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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=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
12.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
12.3 Slope equation: m=y2−y1x2−x1m = \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−y1=m(x−x1)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 Money related questions in linear equations
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 ax2+bx+cax^2 + bx + c
17.8 Factoring polynomials: ax2+bx+cax^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 Arithmetic sequences
29.2 Arithmetic series
29.3 Geometric sequences
29.4 Geometric series
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 = oh \frac{o}{h} )
34.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
34.3 Use tangent ratio to calculate angles and sides (Tan = oa \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

44 Chapters · 284 Topics · 1876 Videos

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