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Math 30-2 (Alberta) Topics

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1Rational Expressions

1.1Simplifying rational expressions and restrictions
1.2Adding and subtracting rational expressions (free lessons)
1.3Multiplying rational expressions
1.4Dividing rational expressions
1.5Solving rational equations
1.6Applications of rational equations
1.7Simplifying complex fractions
1.8Partial Fraction Decomposition

2Polynomial Functions

2.1What is a polynomial function? (free lessons)
2.2Polynomial long division (free lessons)
2.3Polynomial synthetic division
2.4Remainder theorem
2.5Factor theorem
2.6Rational zero theorem
2.7Characteristics of polynomial graphs
2.8Multiplicities of polynomials
2.9Imaginary zeros of polynomials
2.10Determining the equation of a polynomial function
2.11Applications of polynomial functions
2.12Solving polynomial inequalities
2.13Fundamental theorem of algebra
2.14Descartes’ rule of signs

3Exponential Functions

3.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
3.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
3.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
3.4Exponents: Negative exponents
3.5Exponents: Zero exponent: a0=1 a^0 = 1
3.6Exponents: Rational exponents
3.7Solving exponential equations using exponent rules
3.8Graphing exponential functions
3.9Graphing transformations of exponential functions
3.10Finding an exponential function given its graph

4Logarithmic Functions

4.1What is a logarithm?
4.2Converting from logarithmic form to exponential form (free lessons)
4.3Evaluating logarithms without a calculator
4.4Common logarithms
4.5Natural log: ln
4.6Evaluating logarithms using change-of-base formula
4.7Converting from exponential form to logarithmic form (free lessons)
4.8Solving exponential equations with logarithms
4.9Product rule of logarithms (free lessons)
4.10Quotient rule of logarithms
4.11Combining product rule and quotient rule in logarithms
4.12Evaluating logarithms using logarithm rules
4.13Solving logarithmic equations (free lessons)
4.14Graphing logarithmic functions
4.15Finding a logarithmic function given its graph

5Applications of Exponential and Logarithmic Functions

5.1Exponential growth and decay by a factor
5.2Exponential decay: Half-life (free lessons)
5.3Exponential growth and decay by percentage
5.4Finance: Compound interest
5.5Continuous growth and decay
5.6Logarithmic scale: Richter scale (earthquake)
5.7Logarithmic scale: pH scale
5.8Logarithmic scale: dB scale
5.9Finance: Future value and present value

6Data Collection

6.1Influencing factors in data collection (free lessons)
6.2Data collection
6.3Introduction to probability

7Permutations and Combinations

7.1Fundamental counting principle
7.2Factorial notation
7.3Path counting problems
7.4Permutation vs. Combination
7.5Permutations
7.6Combinations
7.7Problems involving both permutations and combinations
7.8Pascal's triangle
7.9Binomial theorem

8Probability

8.1Introduction to probability
8.2Determining probabilities using tree diagrams and tables (free lessons)
8.3Probability of independent events
8.4Probability with Venn diagrams
8.5Addition rule for "OR"
8.6Multiplication rule for "AND"
8.7Conditional probability
8.8Probability with permutations and combinations

9Scatter Plots and Best Fit Line

9.1Bivariate, scatter plots and correlation
9.2Regression analysis
9.3Equation of the best fit line
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