41.4Properties of scalar multiplication

42Determinants and Inverses of Matrices

42.1The determinant of a 2 x 2 matrix
42.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
42.3The Inverse of a 2 x 2 matrix
42.4The inverse of 3 x 3 matrices with matrix row operations
42.5The inverse of 3 x 3 matrix with determinants and adjugate
42.62 x 2 invertible matrix
42.7Solving linear systems using Cramer's Rule
42.8Solving linear systems using 2 x 2 inverse matrices
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