grade: algebra ii enduring skill 1: develop an

Grade: Algebra II

Enduring Skill 1:

Develop an understanding of the structural similarities

between the system of polynomials and the system of

integers.

Demonstrators and Related Standards:

1. Perform arithmetic operations with complex numbers. (N.CN.1; N.CN.2)

2. Use complex numbers in polynomial identities and equations. (N.CN.2;

N.CN.7; N.CN.8; N.CN.9)

3. Interpret the structure of expressions. (A.SSE.1; A.SSE.2)

4. Write expressions in equivalent forms to solve problems. (A.SSE.2; A.SSE. 4)

5. Perform arithmetic operations on polynomials. (A.APR.1)

6. Understand the relationship between zeros and factors of polynomials. (A.APR.2;

A.APR.3)

7. Use polynomial identities to solve problems. (A.APR.4; A.APR.5)

8. Rewrite rational expressions. (A.APR.6; A.APR.7)

9. Understand solving equations as a process of reasoning and explain the reasoning.

(A.REI.2)

10. Represent and solve equations and inequalities graphically. (A.REI.11)

11. Analyze functions using different representations. (F.IF.7)

Assessment Items:

1. ES 1, Demonstrator 1, Standards (N.CN.1; N.CN.2)

Let m and n be real numbers. Find the real and imaginary parts of (3 + mi)(n – 2i).

A. Real: (3n – 2m); Imaginary: (6 – mn)i

B. Real: (3n – 2m); Imaginary: (mn – 6)i

C. Real: (3n + 2m); Imaginary: (mn – 6)i

D. Real: 3n; Imaginary: 2mi


What is (8 - 18i) - (-3 -13i)?

A. 5 - 31i

B. 5 -5i

C. 11 - 31i

D. 11 - 5i


What is (−5

6−

1

3𝑖) + (

1

2−

1

6𝑖) ?

A. - 1

3−

1

6𝑖

B. −1

3+

1

6𝑖

C. 1

3−

1

6𝑖

D. 1

3+

1

6𝑖


What is the product of ( 5 - √-6) and (9 + √-100)?

A. 45 - 10√6 + (50 - 9√6)i

B. 10√6 + 45 + (50 + 9√6)i

C. 45 - 10√6 + (50 + 9√6)i

D. 10√6 + 45 + (50 - 9√6)i

5. ES 1, Demonstrator 1, Standards (N.CN.1;N.CN.2)

Simplify the expression.

6. ES 1, Demonstrator 2, Standards (N.CN.2; N.CN.7; N.CN.8; N.CN.9)

Solve the equation:


Solve the equation:


Solve the equation:

9. ES 1, Demonstrator 3, Standards (A.SSE.1; A.SSE.2)

Factor the expression 9x2 +16

A. (3x+ 4i)(3x - 4i)

B. (3x + 4)(3x - 4)

C. (9x + 4i)(x - 4i)

D. (3x + 4i)2


State the possible number of real zeros of the function. Then find all rational zeros.


State the number of complex zeros, the possible number of real and imaginary

zeros, the possible number of positive and negative zeros, and the possible rational

zeros for the function. Then find all rational zeros.


Find a value for a, a value for k, and a value for n so that:

(3x + 2)(2x - 5) = ax2 + kx + n

A. a = 6, k = -19, n = -10

B. a = 6, k = 19, n = -10

C. a = 6, k = -11, n = -10

D. a = 6, k = 11, n = -10

13. ES 1, Demonstrator 4, Standards (A.SSE.2; A.SSE. 4)

Which expression is equivalent to y = x4 - x2 - 56?

A. y = (x2 + 10)(x2 + 7)

B. y = (x2 - 8)(x2 + 8)

C. y = 2(x2 - 8)(x2 + 4)

D. y = (x2 - 8)(x2 + 7)


Factor completely: x2 - 2xy - 24y2

A. (x - 6y)(x + 4y)

B. (x + 6y)(x + 4y)

C. (x + 6y)(x - 4y)

D. (x - 6y)(x - 4y)


Factor p2 - 81 completely.

A. (p - 9)2

B. (p + 9)(p - 9)

C. (p + 9)2

D. Not factorable


How many terms are there in a geometric sequence if the first term is 14,

the common ratio is 3, and the sum of the series is 1,240,022?

A. 88,573 terms

B. 5 terms

C. 14 terms

D. 11 terms

17. ES 1, Demonstrator 5, Standards (A.APR.1)

(-11 + 9v + 9v4) + (11 + 10v3 + 7v)

A. 10v4 + 10v3 +16v - 8

B. 9v4 + 10v3 +16v - 8

C. 10v4 + 2v3 + 16v - 8

D. 9v4 + 10v3 + 16v


(13r4 - 4r + 9r2) - (12r4 + r5 + r2)

A. -r5 + r4 + 15r2 + 9r

B. -r5 + r4 + 8r2 - 4r

C. -r5 + r4 + 8r2 + 9r

D. -r5- 5r4 + 8r2 + 9r


Simplify (8v2 - v - 3)(-4v2 + 4v + 2).

A. 56v4 + 17v3 - 53v2 + 14v - 16

B. -32v4 + 36v3 + 24v2 - 14v - 6

C. -32v4 - 4v2 - 6

D. 56v4 + 31v3 - 47v2 - 2v - 16

20. ES 1, Demonstrator 6, Standards (A.APR.2; A.APR.3)

Is the binomial (k - 2) a factor of (k3 + 7k - 10k - 26)?

A. Yes

B. No

C. Cannot determine


What is the remainder when (a4 - 2a3 - 9a2 - 33a + 5) is divided by (a – 5)?

A. -9

B. 11

C. -10

D. -7



Find the coefficient described:


Find the coefficient described:


Simplify:


Simplify:


Simplify:


Simplify:


Divide (x4 + 10x3 + 29x2 + 32x + 27) by (x + 3).

A. x3 + 7x2 + 8x + 11 + 7/(x + 3)

B. x3 + 7x2 + 8x + 9 - 1/(x + 3)

C. x3 + 7x2 + 8x + 8 + 3/(x + 3)

D. x3 + 7x2 + 8x + 7 + 3/(x + 3)

30. ES 1, Demonstrator 9, Standards (A.REI.2)

𝑣2−𝑣−6

6𝑣=

𝑣−6

6+

1

6

31. ES 1, Demonstrator 9, Standards (A.REI.2)

32. ES 1, Demonstrator 10, Standards (A. REI.11)

Find the real zeros of the function by graphing.



34. ES 1, Demonstrator 11, Standards (F.IF.7)

Graph y = 5x + 7

Graph y = |2x – 1|

Graph y = x2 + 4x – 5

Graph y = 𝑥+3

4𝑥−2




Identify the graph of

Grade: Algebra II

Enduring Skill 2:

Build on and extend previous work with functions,

trigonometric ratios, and circles in Geometry to model

periodic phenomena in the coordinate plane.


1. Extend the domain of trigonometric functions using the unit circle.

(F.TF.1; F.TF.2)

2. Model periodic phenomena with trigonometric functions. (F.TF.5)

3. Prove and apply basic trigonometric identities. (F.TF.8)

Assessment Items:

1. ES 2, Demonstrator 1, Standards (F.TF.1; F.TF.2)

Find the length of the arc.


Find the length of the arc.


Find the indicated trigonometric function.


Find the indicated trigonometric function.

5. ES 2, Demonstrator 2, Standard (F.TF.5)

Find the amplitude and period of each function. Then graph.

6. ES 2, Demonstrator 2, Standards (F.TF.5)

Find the amplitude and period of each function. Then grap


Find an expression that completes the fundamental trigonometric identity: csc(-x)

A. –csc x

B. csc x

C. –sin x

D. sin x



Grade: Algebra II

Enduring Skill 3:

Students synthesize and generalize what they have

learned about a variety of function families.


1. Create equations that describe numbers or relationships. (A.CED.1; A.CED.2;

A.CED.3; A.CED.4)

2. Interpret functions that arise in applications in terms of context. (F.IF.4; F.IF.5;

F.IF.6)

3. Analyze functions using different representations, e.g. tables, graphs, equations.

(F.IF7, F.IF.8)

4. Build a function that models a relationship between two quantities. (F.BF.1)

5. Build new functions from existing functions. (F.BF.3, F.BF.4)

6. Construct and compare linear, quadratic, and exponential models and solve

problems. (F.LE.4)

Assessment Items:

1. ES 3, Demonstrator 1, Standards (A.CED.1; A.CED.2; A.CED.3; A.CED.4)

A repairman charges $60 for a service call, plus $35 per hour for labor. If your

total bill was $173.75, how many hours did the repair take?

a. 3 hours and 14 minutes

b. 3 hours and 25 minutes

c. 3 hours and 5 minutes

d. 3 hours and 15 minutes


A hallway requires 44 ft2 of carpeting. The length of the hallway is 3 feet more

than 2 times its width. How long is the hallway?

a. 4 ft

b. 11 ft

c. 5.5 ft

d. 8 ft


You have earned $4577.70 in interest over a 20-year period in a savings account

that had an initial investment of $5000. If the interest was compounded

continuously at what rate was your saving account earning you money?

a. 3.5%

b. 3.25%

c. 3%

d. 3.75%



6. ES 3, Demonstrator 2, Standards (F.IF.4; F.IF.5; F.IF.6)

What is the end behavior of the following function?

.

7. ES 3, Demonstrator 3, Standards (F.IF.7; F.IF.8)

8. ES 3, Demonstrator 3, Standards (F.IF.7; F.IF.8)

9. ES 3, Demonstrator 3 and 4, Standards (F.IF.7; F.IF.8; F.BF.1)

10. ES 3, Demonstrator 5, Standards (F.BF.3;F.BF.4)

11. ES 3, Demonstrator 5, Standards (F.BF.3;F.BF.4)

Grade: Algebra II

Enduring Skill 4:

Students relate the visual displays and summary

statistics from earlier grades to different types of data

and to probability distributions.


1. Summarize, represent, and interpret data on a single count or measurement variable.

(S.ID.4)

2. Understand and evaluate random processes underlying statistical experiments.

(S.IC.1; S.IC.2)

3. Make inferences and justify conclusions from sample surveys, experiments, and

observational studies. (S.IC.3, S.IC.4; S.IC.5; S.IC.6)

4. Use probability to evaluate outcomes of decisions. (S.MD.6; S.MD.7)

Assessment Items:

1. ES 4, Demonstrator 1, Standards (S.ID.4)


A. 10

B. 5

C. 105

D. 126


4. ES 4, Demonstrator 2, Standards (S.IC.1; S.IC.2)

5. ES 4, Demonstrator 2, Standards (S.IC.1;S.IC.2)

6. ES 4, Demonstrator 2, Standards (S.IC.1;S.IC.2)

7. ES 4, Demonstrator 3, Standards (S.IC.3;S.IC.4;S.IC.5;S.IC.6)

8. ES 4, Demonstrator 3, Standards (S.IC.3; S.IC.4; S.IC.5; S.IC.6)

9. ES 4, Demonstrator 3, Standards (S.IC.3; S.IC.4; S.IC.5; S.IC.6)

10. ES 4, Demonstrator 4, Standards (S.MD.6;S.MD.7)

11. ES 4, Demonstrator 4, Standards (S.MD.6; S.MD.7)



grade: algebra ii enduring skill 1: develop an

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