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ACT Compass Math Prep

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ACT Compass Test Prep Topics

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1. Numbers and Relations

1.1

Place value

1.2

Comparing and ordering numbers

1.3

Rounding numbers

2. Number Theory

2.1

Divisibility Rules

2.2

Determining Common Factors

2.3

Determining Common Multiples

3. Operations with Decimals

3.1

Adding and subtracting decimals

3.2

Multiplying decimals

3.3

Dividing decimals

3.4

Order of operations (PEMDAS)

4. Number System and Radicals

4.1

Understanding the number systems

4.2

Prime factorization

4.3

Greatest Common Factors (GCF)

4.4

Least Common Multiple (LCM)

4.5

Rational vs. Irrational numbers

4.6

Converting repeating decimals to fractions

5. Adding and Substracting Fractions

5.1

Using models to add and subtract fractions

5.2

Adding fractions with like denominators

5.3

Subtracting fractions with like denominators

5.4

Adding and subtracting fractions with unlike denominators

5.5

Adding and subtracting mixed numbers

6. Multiplying and Dividing Fractions

6.1

Multiplying fractions and whole numbers

6.2

Dividing fractions with whole numbers

6.3

Multiplying proper fractions

6.4

Multiplying improper fractions and mixed numbers

6.5

Dividing fractions and mixed numbers

6.6

Applications of fraction operations

7. Fractions, Decimals, and Percents

7.1

Representing percents

7.2

Percent of a number

7.3

Converting among decimals, fractions, and percents

7.4

Adding and multiplying percents

7.5

Applications of percents

7.6

Taxes, discounts, tips and more

7.7

Simple interest

8. Introduction to Variables and Expressions

8.1

Evaluating algebraic expressions

9. Introduction to Equations

9.1

Solving one - step equations: x + a = b

10. Solving Linear Equations

10.1

Solving linear equations using multiplication and division

10.2

Solving two-step linear equations: ax + b = c, x/a + b = c

10.3

Solving linear equations using distributive property: a(x + b) = c

10.4

Solving linear equations with variables on both sides

10.5

Solving literal equations

11. Introduction to Relations and Functions

11.1

Relationship between two variables

11.2

Understand relations between x- and y-intercepts

11.3

Domain and range of a function

11.4

Identifying functions

11.5

Function notation

12. Linear Functions

12.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

12.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

12.3

Slope equation:

m = \frac{y_2-y_1}{x_2- x_1}

12.4

Slope intercept form: y = mx + b

12.5

General form: Ax + By + C = 0

12.6

Point-slope form:

y - y_1 = m (x - x_1)

12.7

Rate of change

12.8

Graphing linear functions using table of values

12.9

Graphing linear functions using x- and y-intercepts

12.10

Graphing from slope-intercept form y=mx+b

12.11

Graphing linear functions using a single point and slope

12.12

Word problems of graphing linear functions

12.13

Parallel and perpendicular lines in linear functions

12.14

Applications of linear relations

13. Linear Equations

13.1

Introduction to linear equations

13.2

Introduction to nonlinear equations

13.3

Special case of linear equations: Horizontal lines

13.4

Special case of linear equations: Vertical lines

13.5

Parallel line equation

13.6

Perpendicular line equation

13.7

Combination of both parallel and perpendicular line equations

13.8

Applications of linear equations

14. Solving Systems of Linear Equations

14.1

Determining number of solutions to linear equations

14.2

Solving systems of linear equations by graphing

14.3

Using elimination method to solve systems of equations

14.4

Using substitution method to solve systems of equations

14.5

14.6

Unknown number related questions in linear equations

14.7

Distance and time related questions in linear equations

14.8

Rectangular shape related questions in linear equations

15. Exponents

15.1

Product rule of exponents

15.2

Quotient rule of exponents

15.3

Power of a product rule

15.4

Power of a quotient rule

15.5

Power of a power rule

15.6

Negative exponent rule

15.7

Combining the exponent rules

15.8

Scientific notation

15.9

Convert between radicals and rational exponents

15.10

Solving for exponents

16. Operations with Polynomials

16.1

What is a polynomial?

16.2

Polynomial components

16.3

Multiplying monomial by monomial

16.4

Multiplying monomial by binomial

16.5

Multiplying binomial by binomial

16.6

Multiplying polynomial by polynomial

16.7

Applications of polynomials

17. Factoring Polynomial Expressions

17.1

Common factors of polynomials

17.2

Factoring polynomials by grouping

17.3

Solving polynomials with the unknown "b" from x^2 + bx + c

17.4

Solving polynomials with the unknown "c" from x^2 + bx + c

17.5

Factoring polynomials: x^2 + bx + c

17.6

Applications of polynomials: x^2 + bx + c

17.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

17.8

Factoring polynomials:

ax^2 + bx + c

17.9

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

17.10

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

17.11

Evaluating polynomials

17.12

Using algebra tiles to factor polynomials

17.13

Solving polynomial equations

17.14

Word problems of polynomials

18. Factoring Trinomials (Advanced)

18.1

Factor by taking out the greatest common factor

18.2

Factor by grouping

18.3

Factoring difference of squares: x^2 - y^2

18.4

Factoring trinomials

18.5

Factoring difference of cubes

18.6

Factoring sum of cubes

19. Rational Expressions

19.1

Simplifying rational expressions and restrictions

19.2

Adding and subtracting rational expressions

19.3

Multiplying rational expressions

19.4

Dividing rational expressions

19.5

Solving rational equations

19.6

Applications of rational equations

19.7

Simplifying complex fractions

19.8

Partial fraction decomposition

20. Reciprocal Functions

20.1

Graphing reciprocals of linear functions

20.2

Graphing reciprocals of quadratic functions

21. Radicals

21.1

Square and square roots

21.2

Cubic and cube roots

21.3

Evaluating and simplifying radicals

21.4

Converting radicals to mixed radicals

21.5

Converting radicals to entire radicals

21.6

Adding and subtracting radicals

21.7

Multiplying and dividing radicals

21.8

Rationalize the denominator

22. Radicals (Advanced)

22.1

Operations with radicals

22.2

Conversion between entire radicals and mixed radicals

22.3

Adding and subtracting radicals

22.4

Multiplying radicals

22.5

Solving radical equations

23. Ratios, Rates, and Proportions

23.1

Ratios

23.2

Rates

23.3

Proportions

24. Angles, Lines, and Transversals

24.1

Pairs of lines and angles

24.2

Parallel lines and transversals

24.3

Parallel line proofs

24.4

Perpendicular line proofs

25. Scale Factors and Similarity

25.1

Enlargements and reductions with scale factors

25.2

Scale diagrams

25.3

Similar triangles

25.4

Similar polygons

26. Surface Area and Perimeter of Polygons

26.1

Classifying Triangles

27. Circles

27.1

Circles and circumference

27.2

Arcs of a circle

27.3

Areas and sectors of circles

27.4

Angles in a circle

27.5

Chord properties in circles

27.6

Tangent properties in circles

27.7

Central and inscribed angles in circles

27.8

Equation of a circle

28. Statistics

28.1

Median and mode

28.2

Mean

28.3

Range and outliers

28.4

Application of averages

29. Sequences and Series

29.1

29.2

29.3

29.4

29.5

Infinite geometric series

29.6

Sigma notation

29.7

Arithmetic mean vs. Geometric mean

30. Functions

30.1

Function notation

30.2

Operations with functions

30.3

Adding functions

30.4

Subtracting functions

30.5

Multiplying functions

30.6

Dividing functions

30.7

Composite functions

30.8

Inequalities of combined functions

30.9

Inverse functions

30.10

One to one functions

30.11

Difference quotient: applications of functions

31. Exponential Functions

31.1

Exponents: Product rule (a^x)(a^y) = a^(x+y)

31.2

Exponents: Division rule (a^x / a^y) = a^(x-y)

31.3

Exponents: Power rule (a^x)^y = a^(x * y)

31.4

Exponents: Negative exponents

31.5

Exponents: Zero exponent: a^0 = 1

31.6

Exponents: Rational exponents

31.7

Solving exponential equations using exponent rules

31.8

Graphing exponential functions

31.9

Graphing transformations of exponential functions

31.10

Finding an exponential function given its graph

32. Logarithmic Functions

32.1

What is a logarithm?

32.2

Converting from logarithmic form to exponential form

32.3

Evaluating logarithms without a calculator

32.4

Common logarithms

32.5

Natural log: ln

32.6

Evaluating logarithms using change-of-base formula

32.7

Converting from exponential form to logarithmic form

32.8

Solving exponential equations with logarithms

32.9

Product rule of logarithms

32.10

Quotient rule of logarithms

32.11

Combining product rule and quotient rule in logarithms

32.12

Evaluating logarithms using logarithm rules

32.13

Solving logarithmic equations

32.14

Graphing logarithmic functions

32.15

Finding a logarithmic function given its graph

33. Applications of Exponential and Logarithmic Functions

33.1

Exponential growth and decay by a factor

33.2

Exponential decay: Half-life

33.3

Exponential growth and decay by percentage

33.4

Finance: Compound interest

33.5

Continuous growth and decay

33.6

Logarithmic scale: Richter scale (earthquake)

33.7

Logarithmic scale: pH scale

33.8

Logarithmic scale: dB scale

33.9

Finance: Future value and present value

34. Right Triangle Trigonometry

34.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

34.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

34.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

34.4

Combination of SohCahToa questions

34.5

Solving expressions using 45-45-90 special right triangles

34.6

Solving expressions using 30-60-90 special right triangles

34.7

Word problems relating ladder in trigonometry

34.8

Word problems relating guy wire in trigonometry

34.9

Other word problems relating angles in trigonometry

35. Laws of sines and cosines

35.1

Law of sines

35.2

Law of cosines

35.3

Applications of the sine law and cosine law

36. Bearings

36.1

Introduction to bearings

36.2

Bearings and direction word problems

36.3

Angle of elevation and depression

37. Trigonometric Ratios and Angle Measure

37.1

Angle in standard position

37.2

Coterminal angles

37.3

Reference angle

37.4

Find the exact value of trigonometric ratios

37.5

ASTC rule in trigonometry (All Students Take Calculus)

37.6

Unit circle

37.7

Converting between degrees and radians

37.8

Trigonometric ratios of angles in radians

37.9

Radian measure and arc length

38. Graphs of Trigonometric Functions

38.1

Sine graph: y = sin x

38.2

Cosine graph: y = cos x

38.3

Tangent graph: y = tan x

38.4

Cotangent graph: y = cot x

38.5

Secant graph: y = sec x

38.6

Cosecant graph: y = csc x

38.7

Graphing transformations of trigonometric functions

38.8

Determining trigonometric functions given their graphs

39. Trigonometric Identities

39.1

Quotient identities and reciprocal identities

39.2

Pythagorean identities

39.3

Sum and difference identities

39.4

Cofunction identities

39.5

Double-angle identities

40. Solving Trigonometric Equations

40.1

Solving first degree trigonometric equations

40.2

Determining non-permissible values for trig expressions

40.3

Solving second degree trigonometric equations

40.4

Solving trigonometric equations involving multiple angles

40.5

Solving trigonometric equations using pythagorean identities

40.6

Solving trigonometric equations using sum and difference identities

40.7

Solving trigonometric equations using double-angle identities

41. Imaginary and Complex Numbers

41.1

Introduction to imaginary numbers

41.2

Complex numbers and complex planes

41.3

Adding and subtracting complex numbers

41.4

Complex conjugates

41.5

Multiplying and dividing complex numbers

41.6

Distance and midpoint of complex numbers

41.7

Angle and absolute value of complex numbers

41.8

Polar form of complex numbers

41.9

Operations on complex numbers in polar form

42. Introduction to Matrices

42.1

Notation of matrices

42.2

Adding and subtracting matrices

42.3

Scalar multiplication

42.4

Matrix multiplication

42.5

The three types of matrix row operations

42.6

Representing a linear system as a matrix

42.7

Solving a linear system with matrices using Gaussian elimination

43. Properties of Matrices

43.1

Zero matrix

43.2

Identity matrix

43.3

Properties of matrix addition

43.4

Properties of scalar multiplication

44. Determinants and Inverses of Matrices

44.1

The determinant of a 2 x 2 matrix

44.2

The determinant of a 3 x 3 matrix (General & Shortcut Method)

44.3

The inverse of a 2 x 2 matrix

44.4

The inverse of 3 x 3 matrices with matrix row operations

44.5

The inverse of 3 x 3 matrix with determinants and adjugate

44.6

2 x 2 invertible matrix

44.7

Solving linear systems using Cramer's Rule

44.8

Solving linear systems using 2 x 2 inverse matrices

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