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Utah - Mathematics: Mathematics III Honors
UT--Core Standards | Adopted: 2016
N: : Number and Quantity
N.CN: : Complex Number System
(Framing Text): : Perform arithmetic operations with complex numbers.
N.CN.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
(Framing Text): : Represent complex numbers and their operations on the complex plane.
N.CN.4: : Represent complex numbers on the complex plane in rectangular form and polar form (including real and imaginary numbers), and explain why the rectangular form of a given complex number represents the same number.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
(Framing Text): : Use complex numbers in polynomial identities and equations.
N.CN.10: : Multiply complex numbers in polar form and use DeMoivre’s Theorem to find roots of complex numbers.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
F: : Functions
F.IF: : Interpreting Functions
(Framing Text): : Analyze functions using different representations.
F.IF.7: : Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F.IF.7.d: : Graph rational functions, identifying zeros, asymptotes, and point discontinuities when suitable factorizations are available, and showing end behavior.
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Rational Functions](/Assets/img/blank.gif)
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
F.BF: : Building Functions
(Framing Text): : Build new functions from existing functions.
F.BF.4: : Find inverse functions.
F.BF.4.b: : Verify by composition that one function is the inverse of another.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
F.BF.4.c: : Read values of an inverse function from a graph or a table, given that the function has an inverse.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
F.BF.5: : Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
F.TF: : Trigonometric Functions
(Framing Text): : Prove and apply trigonometric identities.
F.TF.9: : Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems.
![Screenshot of Simplifying Trigonometric Expressions](/Assets/img/blank.gif)
Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Sum and Difference Identities for Sine and Cosine](/Assets/img/blank.gif)
Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
S: : Statistics and Probability
S.CP: : Conditional Probability and the Rules of Probability
(Framing Text): : Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.9: : Use permutations and combinations to compute probabilities of compound events and solve problems.
![Screenshot of Binomial Probabilities](/Assets/img/blank.gif)
Binomial Probabilities
Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
Correlation last revised: 9/16/2020
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