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  1. 1Numbers and Relations
    1. 1.1Place value
    2. 1.2Comparing and ordering numbers
    3. 1.3Rounding numbers
  2. 2Number Theory
    1. 2.1Divisibility Rules
    2. 2.2Determining Common Factors
    3. 2.3Determining Common Multiples
  3. 3Operations with Decimals
    1. 3.1Adding and subtracting decimals
    2. 3.2Multiplying decimals
    3. 3.3Dividing decimals
    4. 3.4Order of operations (PEMDAS)
  4. 4Number System and Radicals
    1. 4.1Understanding the number systems
    2. 4.2Prime factorization
    3. 4.3Greatest Common Factors (GCF)
    4. 4.4Least Common Multiple (LCM)
    5. 4.5Rational vs. Irrational numbers
    6. 4.6Converting repeating decimals to fractions
  5. 5Adding and Substracting Fractions
    1. 5.1Using models to add and subtract fractions
    2. 5.2Adding fractions with like denominators
    3. 5.3Subtracting fractions with like denominators
    4. 5.4Adding and subtracting fractions with unlike denominators
    5. 5.5Adding and subtracting mixed numbers
  6. 6Multiplying and Dividing Fractions
    1. 6.1Multiplying fractions and whole numbers
    2. 6.2Dividing fractions with whole numbers
    3. 6.3Multiplying proper fractions
    4. 6.4Multiplying improper fractions and mixed numbers
    5. 6.5Dividing fractions and mixed numbers
    6. 6.6Applications of fraction operations
  7. 7Fractions, Decimals, and Percents
    1. 7.1Representing percents
    2. 7.2Percent of a number
    3. 7.3Converting among decimals, fractions, and percents
    4. 7.4Adding and multiplying percents
    5. 7.5Applications of percents
    6. 7.6Taxes, discounts, tips and more
    7. 7.7Simple interest
  8. 8Introduction to Variables and Expressions
    1. 8.1Evaluating algebraic expressions
  9. 9Introduction to Equations
    1. 9.1Solving one - step equations: x+a=bx + a = b
  10. 10Solving Linear Equations
    1. 10.1Solving linear equations using multiplication and division
    2. 10.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
    3. 10.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c
    4. 10.4Solving linear equations with variables on both sides
    5. 10.5Solving literal equations
  11. 11Introduction to Relations and Functions
    1. 11.1Relationship between two variables
    2. 11.2Understand relations between x- and y-intercepts
    3. 11.3Domain and range of a function
    4. 11.4Identifying functions
    5. 11.5Function notation
  12. 12Linear Functions
    1. 12.1Distance formula: d=(x2x1)2+(y2y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 12.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 12.3Slope equation: m=y2y1x2x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 12.4Slope intercept form: y = mx + b
    5. 12.5General form: Ax + By + C = 0
    6. 12.6Point-slope form: yy1=m(xx1)y - y_1 = m (x - x_1)
    7. 12.7Rate of change
    8. 12.8Graphing linear functions using table of values
    9. 12.9Graphing linear functions using x- and y-intercepts
    10. 12.10Graphing from slope-intercept form y=mx+b
    11. 12.11Graphing linear functions using a single point and slope
    12. 12.12Word problems of graphing linear functions
    13. 12.13Parallel and perpendicular lines in linear functions
    14. 12.14Applications of linear relations
  13. 13Linear Equations
    1. 13.1Introduction to linear equations
    2. 13.2Introduction to nonlinear equations
    3. 13.3Special case of linear equations: Horizontal lines
    4. 13.4Special case of linear equations: Vertical lines
    5. 13.5Parallel line equation
    6. 13.6Perpendicular line equation
    7. 13.7Combination of both parallel and perpendicular line equations
    8. 13.8Applications of linear equations
  14. 14Solving Systems of Linear Equations
    1. 14.1Determining number of solutions to linear equations
    2. 14.2Solving systems of linear equations by graphing
    3. 14.3Using elimination method to solve systems of equations
    4. 14.4Using substitution method to solve systems of equations
    5. 14.5Money related questions in linear equations
    6. 14.6Unknown number related questions in linear equations
    7. 14.7Distance and time related questions in linear equations
    8. 14.8Rectangular shape related questions in linear equations
  15. 15Exponents
    1. 15.1Product rule of exponents
    2. 15.2Quotient rule of exponents
    3. 15.3Power of a product rule
    4. 15.4Power of a quotient rule
    5. 15.5Power of a power rule
    6. 15.6Negative exponent rule
    7. 15.7Combining the exponent rules
    8. 15.8Scientific notation
    9. 15.9Convert between radicals and rational exponents
    10. 15.10Solving for exponents
  16. 16Operations with Polynomials
    1. 16.1What is a polynomial?
    2. 16.2Polynomial components
    3. 16.3Multiplying monomial by monomial
    4. 16.4Multiplying monomial by binomial
    5. 16.5Multiplying binomial by binomial
    6. 16.6Multiplying polynomial by polynomial
    7. 16.7Applications of polynomials
  17. 17Factoring Polynomial Expressions
    1. 17.1Common factors of polynomials
    2. 17.2Factoring polynomials by grouping
    3. 17.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
    4. 17.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
    5. 17.5Factoring polynomials: x2+bx+cx^2 + bx + c
    6. 17.6Applications of polynomials: x2+bx+cx^2 + bx + c
    7. 17.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
    8. 17.8Factoring polynomials: ax2+bx+cax^2 + bx + c
    9. 17.9Factoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2
    10. 17.10Find the difference of squares: (ab)(a+b)=(a2b2)(a - b)(a + b) = (a^2 - b^2)
    11. 17.11Evaluating polynomials
    12. 17.12Using algebra tiles to factor polynomials
    13. 17.13Solving polynomial equations
    14. 17.14Word problems of polynomials
  18. 18Factoring Trinomials (Advanced)
    1. 18.1Factor by taking out the greatest common factor
    2. 18.2Factor by grouping
    3. 18.3Factoring difference of squares: x2y2x^2 - y^2
    4. 18.4Factoring trinomials
    5. 18.5Factoring difference of cubes
    6. 18.6Factoring sum of cubes
  19. 19Rational Expressions
    1. 19.1Simplifying rational expressions and restrictions
    2. 19.2Adding and subtracting rational expressions
    3. 19.3Multiplying rational expressions
    4. 19.4Dividing rational expressions
    5. 19.5Solving rational equations
    6. 19.6Applications of rational equations
    7. 19.7Simplifying complex fractions
    8. 19.8Partial fraction decomposition
  20. 20Reciprocal Functions
    1. 20.1Graphing reciprocals of linear functions
    2. 20.2Graphing reciprocals of quadratic functions
  21. 21Radicals
    1. 21.1Square and square roots
    2. 21.2Cubic and cube roots
    3. 21.3Evaluating and simplifying radicals
    4. 21.4Converting radicals to mixed radicals
    5. 21.5Converting radicals to entire radicals
    6. 21.6Adding and subtracting radicals
    7. 21.7Multiplying and dividing radicals
    8. 21.8Rationalize the denominator
  22. 22Radicals (Advanced)
    1. 22.1Operations with radicals
    2. 22.2Conversion between entire radicals and mixed radicals
    3. 22.3Adding and subtracting radicals
    4. 22.4Multiplying radicals
    5. 22.5Solving radical equations
  23. 23Ratios, Rates, and Proportions
    1. 23.1Ratios
    2. 23.2Rates
    3. 23.3Proportions
  24. 24Angles, Lines, and Transversals
    1. 24.1Pairs of lines and angles
    2. 24.2Parallel lines and transversals
    3. 24.3Parallel line proofs
    4. 24.4Perpendicular line proofs
  25. 25Scale Factors and Similarity
    1. 25.1Enlargements and reductions with scale factors
    2. 25.2Scale diagrams
    3. 25.3Similar triangles
    4. 25.4Similar polygons
  26. 26Surface Area and Perimeter of Polygons
    1. 26.1Classifying Triangles
  27. 27Circles
    1. 27.1Circles and circumference
    2. 27.2Arcs of a circle
    3. 27.3Areas and sectors of circles
    4. 27.4Angles in a circle
    5. 27.5Chord properties in circles
    6. 27.6Tangent properties in circles
    7. 27.7Central and inscribed angles in circles
    8. 27.8Equation of a circle
  28. 28Statistics
    1. 28.1Median and mode
    2. 28.2Mean
    3. 28.3Range and outliers
    4. 28.4Application of averages
  29. 29Sequences and Series
    1. 29.1Arithmetic sequences
    2. 29.2Arithmetic series
    3. 29.3Geometric sequences
    4. 29.4Geometric series
    5. 29.5Infinite geometric series
    6. 29.6Sigma notation
    7. 29.7Arithmetic mean vs. Geometric mean
  30. 30Functions
    1. 30.1Function notation
    2. 30.2Operations with functions
    3. 30.3Adding functions
    4. 30.4Subtracting functions
    5. 30.5Multiplying functions
    6. 30.6Dividing functions
    7. 30.7Composite functions
    8. 30.8Inequalities of combined functions
    9. 30.9Inverse functions
    10. 30.10One to one functions
    11. 30.11Difference quotient: applications of functions
  31. 31Exponential Functions
    1. 31.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
    2. 31.2Exponents: Division rule axay=a(xy){a^x \over a^y}=a^{(x-y)}
    3. 31.3Exponents: Power rule (ax)y=a(xy) (a^x)^y = a^{(x\cdot y)}
    4. 31.4Exponents: Negative exponents
    5. 31.5Exponents: Zero exponent: a0=1 a^0 = 1
    6. 31.6Exponents: Rational exponents
    7. 31.7Solving exponential equations using exponent rules
    8. 31.8Graphing exponential functions
    9. 31.9Graphing transformations of exponential functions
    10. 31.10Finding an exponential function given its graph
  32. 32Logarithmic Functions
    1. 32.1What is a logarithm?
    2. 32.2Converting from logarithmic form to exponential form
    3. 32.3Evaluating logarithms without a calculator
    4. 32.4Common logarithms
    5. 32.5Natural log: ln
    6. 32.6Evaluating logarithms using change-of-base formula
    7. 32.7Converting from exponential form to logarithmic form
    8. 32.8Solving exponential equations with logarithms
    9. 32.9Product rule of logarithms
    10. 32.10Quotient rule of logarithms
    11. 32.11Combining product rule and quotient rule in logarithms
    12. 32.12Evaluating logarithms using logarithm rules
    13. 32.13Solving logarithmic equations
    14. 32.14Graphing logarithmic functions
    15. 32.15Finding a logarithmic function given its graph
  33. 33Applications of Exponential and Logarithmic Functions
    1. 33.1Exponential growth and decay by a factor
    2. 33.2Exponential decay: Half-life
    3. 33.3Exponential growth and decay by percentage
    4. 33.4Finance: Compound interest
    5. 33.5Continuous growth and decay
    6. 33.6Logarithmic scale: Richter scale (earthquake)
    7. 33.7Logarithmic scale: pH scale
    8. 33.8Logarithmic scale: dB scale
    9. 33.9Finance: Future value and present value
  34. 34Right Triangle Trigonometry
    1. 34.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
    2. 34.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
    3. 34.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
    4. 34.4Combination of SohCahToa questions
    5. 34.5Solving expressions using 45-45-90 special right triangles
    6. 34.6Solving expressions using 30-60-90 special right triangles
    7. 34.7Word problems relating ladder in trigonometry
    8. 34.8Word problems relating guy wire in trigonometry
    9. 34.9Other word problems relating angles in trigonometry
  35. 35Laws of sines and cosines
    1. 35.1Law of sines
    2. 35.2Law of cosines
    3. 35.3Applications of the sine law and cosine law
  36. 36Bearings
    1. 36.1Introduction to bearings
    2. 36.2Bearings and direction word problems
    3. 36.3Angle of elevation and depression
  37. 37Trigonometric Ratios and Angle Measure
    1. 37.1Angle in standard position
    2. 37.2Coterminal angles
    3. 37.3Reference angle
    4. 37.4Find the exact value of trigonometric ratios
    5. 37.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 37.6Unit circle
    7. 37.7Converting between degrees and radians
    8. 37.8Trigonometric ratios of angles in radians
    9. 37.9Radian measure and arc length
  38. 38Graphs of Trigonometric Functions
    1. 38.1Sine graph: y = sin x
    2. 38.2Cosine graph: y = cos x
    3. 38.3Tangent graph: y = tan x
    4. 38.4Cotangent graph: y = cot x
    5. 38.5Secant graph: y = sec x
    6. 38.6Cosecant graph: y = csc x
    7. 38.7Graphing transformations of trigonometric functions
    8. 38.8Determining trigonometric functions given their graphs
  39. 39Trigonometric Identities
    1. 39.1Quotient identities and reciprocal identities
    2. 39.2Pythagorean identities
    3. 39.3Sum and difference identities
    4. 39.4Cofunction identities
    5. 39.5Double-angle identities
  40. 40Solving Trigonometric Equations
    1. 40.1Solving first degree trigonometric equations
    2. 40.2Determining non-permissible values for trig expressions
    3. 40.3Solving second degree trigonometric equations
    4. 40.4Solving trigonometric equations involving multiple angles
    5. 40.5Solving trigonometric equations using pythagorean identities
    6. 40.6Solving trigonometric equations using sum and difference identities
    7. 40.7Solving trigonometric equations using double-angle identities
  41. 41Imaginary and Complex Numbers
    1. 41.1Introduction to imaginary numbers
    2. 41.2Complex numbers and complex planes
    3. 41.3Adding and subtracting complex numbers
    4. 41.4Complex conjugates
    5. 41.5Multiplying and dividing complex numbers
    6. 41.6Distance and midpoint of complex numbers
    7. 41.7Angle and absolute value of complex numbers
    8. 41.8Polar form of complex numbers
    9. 41.9Operations on complex numbers in polar form
  42. 42Introduction to Matrices
    1. 42.1Notation of matrices
    2. 42.2Adding and subtracting matrices
    3. 42.3Scalar multiplication
    4. 42.4Matrix multiplication
    5. 42.5The three types of matrix row operations
    6. 42.6Representing a linear system as a matrix
    7. 42.7Solving a linear system with matrices using Gaussian elimination
  43. 43Properties of Matrices
    1. 43.1Zero matrix
    2. 43.2Identity matrix
    3. 43.3Properties of matrix addition
    4. 43.4Properties of scalar multiplication
  44. 44Determinants and Inverses of Matrices
    1. 44.1The determinant of a 2 x 2 matrix
    2. 44.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
    3. 44.3The inverse of a 2 x 2 matrix
    4. 44.4The inverse of 3 x 3 matrices with matrix row operations
    5. 44.5The inverse of 3 x 3 matrix with determinants and adjugate
    6. 44.62 x 2 invertible matrix
    7. 44.7Solving linear systems using Cramer's Rule
    8. 44.8Solving linear systems using 2 x 2 inverse matrices

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FAQs
  • 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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