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Pre-AP Algebra II – Chapter 4 Test Review Standards/Goals:

A.1.c./A.SSE.2: I can take a quadratic expression and identify different ways to rewrite it. C.1.a./N.CN.1:

o I can understand that every complex number is written in the form of: a + bi. o I can recognize when a number is to be written as an imaginary number o I can use the conjugate when finding the quotient of complex numbers.

C.1.b./ N.CN.2.: I can add, subtract, and multiply complex numbers. C.1.c./N.CN.2.:

o I can simplify quotients of complex numbers. o I can factor a quadratic using complex conjugates. o I can find the imaginary solution of a quadratic.

E.1.a./A.REI.4.b/F.IF.8a.: o I can solve a quadratic equation by completing the square. o I can solve an equation by find square roots. o I can solve a perfect square trinomial equation o I can use factoring and other methods to find the ‘zeros’ of a quadratic function.

E.1.a./A.REI.4.b.: o I can solve quadratic equations using the quadratic formula. o I can solve a quadratic inequality. o I can identify the ‘zero’s’ of a quadratic function.

E.1.b./A.REI.4.b.: I can use the discriminant the number and type of roots for a given quadratic equation. E.1.d./A.CED.3.:

o I can solve quadratic systems graphically and algebraically with and without technology. o I can represent constraints by equations or inequalities and by systems of equations and/or

inequalities. o I can solve a system of linear OR quadratic equations by graphing

E.2.a./F.BF.3.: o I can determine the transformations that may occur with a quadratic function and decide whether it

is a reflection, stretch, compression or a translation/shift and in what direction and by how many units

o I can identify the shape of a graph of a quadratic function. o I can identify both standard and vertex form of a quadratic function. o I can determine whether a quadratic function has a maximum or a minimum. o I can determine the domain and range of a quadratic function and graph the function with and

without technology. o I can solve a system of linear OR quadratic equations by using substitution.

E.2.c.: I can solve a system of quadratic inequalities and can use the graph to determine a solution set. F.1.b.: I can find the zeros of a polynomial (specifically quadratics) in a variety of different ways. (AP Statistics): S.CP.9.(+)

o I can recognize when a distribution is binomial or not. o I can use properties of binomials to find probabilities. o I can apply the binomial properties to real-life scenarios.

(AP Calculus): A.1.g./F.IF.7.b: I can graph and evaluate(for input values) a piecewise function.

PRACTICE MULTIPLE CHOICE: #1. E.2.a.: A rectangle has a width of 2 – x, and a length of 4x. The maximum area of this rectangle must be:

a. 4 square units b. 6 square units c. 8 square units d. 16 square units

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#2. C.1.b./N.CN.2.: What is the simplified form of (-5i)(-3i)? a. -15i b. -15 c. 15 d. 15i

#3. E.2.a./F.BF.3.: Which of the following best describes how to transform to the graph of:

? a. Translate 2.5 units left, stretch by a factor of 4, translate 3 units down. b. Translate 3 units right and 2.5 units down, stretch by a factor of 4. c. Translate 2.5 units right, stretch by a factor of 4, translate 3 units down. d. Stretch by a factor of 4, translate 2.5 units left and 3 units down.

#4. C.1.b./N.CN.2.: Simplify: (5 + 6i) + (2 – 3i).

a. 7 + 3i b. 3 + 3i c. 4 d. 7 – 3i

#5. E.2.a./ F.IF.8a.: What is the maximum value of the function ?

a. 4 b. -8 c. 8 d. 2

#6. A.APR.3 The quadratic function f(x) = has a y-intercept of:

a. (0, -25) b. (0, -7) c. (0, -14) d. (0, -18)

#7. C.1.b./N.CN.2.: What is the complex conjugate of: ½ - 2i?

a. 2 – 2i b. 2 – ½ i c. ½ i – 2 d. ½ + 2i

#8. E.2.a./ F.IF.8a.: Suppose you have 56 feet of fencing to enclose a rectangular dog pen. The function: A = 28x – , where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.

a. Width = 14 ft; area = 196 square feet b. Width = 14 ft; area = 588 square feet c. Width = 28 ft; area = 420 square feet d. Width = 28 ft; area = 196 square feet

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#9. E.1.c./N.CN.7.: Solve: using the quadratic formula. a. No solution b. 0, -6 c. -3 ± 3i

d. -3 ± 3√

#10. E.1.d.: Solve by graphing the related function.

#11. E.1.a.: The formula L = gives the approximate runway length required to land a small plane. ‘L’ is the length of the runway, in feet, and‘s’ is the landing speed of the airplane, in feet per second. The pilot knows that the runway is 2,400 feet long. To the nearest foot per second, what is the maximum safe landing speed?

a. 50 b. 90 c. 140 d. 170

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#12. E.2.a.: Which function has the same range as ? a. b. c. d.

#13. E.1.a.: What is the solution set for ?

a. {

√ }

b. {

√ }

c. {

√ }

d. {

√ }

#14. E.1.a.: What are the solutions for ?

a. √

b. √ c. 7, 1

d. √ #15. E.1.b.: Which quadratic equation has only non-real complex roots?

a. b. c. d.

#16. E.2.a.: Which equation is the reflection of across the x-axis?

a. b. c. d.

#17. E.2.a.: If f(x) = | | , what is the vertex of y = f(x + 2) – 1?

a. (-2, -1) b. (-1, -3) c. (2, -1) d. (3, -3)

#18. E.1.b.: What condition will yield non-real zeros of a quadratic function f(x) = ?

a. b. c. 2a < 0 d.

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#19. C.1.b./N.CN.2.: What is the simplified form of ? a. 73 b. 16 – 6i c. 55 – 48i d. 55 + 48i

#20. E.2.a.: Andrew threw a spear into the air. The function = can be used to determine the height, ‘h’ of the spear after ‘t’ seconds. What is the maximum height that the spear reached?

a. 30 feet b. 50 feet c. 60 feet d. 90 feet e. 120 feet

POWER STANDARD: I can graph a quadratic equation. #1. Multiple choice: Which graph represents the function: ?

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#2. Multiple choice: Which graph represents the function?

POWER STANDARD: I can solve a quadratic equation. #1. Find the zeros of the following quadratic by using the quadratic formula:

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#2. Solve the following: a. b. c.

#3. Solve using the zero product property: (2x + 8)(x – 10) = 0.

#4. The factored form of a quadratic is given by: f(x) = (x – 9)(x + b). If f(x) has a y-intercept at (0, -27), the value of ‘b’ must be what?

POWER STANDARD: I can graph and solve a quadratic inequality. Solve each. Write in interval and set notation to represent the solutions. #1. #2.

#3. #4.

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POWER STANDARD: I can determine the number and types of roots of a quadratic equation using the discriminant. #1. Mark is working with the quadratic function . Determine the number and type of roots for the equation using the discriminant.

#2. Consider the following quadratic: . Determine the discriminant of the quadratic and state the number and types of ‘roots’ that this quadratic will have. #3. Consider the parabolas shown below. What are some possible discriminant values for each.

POWER STANDARD: I can determine the domain and range of a quadratic function. #1. State the domain and range of the following parabolas.

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POWER STANDARD: I can graph and determine solutions for a system of quadratic equations or inequalities. #1. Use a graphing calculator to find the solution set of:

{

#2. Use a graphing calculator to find the solution set of:

{

#3. What are the TWO points of intersection for this system of equations?

{

#4. Given x > 0, at what value of x will ?

POWER STANDARD: I can manipulate complex numbers (imaginary). Let m = 5 – 4i and h = 2 + 3i #1. Find m – 6h #2. Find m · h

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#3. What is

? #3. What is m + h?

Simplify each:

#4. √ #5. √

#5. (10i)(-12i) #7. ( √ ) √

#8. #9. (7 + 5i) + (3 – 8i) #10. 3i + -17 – 8i + 12 #11. 5 + 10i + -17i - 9 #12. What is the complex conjugate of ¾ + 9i? #13. What is the complex conjugate of – 12i?

#14. MULTIPLE CHOICE: What is the complex conjugate of

?

a. i + 3 b. –i + 3

c.

d.

#15. MULTIPLE CHOICE: If c – d = 7 and c = 3 – 4i, what is d?

a. -4 – 4i b. -4 + 4i c. 4 – 4i d. 4 + 4i

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#16. MULTIPLE CHOICE: What is the product of (4 – 3i) and (-7 – 2i)? a. -23 + 13i b. -23 – 29i c. -34 + 13i d. -34 – 29i

#17. MULTIPLE CHOICE: Rationalize

a. -1 b. 1 c. –i d. i

Other EXAMPLES: #1. What would the vertex be of the following functions?:

a. b. C.

#2. Find the y-intercept of: . Additionally, if this function is reflected across the y-axis, then what are the coordinates after this reflection has occurred? #3. A rectangular garden has a length that is 7 feet longer than 3 times its width. If the area is 100 square feet, what is the length of the garden to the nearest tenth? #4. A rectangle has a width of 4 – x and a length of 6x. What is the width, length and maximum area of the rectangle?

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#5. Find the maximum value of: . Additionally, state the y-intercept.

Suppose that g(x) = 7x + 9 and w(x) = #6. Find (g + w)(-2) #7. Find (w – g)(4)

#8. Find (g w)(-6) #9. Find

#10. FREE RESPONSE PRACTICE: There are twenty-five multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth five points and only one option per question is correct. Suppose the student guesses the answer to each question, and the guesses from question to question are independent. The distribution of X = the number of questions the student will get correct, will be?

a. What is the probability that he gets at least 12 questions correct?

b. What is the probability that he gets exactly 7 questions correct?

c. What is the probability that he gets fewer than 10 questions correct?

d. What is the probability that he gets no more than 8 questions correct?

e. What is the probability that he gets more than 14 questions correct?