1 Chapter 6 Test Review

Pre-AP Algebra II – Chapter 6 Test Review Standards/Goals:

C.1.d./F.BF.1.c.: I can use the idea of composition to evaluate radical functions.

E.2.b./F.BF.3.: I can use transformations (translations, reflections, etc…) to draw the graph of a relation and determine a relation that fits a graph.

(Pre-Calculus Skill): F.BF.4a.: o I can find the inverse of a function. o I can determine whether a function is one to one or not.

E.2.a./F.IF.1: o I can understand what a relation and a function is. o I can understand that a function assigns to each element of a domain, EXACTLY one element of the range.

G.1.b.: I can simplify radicals that have various indices. G.1.c./ASSE.2.:

o I can use properties of roots and rational exponents to simplify expressions. o I can take the structure of an expression and identify different ways to rewrite it

G.1.d.: I can add, subtract, multiply, and divide expressions containing radicals. G.1.e.: I can rationalize denominators containing radicals and find the simplest common denominator.

o I can use the FOIL method to multiply binomials that have radical expressions. o I can multiply binomial expressions using conjugates.

G.1.f.: I can evaluate expressions and solve equations containing ‘nth’ roots or rational exponents. G.1.g./A.REI.2./A.CED.4.:

o I can solve simple rational and radical equations in one variable. o I can show how to arrive at ‘extraneous’ solutions. o I can rearrange formulas to highlight a quantity of interest, using the same techniques and methods as

you would use to solve an equation.

What is the simplified form of the following expressions:

#1. √81𝑥12𝑦26 #2. √112𝑥9𝑦10

#3. √48𝑤𝑧43√4𝑤23

#4. 9

3 + √7

#5. 5√63 − 3√18 #6. (2√3)2 −(2 – 3√5)(3 + 4√5)

#7. √25𝑟4𝑠5

16𝑠5 #8.

√45𝑥7

√125𝑥𝑦4

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#9. What is the real cube root of -216? #10. What is the real fourth root of −81

625?

Let f(x) = -3√𝒙 + 16 and g(x) = 𝟐𝒙𝟐 + 𝟏𝟗. #11. What is the domain of f(x)? #12. What is the domain of g(x)? #13. What is f ᵒ g (x)? #14. What is g(-3)?

Let f(x) = √𝒙 + 𝟐 and g(x) = 3x – 9.

#15. Find the domain of 𝑓

𝑔(x). #16. What is g ᵒ f (16)? #17. Find f(48).

Consider the following function: 𝒚 = −𝟑√𝒙 + 𝟗 − 𝟏𝟔 #18. What is the domain for the function given?

#19. What are the transformations for the function?

#20. What is the DOMAIN of 4

5−√𝑥+10?

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#21. Simplify: 8

5+√2 #22. Find the complex conjugate: -4 +√−20

Solve the following: #23. √5𝑥 − 2 − 7 = 3 #24. √5𝑥 − 2 + 7 = 3

#25. 3𝑥1

2 − 10 = 2 #26. √3𝑥 + 7 = 𝑥 − 1

#27. √3𝑥 = √𝑥 + 6 #28. √7𝑚 + 9 = √6𝑚 + 8

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FLASHBACK: Quadratics/Discriminant: FIRST: Find the discriminant of each and then state the number and type of roots that each will have. SECOND: Solve each using the quadratic formula: #1. 8𝑛2 − 4𝑛 = 18 #2. 8𝑎2 + 6𝑎 = −5

#3. Suppose the following was reflected across the x-axis. What would its equation be, after this reflection? 𝑦 = 𝑥2 + 9𝑥 − 17 #4. The factored form of a quadratic is given by: f(x) = (x + w)(x +12). If f(x) has a y-intercept at (0,24), the value of ‘w’ must be: #5. What value for ‘w’ would result in |𝑥 + 8| + 𝑤 = 18 having no solution? #6. What value for ‘w’ would result in 𝑤|2𝑥 − 8| > 40 in having no solution? #7. What value for ‘w’ would result in 𝑥2 + 6𝑥 + 𝑤 in having TWO complex conjugate solutions?

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#8. What value for ‘w’ would result in 𝑥2 + 8𝑥 + 𝑤 in having ONE real solution? #9. What value for ‘w’ would result in 𝑥2 + 10𝑥 + 𝑤 in having TWO complex conjugate solutions?

#10. What is the domain of 𝑓(𝑥) = √𝑥 − 9?

#11. Simplify: (3√7)2 − (7 + √−10)(7 − √−10).

#12. Solve: 10𝑥1

2 − 40 = 400

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POWER STANDARDS: CHAPTER 1: I can solve a system of equations with THREE variables. Find x, y, and z from the following system:

CHAPTER 2: I can graph and solve an absolute value inequality. I can graph and solve a compound inequality. Solve, graph and write answer in interval form: #1. −6|𝑥| + 36 < 18 #2. -5 < 2x – 8 ≤ 15

#3. Find the minimum and maximum values for the following objective function:

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CHAPTERS 3: I can determine the domain and range of a function algebraically. Find the domain of each:

#1. 𝑓(𝑥) = √𝑥 − 8 #2. 𝑓(𝑥) = 2𝑥2 − 8𝑥 #3. f(x) = -5x + 10 CHAPTER 4: I can graph and solve a quadratic inequality. Solve and graph the following. Write the answer in interval notation.

#1. 𝑥2 − 3𝑥 + 4 ≤ 2𝑥 − 2 #2. 𝑥2 − 5𝑥 + 4 > 2𝑥 − 6

CHAPTER 4: I can manipulate complex numbers (imaginary). Simplify the following expression:

#1. 25 − 𝑖2

5 − 𝑖 #2.

7 + 2𝑖

4 − 5𝑖

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CHAPTER 5: I can recognize and determine the zeros/ x-intercepts/ solutions/ factors of a polynomial equation. #1. The graph of a quadratic function has x-intercepts at (-5, 0) and (-9, 0). Which values of ‘x’ are roots of the quadratic function? #2. A certain ninth degree polynomial function can be factored as:

(𝒙 − 𝟏𝟏)(𝒙 + 𝟐)𝟑(𝒙𝟐 + 𝟏)(𝒙 − 𝟓)𝟑 How many x-intercepts does this function have?

CHAPTER 6: I can manipulate and evaluate a radical expression. Simplify the following expressions:

#1. 7

3− √5 #2. 2√50 − √32

x f(x)

1 4

2 1

3 5

4 2

5 3

Consider the tables above. Find the following:

#1. Find f(g(5)) #2. Find g(f(1)) #3. Find 𝑓(𝑔−1(5)) #4. Find 𝑔−1(𝑓−1(4))

x g(x)

1 5

2 3

3 1

4 4

5 2

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#1. SAMPLE EOC MULTIPLE CHOICE QUESTION:

#2. SAMPLE EOC MULTIPLE CHOIC QUESTION:

#3. SAMPLE EOC MULTIPLE CHOICE QUESTION:

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#4. SAMPLE EOC MULTIPLE CHOICE QUESTION:

#5. SAMPLE EOC MULTIPLE CHOICE QUESTION:

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