Algebra 2 Enrichment Packet - Answer Key PDF

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Summary

Algebra 2 Summer practice work, to put you ahead of the game....

Description

Algebra 2 Enrichment/Instructional Packet Answer Key

Mathematics

Prince George’s County Public Schools Division of Academics Department of Curriculum and Instruction

The teacher will not grade this packet.

This Enrichment Packet has been compiled to complement high school mathematics classroom instruction aligned to the Maryland College and Career Ready Standards (MCCRS). The packet is intended to be used for review and practice of previously taught and new concepts.

We strongly encourage you to work diligently to complete the activities. You may experience some difficulty with some activities in this packet, but we encourage you to think critically and creatively and complete them to the best of your ability.

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Week 1

Resource: enVision Algebra 2 Lesson: 2-4 Complex Numbers and Operations Objective: Students will be able to: Add, subtract, and multiply complex numbers using the properties of operations and the relation i 2 = −1. Use complex numbers to represent numbers that are not on the real number line. Content Standards: N.CN.1 Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real. N.CN.2 Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

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Week 1 MCAP Practice Assessment Problems Problem #1

ANSWER

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Problem #2

0+5i

Problem #3 - D

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Week 2

Resource: enVision Algebra 2 Lesson: 2-6 The Quadratic Formula Objective: Students will be able to: Use the Quadratic Formula to solve quadratic equations that have complex solutions. Content Standards: N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. A.REI.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

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Week 2 MCAP Practice Assessment Problems Problem #1 - C Show your work.

Problem #2 Show your work.

Answer

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Show your work.

C

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Week 3

Resource: enVision Algebra 2 Lesson: 3-1 Graphing Polynomial Functions Objective: Students will be able to: Graph polynomial functions and show the key features of the graph. Predict the end behavior of polynomial functions by interpreting the leading coefficients and degrees. Sketch graphs showing key features, given a verbal description.

Content Standards: F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

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Week 3 MCAP Practice Assessment Problems Created March 2020

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Problem #1

Answer

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Week 4 Resource: enVision Algebra 2 Created March 2020

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Lesson: 3-4 Dividing Polynomials Objective: Students will be able to: Divide polynomial expressions using long division. Use synthetic division to rewrite rational expressions. Content Standards: A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x). A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

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Week 4 MCAP Practice Assessment Problems

Problem #1

3 Problem #2

B Problem #3

A

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Week 5 Resource: enVision Algebra 2 Lesson: 3-5 Zeros of Polynomial Functions Objective: Students will be able to: Identify the zeros of a function by factoring or using synthetic division. Use the zeros of a polynomial function to sketch its graph. Content Standards: A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. F.IF7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

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MCAP Practice Assessment Problems Problem #1 Venetta opened several deli sandwich franchises in 2000. The profit P (in hundreds of dollars) of the franchise in t years (since the franchise opened) can be modeled by the function P(t) = t3 + t2 - 6t. Part A Sketch the graph of the function.

Part B Based on the model, during what years did Venetta not make a profit? After 2003, 2004, ...

Part C If the model is appropriate, predict the amount of profit Veneta will receive from her franchise in 2020. 7680

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Resource: enVision Algebra 2 Lesson: 4-5 Solving Rational Equations Objective: Students will be able to: Solve rational equations in one variable. Identify extraneous solutions to rational equations and give examples of how they arise. Content Standards: A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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Week 6 MCAP Practice Assessment Problems Problem #1

4 Problem #2

5.5 Problem #3

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Resource: enVision Algebra 2 Lesson: 6-1 Key Features of Exponential Functions Objective: Students will be able to: Interpret key features of exponential functions represented by graphs, tables, and equations. Graph transformations of exponential functions showing intercepts and end behavior. Model quantities that increase or decrease by a fixed percent each time period using exponential functions Content Standards: F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

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Extension MCAP Practice Assessment Problems Created March 2020

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Problem 1 -

D

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Problem 2

C Problem 3

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ANSWER 2 age 15 to age 20

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