High School Mathematics 2 – New Nation Academy

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Functions 8 Topics

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Find values of functions from graphs

Add, subtract, multiply, and divide functions

Composition of functions

Identify inverse functions

Find values of inverse functions from tables

Find values of inverse functions from graphs

Find inverse functions and relations

How polynomials behave

Rational functions 1 Topic

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Find the limit at a vertical asymptote of a rational function I

Trigonometric functions 16 Topics

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Convert between radians and degrees

Quadrants

Co-terminal and reference angles

Find trigonometric ratios using right triangles

Find trigonometric ratios using the unit circle

Find trigonometric ratios using reference angles

Inverses of trigonometric functions

Find properties of sine functions

Write equations of sine functions from graphs

Write equations of sine functions using properties

Graph sine functions

Find properties of cosine functions

Write equations of cosine functions from graphs

Write equations of cosine functions using properties

Graph cosine functions

Graph sine and cosine functions

Exponential and logarithmic functions 9 Topics

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Domain and range of exponential and logarithmic functions

Convert between exponential and logarithmic form

Evaluate logarithms

Change of base formula

Product property of logarithms

Quotient property of logarithms

Power property of logarithms

Evaluate logarithms using properties

Describe linear and exponential growth and decay

Introduction to limits 3 Topics

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Find limits using graphs

Find one-sided limits using graphs

Determine if a limit exists

Calculate limits 8 Topics

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Find limits using addition, subtraction, and multiplication laws

Find limits using the division law

Find limits using power and root laws

Find limits using limit laws

Find limits of polynomials and rational functions

Find limits involving factorization and rationalization

Find limits involving absolute value functions

Find limits involving trigonometric functions

Limits involving infinity 3 Topics

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Find limits at vertical asymptotes using graphs

Determine end behavior using graphs

Determine end behavior of polynomial and rational functions

Continuity 8 Topics

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Identify graphs of continuous functions

Determine continuity using graphs

Determine one-sided continuity using graphs

Find and analyze points of discontinuity using graphs

Determine continuity on an interval using graphs

Determine the continuity of a piecewise function at a point

Make a piecewise function continuous

Intermediate Value Theorem

Introduction to derivatives 6 Topics

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Average rate of change

Find instantaneous rates of change

Velocity as a rate of change

Find values of derivatives using limits

Find the slope of a tangent line using limits

Find equations of tangent lines using limits

Derivative rules 7 Topics

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Sum and difference rules

Inverse function rule

Calculate derivatives 14 Topics

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Find derivatives of polynomials

Find derivatives of rational functions

Find derivatives of trigonometric functions I

Find derivatives of trigonometric functions II

Find derivatives of exponential functions

Find derivatives of logarithmic functions

Find derivatives of inverse trigonometric functions

Find derivatives of radical functions

Find derivatives using the product rule I

Find derivatives using the product rule II

Find derivatives using the quotient rule I

Find derivatives using the quotient rule II

Find derivatives using the chain rule I

Find derivatives using the chain rule II

Derivative strategies 3 Topics

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Find derivatives using implicit differentiation

Find tangent lines using implicit differentiation

Find derivatives using logarithmic differentiation

Calculate higher derivatives 5 Topics

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Find higher derivatives of polynomials

Find higher derivatives of rational and radical functions

Find second derivatives of trigonometric, exponential, and logarithmic functions

Find higher derivatives of exponential and trigonometric functions

Find higher derivatives of logarithmic and power function

Probability 10 Topics

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Introduction to probability

Calculate probabilities of events

Combinations and permutations

Find probabilities using combinations and permutations

Find probabilities using two-way frequency tables

Identify independent events

Find conditional probabilities

Independence and conditional probability

Find conditional probabilities using two-way frequency tables

Find probabilities using the addition rule

Probability distributions 18 Topics

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Identify discrete and continuous random variables

Write a discrete probability distribution

Graph a discrete probability distribution

Expected values of random variables

Variance of random variables

Standard deviation of random variables

Write the probability distribution for a game of chance

Expected values for a game of chance

Choose the better bet

Find probabilities using the binomial distribution

Mean, variance, and standard deviation of binomial distributions

Find probabilities using the normal distribution I

Find probabilities using the normal distribution II

Find z-values

Find values of normal variables

Distributions of sample means

The Central Limit Theorem

Use normal distributions to approximate binomial distributions

Statistics 16 Topics

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Identify biased samples

Variance and standard deviation

Identify an outlier

Identify an outlier and describe the effect of removing it

Outliers in scatter plots

Match correlation coefficients to scatter plots

Calculate correlation coefficients

Find the equation of a regression line

Interpret regression lines

Analyze a regression line of a data set

Analyze a regression line using statistics of a data set

Find confidence intervals for population means

Find confidence intervals for population proportions

Interpret confidence intervals for population means

Experiment design

Analyze the results of an experiment using simulations

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