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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.

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.

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.

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.

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

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.

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.

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.

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.

Simplifying Trigonometric Expressions

Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

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.

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

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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