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Functions, polynomials, exponential and logarithmic equations, systems of equations, graphing techniques, rational expressions, and quadratic equations.

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College Algebra Topics

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1. Surface Area and Volume

1.1

Introduction to surface area of 3-dimensional shapes

1.2

Nets of 3-dimensional shapes

1.3

Surface area of 3-dimensional shapes

1.4

Surface area of prisms

1.5

Surface area of cylinders

2. Rational Numbers

2.1

Comparing and ordering rational numbers

2.2

Solving problems with rational numbers in decimal form

2.3

Solving problems with rational numbers in fraction form

2.4

Determine square roots of rational numbers

3. Powers and Exponents

3.1

Using exponents to describe numbers

3.2

Exponent rules

3.3

Order of operations with exponents

3.4

Using exponents to solve problems

4. Number System and Radicals

4.1

Understanding the number systems

4.2

Prime factorisation

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. Radicals

5.1

Square and square roots

5.2

Cubic and cube roots

5.3

Evaluating and simplifying radicals

5.4

Converting radicals to mixed radicals

5.5

Converting radicals to entire radicals

5.6

Adding and subtracting radicals

5.7

Multiplying and dividing radicals

5.8

Rationalize the denominator

5.9

Operations with radicals

5.10

Conversion between entire radicals and mixed radicals

5.11

Adding and subtracting radicals

5.12

Multiplying radicals (advanced)

5.13

Solving radical equations (advanced)

6. Exponents

6.1

Product rule of exponents

6.2

Quotient rule of exponents

6.3

Power of a product rule

6.4

Power of a quotient rule

6.5

Power of a power rule

6.6

Negative exponent rule

6.7

Combining the exponent rules

6.8

Scientific notation

6.9

Rational exponents

6.10

Solving for exponents

7. Operations of Polynomials

7.1

What is a polynomial?

7.2

Polynomial components

7.3

Multiplying monomial by monomial

7.4

Multiplying monomial by binomial

7.5

Multiplying binomial by binomial

7.6

Multiplying polynomial by polynomial

7.7

Applications of polynomials

8. Factorising Polynomial Expressions

8.1

Common factors of polynomials

8.2

Factorising polynomials by grouping

8.3

Solving polynomials with unknown coefficients

8.4

Solving polynomials with unknown constant terms

8.5

Factorising polynomials: x^2 + bx + c

8.6

Applications of polynomials: x^2 + bx + c

8.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

8.8

Factorising polynomials:

ax^2 + bx + c

8.9

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

8.10

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

8.11

Evaluating polynomials

8.12

Using algebra tiles to factorise polynomials

8.13

Solving polynomial equations

8.14

Word problems of polynomials

9. Introduction to Relations and Functions

9.1

Relationship between two variables

9.2

Understand relations between x- and y-intercepts

9.3

Domain and range of a function

9.4

Identifying functions

9.5

Function notation

10. Linear Functions

10.1

Distance formula:

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

10.2

Midpoint formula:

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

10.3

Gradient equation:

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

10.4

Gradient intercept form: y = mx + b

10.5

General form: Ax + By + C = 0

10.6

Gradient-point form:

y - y_1 = m (x - x_1)

10.7

Rate of change

10.8

Graphing linear functions using table of values

10.9

Graphing linear functions using x- and y-intercepts

10.10

Graphing from slope-intercept form y=mx+b

10.11

Graphing linear functions using a single point and gradient

10.12

Word problems of graphing linear functions

10.13

Parallel and perpendicular lines in linear functions

10.14

Applications of linear relations

11. Absolute Value Functions

11.1

Absolute value functions

11.2

Solving absolute value equations

11.3

Solving absolute value inequalities

12. Linear Equations

12.1

Introduction to linear equations

12.2

Introduction to nonlinear equations

12.3

Special case of linear equations: Horizontal lines

12.4

Special case of linear equations: Vertical lines

12.5

Parallel line equation

12.6

Perpendicular line equation

12.7

Combination of both parallel and perpendicular line equations

12.8

Applications of linear equations

13. Solving Linear Systems

13.1

Determining number of solutions to linear equations

13.2

Solving systems of linear equations by graphing

13.3

Using elimination method to solve systems of equations

13.4

Using substitution method to solve systems of equations

13.5

13.6

Unknown number related questions in linear equations

13.7

Distance and time related questions in linear equations

13.8

Rectangular shape related questions in linear equations

13.9

Solving 3 variable systems of equations by substitution

13.10

Solving 3 variable systems of equations by elimination

13.11

Solving 3 variable systems of equations (no solution, infinite solutions)

13.12

Word problems relating 3 variable systems of equations

14. Linear Inequalities

14.1

Express linear inequalities graphically and algebraically

14.2

Solving one-step linear inequalities

14.3

Solving multi-step linear inequalities

14.4

Compound inequalities

15. Inequalities in Two Variables

15.1

Graphing linear inequalities in two variables

15.2

Graphing simultaneous linear inequalities

15.3

Graphing quadratic inequalities in two variables

15.4

Graphing simultaneous quadratic inequalities

15.5

Applications of inequalities

15.6

What is linear programming?

15.7

Linear programming word problems

16. Factorising Quadratic Equations

16.1

Factorise by taking out the greatest common factor

16.2

Factorise by grouping

16.3

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

16.4

Factorising trinomials

16.5

Factoring difference of cubes

16.6

Factoring sum of cubes

17. Quadratic Functions

17.1

Characteristics of quadratic functions

17.2

Transformations of quadratic functions

17.3

Quadratic function in general form: y =

ax^2 + bx+c

17.4

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

17.5

Completing the square

17.6

Converting from general to vertex form by completing the square

17.7

Shortcut: Vertex formula

17.8

Graphing parabolas for given quadratic functions

17.9

Finding the quadratic functions for given parabolas

17.10

Applications of quadratic functions

18. Quadratic Equations and Inequalities

18.1

Solving quadratic equations by factorising

18.2

Solving quadratic equations by completing the square

18.3

Using quadratic formula to solve quadratic equations

18.4

Nature of roots of quadratic equations: The discriminant

18.5

Applications of quadratic equations

18.6

Solving quadratic inequalities

19. Graphing Rational Functions

19.1

Graphing reciprocals of linear functions

19.2

Graphing reciprocals of quadratic functions

19.3

Graphs of rational functions

20. Functions

20.1

Function notation

20.2

Operations with functions

20.3

Adding functions

20.4

Subtracting functions

20.5

Multiplying functions

20.6

Dividing functions

20.7

Composite functions

20.8

Inequalities of combined functions

20.9

Inverse functions

20.10

One to one functions

20.11

Difference quotient: applications of functions

21. Direct and Inverse Variation

21.1

Direct variation

21.2

Inverse variation

21.3

Joint and combined variation

22. Piecewise Functions

22.1

Evaluating piecewise functions

22.2

Graphing piecewise linear functions

22.3

Graphing piecewise non-linear functions

23. Transformations of Functions

23.1

Transformations of functions: Horizontal translations

23.2

Transformations of functions: Vertical translations

23.3

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

23.4

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

23.5

Transformations of functions: Horizontal stretches

23.6

Transformations of functions: Vertical stretches

23.7

Combining transformations of functions

23.8

Even and odd functions

24. Exponential Functions

24.1

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

24.2

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

24.3

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

24.4

Exponents: Negative exponents

24.5

Exponents: Zero exponent: a^0 = 1

24.6

Exponents: Rational exponents

24.7

Solving exponential equations using exponent rules

24.8

Graphing exponential functions

24.9

Graphing transformations of exponential functions

24.10

Finding an exponential function given its graph

25. Logarithmic Functions

25.1

What is a logarithm?

25.2

Converting from logarithmic form to exponential form

25.3

Evaluating logarithms without a calculator

25.4

Common logarithms

25.5

Natural log: ln

25.6

Evaluating logarithms using change-of-base formula

25.7

Converting from exponential form to logarithmic form

25.8

Solving exponential equations with logarithms

25.9

Product rule of logarithms

25.10

Quotient rule of logarithms

25.11

Combining product rule and quotient rule in logarithms

25.12

Evaluating logarithms using logarithm rules

25.13

Solving logarithmic equations

25.14

Graphing logarithmic functions

25.15

Finding a logarithmic function given its graph

26. Applications of Exponential and Logarithmic Functions

26.1

Exponential growth and decay by a factor

26.2

Exponential decay: Half-life

26.3

Exponential growth and decay by percentage

26.4

Finance: Compound interest

26.5

Continuous growth and decay

26.6

Logarithmic scale: Richter scale (earthquake)

26.7

Logarithmic scale: pH scale

26.8

Logarithmic scale: dB scale

26.9

Finance: Future value and present value

27. Sequences and Series

27.1

27.2

27.3

27.4

27.5

Infinite geometric series

27.6

Sigma notation

28. Permutations and Combinations

28.1

Fundamental counting principle

28.2

Factorial notation

28.3

Path counting problems

28.4

Permutation vs. Combination

28.5

Permutations

28.6

Combinations

28.7

Problems involving both permutations and combinations

28.8

Pascal's triangle

28.9

Binomial theorem

28Chapters

215Topics

1320Videos

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