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Math 30-2 (Alberta) Topics

Rational Expressions

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Applications of rational equations

Simplifying complex fractions

Partial Fraction Decomposition

Reciprocal Functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Polynomial Functions

What is a polynomial function?

Polynomial long division

Polynomial synthetic division

Remainder theorem

Rational zero theorem

Characteristics of polynomial graphs

Multiplicities of polynomials

Imaginary zeros of polynomials

Determining the equation of a polynomial function

Applications of polynomial functions

Solving polynomial inequalities

Fundamental theorem of algebra

Descartes' rule of signs

Exponential Functions

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

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

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

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Logarithmic Functions

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Applications of Exponential and Logarithmic Functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Data Collection

Influencing factors in data collection

Data collection

Introduction to probability

Permutations and Combinations

Fundamental counting principle

Factorial notation

Path counting problems

Permutation vs. Combination

Problems involving both permutations and combinations

Pascal's triangle

Binomial theorem

Probability

Introduction to probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

Addition rule for "OR"

Multiplication rule for "AND"

Conditional probability

Probability with permutations and combinations

Scatter Plots and Best Fit Line

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

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