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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

7.1Representing percents
7.2Percent of a number
7.3Converting among decimals, fractions, and percents
7.4Adding and multiplying percents
7.5Applications of percents
7.6Taxes, discounts, tips and more
7.7Simple interest

8Introduction to Variables and Expressions

8.1Evaluating algebraic expressions

9Introduction to Equations

9.1Solving one - step equations: x+a=bx + a = b

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
14.3Using elimination method to solve systems of equations
14.4Using substitution method to solve systems of equations
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 the unknown "b" from x2+bx+cx^2 + bx + c
17.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
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+cax^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

20Reciprocal Functions

20.1Graphing reciprocals of linear functions
20.2Graphing reciprocals of quadratic functions

21Radicals

21.1Square and square roots (free lessons)
21.2Cubic and cube roots
21.3Evaluating and simplifying radicals
21.4Converting radicals to mixed radicals
21.5Converting radicals to entire radicals (free lessons)
21.6Adding and subtracting radicals
21.7Multiplying and dividing radicals
21.8Rationalize the denominator

22Radicals (Advanced)

22.1Operations with radicals (free lessons)
22.2Conversion between entire radicals and mixed radicals
22.3Adding and subtracting radicals (free lessons)
22.4Multiplying radicals
22.5Solving radical equations

23Ratios, Rates, and Proportions

23.1Ratios (free lessons)
23.2Rates
23.3Proportions

24Angles, Lines, and Transversals

24.1Pairs of lines and angles
24.2Parallel lines and transversals
24.3Parallel line proofs
24.4Perpendicular line proofs (free lessons)

25Scale Factors and Similarity

25.1Enlargements and reductions with scale factors (free lessons)
25.2Scale diagrams
25.3Similar triangles
25.4Similar polygons

26Surface Area and Perimeter of Polygons

26.1Classifying Triangles

27Circles

27.1Circles and circumference
27.2Arcs of a circle
27.3Areas and sectors of circles
27.4Angles in a circle (free lessons)
27.5Chord properties in circles
27.6Tangent properties in circles
27.7Central and inscribed angles in circles
27.8Equation of a circle

28Statistics

28.1Median and mode
28.2Mean
28.3Range and outliers
28.4Application of averages

29Sequences and Series

29.1Arithmetic sequences (free lessons)
29.2Arithmetic series (free lessons)
29.3Geometric sequences
29.4Geometric series
29.5Infinite geometric series
29.6Sigma notation
29.7Arithmetic mean vs. Geometric mean

30Functions

30.1Function notation (free lessons)
30.2Operations with functions
30.3Adding functions
30.4Subtracting functions
30.5Multiplying functions
30.6Dividing functions
30.7Composite functions (free lessons)
30.8Inequalities of combined functions
30.9Inverse functions (free lessons)
30.10One to one functions
30.11Difference quotient: applications of functions

31Exponential Functions

31.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
31.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
31.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
31.4Exponents: Negative exponents
31.5Exponents: Zero exponent: a0=1 a^0 = 1
31.6Exponents: Rational exponents
31.7Solving exponential equations using exponent rules
31.8Graphing exponential functions
31.9Graphing transformations of exponential functions
31.10Finding an exponential function given its graph

32Logarithmic Functions

32.1What is a logarithm?
32.2Converting from logarithmic form to exponential form (free lessons)
32.3Evaluating logarithms without a calculator
32.4Common logarithms
32.5Natural log: ln
32.6Evaluating logarithms using change-of-base formula
32.7Converting from exponential form to logarithmic form (free lessons)
32.8Solving exponential equations with logarithms
32.9Product rule of logarithms (free lessons)
32.10Quotient rule of logarithms
32.11Combining product rule and quotient rule in logarithms
32.12Evaluating logarithms using logarithm rules
32.13Solving logarithmic equations (free lessons)
32.14Graphing logarithmic functions
32.15Finding a logarithmic function given its graph

33Applications of Exponential and Logarithmic Functions

33.1Exponential growth and decay by a factor
33.2Exponential decay: Half-life (free lessons)
33.3Exponential growth and decay by percentage
33.4Finance: Compound interest
33.5Continuous growth and decay
33.6Logarithmic scale: Richter scale (earthquake)
33.7Logarithmic scale: pH scale
33.8Logarithmic scale: dB scale
33.9Finance: Future value and present value

34Right Triangle Trigonometry

34.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
34.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
34.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
34.4Combination of SohCahToa questions (free lessons)
34.5Solving expressions using 45-45-90 special right triangles (free lessons)
34.6Solving expressions using 30-60-90 special right triangles
34.7Word problems relating ladder in trigonometry
34.8Word problems relating guy wire in trigonometry
34.9Other word problems relating angles in trigonometry

35Laws of sines and cosines

35.1Law of sines
35.2Law of cosines
35.3Applications of the sine law and cosine law

36Bearings

36.1Introduction to bearings
36.2Bearings and direction word problems
36.3Angle of elevation and depression

37Trigonometric Ratios and Angle Measure

37.1Angle in standard position
37.2Coterminal angles (free lessons)
37.3Reference angle
37.4Find the exact value of trigonometric ratios
37.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
37.6Unit circle (free lessons)
37.7Converting between degrees and radians
37.8Trigonometric ratios of angles in radians
37.9Radian measure and arc length

38Graphs of Trigonometric Functions

38.1Sine graph: y = sin x
38.2Cosine graph: y = cos x
38.3Tangent graph: y = tan x
38.4Cotangent graph: y = cot x
38.5Secant graph: y = sec x
38.6Cosecant graph: y = csc x
38.7Graphing transformations of trigonometric functions
38.8Determining trigonometric functions given their graphs

39Trigonometric Identities

39.1Quotient identities and reciprocal identities (free lessons)
39.2Pythagorean identities
39.3Sum and difference identities
39.4Cofunction identities
39.5Double-angle identities (free lessons)

40Solving Trigonometric Equations

40.1Solving first degree trigonometric equations (free lessons)
40.2Determining non-permissible values for trig expressions
40.3Solving second degree trigonometric equations
40.4Solving trigonometric equations involving multiple angles (free lessons)
40.5Solving trigonometric equations using pythagorean identities
40.6Solving trigonometric equations using sum and difference identities
40.7Solving trigonometric equations using double-angle identities

41Imaginary and Complex Numbers

41.1Introduction to imaginary numbers (free lessons)
41.2Complex numbers and complex planes (free lessons)
41.3Adding and subtracting complex numbers
41.4Complex conjugates
41.5Multiplying and dividing complex numbers
41.6Distance and midpoint of complex numbers
41.7Angle and absolute value of complex numbers
41.8Polar form of complex numbers
41.9Operations on complex numbers in polar form

42Introduction to Matrices

42.1Notation of matrices
42.2Adding and subtracting matrices
42.3Scalar multiplication
42.4Matrix multiplication
42.5The three types of matrix row operations
42.6Representing a linear system as a matrix
42.7Solving a linear system with matrices using Gaussian elimination

43Properties of Matrices

43.1Zero matrix
43.2Identity matrix
43.3Properties of matrix addition
43.4Properties of scalar multiplication

44Determinants and Inverses of Matrices

44.1The determinant of a 2 x 2 matrix
44.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
44.3The inverse of a 2 x 2 matrix
44.4The inverse of 3 x 3 matrices with matrix row operations
44.5The inverse of 3 x 3 matrix with determinants and adjugate
44.62 x 2 invertible matrix
44.7Solving linear systems using Cramer's Rule
44.8Solving linear systems using 2 x 2 inverse matrices
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