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Math
- Interpret and rewrite algebraic expressions and equations in equivalent forms.
- Write, solve and graph linear equations, functions and inequalities in one and two variables.
- Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
- Write, solve and graph absolute value equations, functions and inequalities in one and two variables.
- Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
- Solve and graph polynomial equations and functions in one and two variables.
- Solve and graph radical equations and functions in one and two variables.
- Solve and graph rational equations and functions in one and two variables.
- Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.
- Solve problems involving sequences and series.
- Build mathematical foundations for financial literacy.
- Develop an understanding of basic accounting and economic principles.
- Describe the advantages and disadvantages of short-term and long-term purchases.
- Describe the advantages and disadvantages of financial and investment plans, including insurances.
- Prove and apply geometric theorems to solve problems.
- Apply properties of transformations to describe congruence or similarity.
- Use coordinate geometry to solve problems or prove relationships.
- Use geometric measurement and dimensions to solve problems.
- Make formal geometric constructions with a variety of tools and methods.
- Use properties and theorems related to circles.
- Apply geometric and algebraic representations of conic sections.
- Summarize, represent and interpret categorical and numerical data with one and two variables.
- Solve problems involving univariate and bivariate numerical data.
- Solve problems involving categorical data.
- Use and interpret independence and probability.
- Determine methods of data collection and make inferences from collected data.
- Use probability distributions to solve problems.
- Apply recursive methods to solve problems.
- Apply optimization and techniques from Graph Theory to solve problems.
- Apply techniques from Election Theory and Fair Division Theory to solve problems.
- Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
- Apply properties from Set Theory to solve problems.
Florida B.E.S.T. Math
High School: Calculus: Develop an understanding for limits and continuity. Determine limits and continuity.
Demonstrate understanding of the concept of a limit and estimate limits from graphs and tables of values.
- Analyzing unbounded limits: mixed function
- Analyzing unbounded limits: rational function
- Approximating limits using tables
- Conclusions from direct substitution (finding limits)
- Connecting limits and graphical behavior
- Connecting limits and graphical behavior
- Creating tables for approximating limits
- Direct substitution with limits that don't exist
- Estimating limit values from graphs
- Estimating limit values from graphs
- Estimating limit values from graphs
- Estimating limits from tables
- Estimating limits from tables
- Functions with same limit at infinity
- Infinite limits and asymptotes
- Infinite limits: algebraic
- Infinite limits: graphical
- Introduction to infinite limits
- Introduction to limits at infinity
- Limit of (1-cos(x))/x as x approaches 0
- Limit of sin(x)/x as x approaches 0
- Limit properties
- Limits and continuity: FAQ
- Limits at infinity of quotients
- Limits at infinity of quotients (Part 1)
- Limits at infinity of quotients (Part 2)
- Limits at infinity of quotients with square roots
- Limits at infinity of quotients with square roots (even power)
- Limits at infinity of quotients with square roots (odd power)
- Limits at infinity: graphical
- Limits by direct substitution
- Limits by direct substitution
- Limits by factoring
- Limits by factoring
- Limits by rationalizing
- Limits intro
- Limits intro
- Limits intro
- Limits of combined functions
- Limits of combined functions: piecewise functions
- Limits of combined functions: products and quotients
- Limits of combined functions: sums and differences
- Limits of composite functions
- Limits of composite functions: external limit doesn't exist
- Limits of composite functions: internal limit doesn't exist
- Limits of piecewise functions
- Limits of piecewise functions
- Limits of piecewise functions: absolute value
- Limits of trigonometric functions
- Limits of trigonometric functions
- Limits using trig identities
- Next steps after indeterminate form (finding limits)
- One-sided limits from graphs
- One-sided limits from graphs
- One-sided limits from graphs: asymptote
- One-sided limits from tables
- One-sided limits from tables
- Strategy in finding limits
- Strategy in finding limits
- Strategy in finding limits
- Theorem for limits of composite functions
- Theorem for limits of composite functions: when conditions aren't met
- Trig limit using double angle identity
- Trig limit using Pythagorean identity
- Unbounded limits
- Undefined limits by direct substitution
- Using tables to approximate limit values
Determine the value of a limit if it exists algebraically using limits of sums, differences, products, quotients and compositions of continuous functions.
- Limit properties
- Limits of combined functions
- Limits of combined functions: piecewise functions
- Limits of combined functions: products and quotients
- Limits of combined functions: sums and differences
- Limits of composite functions
- Limits of composite functions: external limit doesn't exist
- Limits of composite functions: internal limit doesn't exist
- Theorem for limits of composite functions
- Theorem for limits of composite functions: when conditions aren't met
- Worked example: point where a function is continuous
Find limits of rational functions that are undefined at a point.
- Analyzing unbounded limits: mixed function
- Analyzing unbounded limits: rational function
- Direct substitution with limits that don't exist
- Limits and continuity: FAQ
- Limits by direct substitution
- Limits by factoring
- Limits by factoring
- Limits of combined functions: piecewise functions
- Limits of piecewise functions
- Limits of piecewise functions
- Limits of piecewise functions: absolute value
- Limits using conjugates
- Unbounded limits
Find one-sided limits.
- Analyzing unbounded limits: mixed function
- Analyzing unbounded limits: rational function
- Connecting limits and graphical behavior
- Connecting limits and graphical behavior
- Functions with same limit at infinity
- Infinite limits and asymptotes
- Infinite limits: algebraic
- Infinite limits: graphical
- Introduction to infinite limits
- Limits at infinity of quotients
- Limits at infinity of quotients with square roots
- Limits at infinity: graphical
- Limits of piecewise functions
- One-sided limits from graphs
- One-sided limits from graphs
- One-sided limits from graphs: asymptote
- One-sided limits from tables
- One-sided limits from tables
- Theorem for limits of composite functions
- Unbounded limits
Find limits at infinity.
- Functions with same limit at infinity
- Introduction to limits at infinity
- Limits at infinity of quotients
- Limits at infinity of quotients (Part 1)
- Limits at infinity of quotients (Part 2)
- Limits at infinity of quotients with square roots
- Limits at infinity of quotients with square roots (even power)
- Limits at infinity of quotients with square roots (odd power)
- Limits at infinity: graphical
Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.
- Analyzing unbounded limits: mixed function
- Analyzing unbounded limits: rational function
- Estimating limit values from graphs
- Infinite limits and asymptotes
- Infinite limits: algebraic
- Infinite limits: graphical
- Introduction to infinite limits
- Limits and continuity: FAQ
- Limits at infinity of quotients
- Limits at infinity of quotients (Part 2)
- Unbounded limits
Find special limits by using the Squeeze Theorem or algebraic manipulation.
Find limits of indeterminate forms using L'Hôpital's Rule.
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Define continuity in terms of limits.
- Continuity at a point
- Continuity at a point (algebraic)
- Continuity at a point (graphical)
- Continuity over an interval
- Functions continuous at specific x-values
- Functions continuous on all real numbers
- Limits and continuity: FAQ
- Limits by direct substitution
- Worked example: Continuity at a point (graphical)
- Worked example: point where a function is continuous
- Worked example: point where a function isn't continuous
Given the graph of a function, identify whether a function is continuous at a point. If not, identify the type of discontinuity for the given function.
Apply the Intermediate Value Theorem and the Extreme Value Theorem.
- Intermediate value theorem
- Intermediate value theorem review
- Justification with the intermediate value theorem
- Justification with the intermediate value theorem: equation
- Justification with the intermediate value theorem: table
- Using the intermediate value theorem
- Worked example: using the intermediate value theorem