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SAT Test Prep Topics

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1. Understanding Integers

1.1

1.2

Comparing and ordering numbers

1.3

Rounding numbers

2. Adding and Subtracting Integers

2.1

Introduction to integer addition

2.2

Adding integers

2.3

Introduction to integer subtraction

2.4

Subtracting integers

2.5

Application of integer operations

3. Multiplying and Dividing Integers

3.1

Understanding integer multiplication

3.2

Multiplying integers

3.3

Understanding integer division

3.4

Dividing integers

3.5

Applications of integer operations

4. Number Theory

4.1

Divisibility Rules

4.2

Determining Common Factors

4.3

Determining Common Multiples

4.4

Introduction to exponents

5. Adding and Subtracting 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. Operation with Decimals

7.1

Adding and subtracting decimals

7.2

Multiplying decimals

7.3

Dividing decimals

7.4

Order of operations (BEDMAS)

8. Fractions, Decimals, and Percents

8.1

Representing percents

8.2

Percent of a number

8.3

Converting among decimals, fractions, and percents

8.4

Applications of percents

8.5

Taxes, discounts, tips and more

9. Ratios, Rates, and Proportions

9.1

9.2

9.3

10. Introduction to Variables and Expressions

10.1

Evaluating algebraic expressions

11. Solving Linear Equations

11.1

Solving linear equations using multiplication and division

11.2

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

11.3

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

11.4

Solving linear equations with variables on both sides

11.5

Solving literal equations

12. Linear Inequalities

12.1

Express linear inequalities graphically and algebraically

12.2

Solving one-step linear inequalities

12.3

Solving multi-step linear inequalities

12.4

Compound inequalities

12.5

Graphing linear inequalities in two variables

13. Measuring Systems

13.1

13.2

Imperial systems

13.3

Conversions between metric and imperial systems

13.4

Conversions involve squares and cubic

14. Number System

14.1

Understanding the number systems

14.2

Prime factorization

14.3

Greatest Common Factors (GCF)

14.4

Least Common Multiple (LCM)

14.5

Rational vs. Irrational numbers

14.6

Converting repeating decimals to fractions

15. Radicals

15.1

Operations with radicals

15.2

Conversion between entire radicals and mixed radicals

15.3

Adding and subtracting radicals

15.4

Multiplying radicals

15.5

Solving radical equations

16. Exponents

16.1

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

16.2

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

16.3

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

16.4

Exponents: Negative exponents

16.5

Exponents: Zero exponent: a^0 = 1

16.6

Exponents: Rational exponents

16.7

Scientific notation

16.8

Convert between radicals and rational exponents

16.9

Solving for exponents

16.10

Solving exponential equations using exponent rules

17. Operations of Polynomials

17.1

What is a polynomial?

17.2

Polynomial components

17.3

Multiplying monomial by monomial

17.4

Multiplying monomial by binomial

17.5

Multiplying binomial by binomial

17.6

Multiplying polynomial by polynomial

17.7

Applications of polynomials

18. Introduction to Relations and Functions

18.1

Relationship between two variables

18.2

Understand relations between x- and y-intercepts

18.3

Domain and range of a function

18.4

Identifying functions

18.5

Function notation

19. Linear Functions

19.1

Distance formula:

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

19.2

Midpoint formula:

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

19.3

Slope equation:

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

19.4

Slope intercept form: y = mx + b

19.5

General form: Ax + By + C = 0

19.6

Point-slope form:

y - y_1 = m (x - x_1)

19.7

19.8

Graphing linear functions using table of values

19.9

Graphing linear functions using x- and y-intercepts

19.10

Graphing from slope-intercept form y=mx+b

19.11

Graphing linear functions using a single point and slope

19.12

Word problems of graphing linear functions

19.13

Parallel and perpendicular lines in linear functions

19.14

Applications of linear relations

20. Systems of Equations

20.1

Determining number of solutions to linear equations

20.2

Solving systems of linear equations by graphing

20.3

Using elimination method to solve systems of linear equations

20.4

Using substitution method to solve systems of linear equations

20.5

System of linear-quadratic equations

21. Factoring Polynomials

21.1

Factor by taking out the greatest common factor

21.2

Factor by grouping

21.3

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

21.4

Factoring trinomials

21.5

Factoring difference of cubes

21.6

Factoring sum of cubes

22. Quadratic Functions

22.1

Introduction to quadratic functions

22.2

Transformations of quadratic functions

22.3

Quadratic function in general form: y = ax^2 + bx + c

22.4

Quadratic function in vertex form: y = a(x-p)^2 + q

22.5

Completing the square

22.6

Converting from general to vertex form by completing the square

22.7

Shortcut: Vertex formula

22.8

Graphing quadratic functions: General form VS. Vertex form

22.9

Finding the quadratic functions for given parabolas

22.10

Applications of quadratic functions

23. Solving Quadratic Equations

23.1

Solving quadratic equations by factoring

23.2

Solving quadratic equations by completing the square

23.3

Using quadratic formula to solve quadratic equations

23.4

Nature of roots of quadratic equations: The discriminant

23.5

Applications of quadratic equations

23.6

Solving quadratic inequalities

24. Rational Expressions

24.1

Simplifying rational expressions and restrictions

24.2

Adding and subtracting rational expressions

24.3

Multiplying rational expressions

24.4

Dividing rational expressions

24.5

Solving rational equations

24.6

Applications of rational equations

24.7

Simplifying complex fractions

24.8

Partial fraction decomposition

25. Function Notation

25.1

Function notation

25.2

Operations with functions

25.3

Adding functions

25.4

Subtracting functions

25.5

Multiplying functions

25.6

Dividing functions

25.7

Composite functions

25.8

Inequalities of combined functions

25.9

Inverse functions

25.10

One to one functions

25.11

Difference quotient: applications of functions

26. Transformations of Functions

26.1

Transformations of functions: Horizontal translations

26.2

Transformations of functions: Vertical translations

26.3

Reflection across the y-axis: y = f(-x)

26.4

Reflection across the x-axis: y = -f(x)

26.5

Transformations of functions: Horizontal stretches

26.6

Transformations of functions: Vertical stretches

26.7

Combining transformations of functions

26.8

Even and odd functions

27. Polynomial Functions

27.1

What is a polynomial function?

27.2

Polynomial long division

27.3

Polynomial synthetic division

27.4

Remainder theorem

27.5

27.6

Rational zero theorem

27.7

Characteristics of polynomial graphs

27.8

Multiplicities of polynomials

27.9

Imaginary zeros of polynomials

27.10

Descartes' rule of signs

28. Direct and Inverse Variation

28.1

Direct variation

29. Trigonometry with Right Triangles

29.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

29.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

29.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

29.4

Combination of SohCahToa questions

29.5

Solving expressions using 45-45-90 special right triangles

29.6

Solving expressions using 30-60-90 special right triangles

29.7

Word problems relating ladder in trigonometry

29.8

Word problems relating guy wire in trigonometry

29.9

Other word problems relating angles in trigonometry

30. Trigonometric Ratios and Angle Measure

30.1

Standard angles

30.2

Coterminal angles

30.3

Reference angles

30.4

Find the exact value of trigonometric ratios

30.5

ASTC rule in trigonometry (All Students Take Calculus)

30.6

30.7

Converting between degrees and radians

30.8

Trigonometric ratios of angles in radians

30.9

Radian measure and arc length

31. Law of Sines and Cosines

31.1

31.2

31.3

Applications of the sine law and cosine law

32. Imaginary and Complex Numbers

32.1

Introduction to imaginary numbers

32.2

Adding and subtracting complex numbers

32.3

Complex conjugates

32.4

Multiplying and dividing complex numbers

33. Angles, Lines, and Transversals

33.1

Pairs of lines and angles

33.2

Parallel lines and transversals

33.3

Parallel line proofs

33.4

Perpendicular line proofs

34. Circles

34.1

Circle and circumference

34.2

Angles in a circle

34.3

Arcs of a circle

34.4

Areas and sectors of circles

34.5

Conics - Circle

35. Surface Area and Volume

35.1

Surface area and volume of prisms

35.2

Surface area and volume of pyramids

35.3

Surface area and volume of cylinders

35.4

Surface area and volume of cones

35.5

Surface area and volume of spheres

36. Statistics

36.1

Median and mode

36.2

36.3

Range and outliers

36.4

Application of averages

37. Data and Graphs

37.1

Reading and drawing bar graphs

37.2

Reading and drawing histograms

37.3

Reading and drawing line graphs

37.4

Box-and-whisker plots and scatter plots

37.5

Stem-and-leaf plots

37.6

Reading and drawing Venn diagrams

38. Probability

38.1

Determining probabilities using tree diagrams and tables

38.2

Probability of independent events

38.3

Probability with Venn diagrams

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