Sec Math II SAGE Review Algebra Assessment ID: ib.327049

Sec Math II SAGE Review Algebra

Assessment ID:

ib.327049


Generated On April 29, 2015, 12:12 PM PDT

Illuminate Itembank™


Assessment ID:

ib.327049

Directions: Answer the following question(s).

Section 1

1 A. B. C. D.

Which of the following equations are equivalent to 2x(x – 2) = x? Select two that apply. 2(x – 2) = 0 2x2

5

Assuming the equation 2x2 – x + 5 = 0 is correct, which of the following equations must also be correct? Select three that apply.

A. x=

– 5x = 0

4

2x(x – 2) – x = 0 x(2(x – 2) – x) = 0

B. x=

2

Which of the following values for x are solutions to the equation 2x2 – 3x – 2 = 0? Select two that apply.

4

C. x=

D.

–

x=

2

6

2

E. 2

4 A. B. C. D. E. F.

1 ± i √ 39

1 4

C. 0 D. 1

A. B. C. D. E.

1 ± ( – √ 39 )

4

A. –2 B. 1

3

1 ± √ 1 – 40

Which of the following values are zeros of x(x + 5)(x – 3)? Select three that apply. –5 –3

A. B. C. D. E.

±

i √ 39 4

Which of the following expressions is/are equivalent to 256x? Select three that apply. (64x)4 (16x)2 82x 44x 28x

0

7

3 5

Consider the quadratic equation x2 + 6x – 7 = 0.

Which of the following equations is equivalent to the quadratic equation and can be used to A square has a side length of (2x + 4) inches. solve the quadratic equation? Which expressions represent the area, in square inches, 6)(x square? – 1) = 0 Select three that apply. A. (xof+ this 8x + 16 4x2

+ 16

(2x + 4)2

B. (x + 3)(x + 3) = 0 C. (x + 3)2 = 16 D. (x + 3)2 = 7

2(x + 2)2 4(x + 2)2 4x2 + 16x + 16

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Continue: Turn to the next page. Page 1


Assessment ID:

ib.327049


8

Consider the function ƒ(x) = x2 – 5x – 24.

12

Which of the following expressions is an equivalent expression for ƒ(x) in a form that reveals the zeros of ƒ(x)?

A. B. C. D.

9

(x – 8)(x + 3)

For a physics experiment, students toss a basketball into the air from the top of a school building. They write the expression –16t2 + 48t + 56 to represent the height, in feet, of the basketball after t seconds. Based on this expression, what is the height, in feet, of the school building?

(x – 5)(x + 1) (x – 6)(x + 4)

feet

(x – 3)(x – 2) Consider the function ƒ(x) = x2 – 8x + 28. Write the function in the form of ƒ(x) = a(x – h)2 + k, where a, h and k are constants.

13

What is an equivalent form of the given equation written as the quadratic formula? (x + 3)2 = 5

A.

f(x) =

B.

10

What are the solutions for the given equation? 2x2 – 6x + 6 = 0

A.

C. D.

B.

14

C.

What are the solutions for the given equation? x2 – 12x = –5

D.

A. x = –6 ± i √ 41 B. x = –6 ± i √ 5

11 A. B. C. D.

Which equation shows the minimum or maximum value of ƒ(x) without changing the form of the equation?

C. x = 6 ± √ 7 D. x = 6 ± √ 31

ƒ(x) = –2(x + 5)(x + 1) ƒ(x) = –2x2 – 12x – 10

15

An expression is shown below.

ƒ(x) = –2(x + 3)2 + 8

(–5x2 – 3x) – (2 – 4x + 6x2) + (9x – 10)

ƒ(x) = –2(x2 + 6x + 5)

Write an equivalent expression using the fewest number of terms.




Assessment ID:

ib.327049


16

Complete the square to find the minimum value of the equation x2 + 16x – 36 = 0.

19

Which quadratic function does the graph represent and what are the solutions?

x=

17

Let ƒ(x)= –x2 + 6x – 10. Which statement is true regarding the function ƒ(x)?

A. Since ƒ(x) = –(x – 3)2 + 1, the function has a minimum value of 1.

B. Since ƒ(x) = –(x – 3)2 + 1, the function has a maximum value of 1.

C. Since ƒ(x) = –(x –

3)2

– 1, the function has a

minimum value of –1.

D. Since ƒ(x) = –(x – 3)2 – 1, the function has a maximum value of –1.

18

A.

f x = x+4 2−9 ; x = 1 and x = 7

B.

f x = x−4 2−9 ; x = 1 and x = 7

C.

f x = x−4 2+9 ; x = 4 and x = -9

D.

f x = x+4 2+9 ; x = 9 and x = 4

A quadratic equation is shown below. ƒ(x) = x2 + 14x + 16 Part A: Complete the square of the quadratic equation to write it in ƒ(x) = (x – h)2 + k form. Part B: What is the minimum value of the quadratic equation?

20

What are the solution(s) of 4

x−1 2−3 = 25 ?

A. 3 B. 8 C. 1 ± 7 D. 1 ± 2 7

Part C: Could this quadratic equation be used to model the path a golf ball takes when hit if the ground is represented by the x–axis? Why or why not?




Assessment ID:

ib.327049


21

A teacher asked four students to write an equivalent form of the expression a–3 on the board. Their answers are shown in the table below.

is correct.

A. B. C. D.

Jen Kevin Mark Olivia




Assessment ID:

ib.327049


22 Given of equations?

, which of the following graphs represents the solution to the system

A.

C.

B.

D.




Assessment ID:

ib.327049


23

Use factoring to determine which of the following values are the zeros of the quadratic function f(x) = 2x2 – 7x + 3?

A. x=–

1

and x = –3

x=

1

and x = 3

Find the product. (3t – 2)(4t + 2)

A. B. C. D.

2

B.

26

7t 12t2 + 2t + 4 12t2 – 4 12t2 – 2t – 4

2

C. x=–

3

27

and x = –1

2

D. x=

3

(5x4 – 6x2 + 3x +7) + (x3 + 7x2 + 7x – 2) – (2x4 – 5x3 + 8x)

and x = 1

2

24

Simplify the expression

Which of the following expressions represents the simplified version of the expression below?

10a2bc6

.

2ab4c2

A. 5ab3c4 B. 5ac4 b3

A. B. C. D.

3x4 – 4x3 + x2 + 18x + 5 4x4 + 5x3 + x2 + 2x + 5 3x4 + 6x3 + x2 + 2x + 5 3x8 – 4x6 + x4 + 18x2 + 5

28

C. 8a2b4c3 D. 8ac4 b3

25

Use completing the square to find the minimum value of the quadratic expression x2 – 7x + 3.

y = x2 + 3x – 28 Alex is a scuba diver. His boat is at (0, 0) in the drawing above. He jumps into the water at (4, 0). He follows the equation given above and shown in the drawing. Where does he resurface?

A. –46 B. 37 –

4

C. 3 D. 13 2


A. B. C. D.

(–1.5 , –30.25) (0 , 0) (–6.9 , 0) (–7 , 0)

Stop: You have finished the assessment. Page 6

Geometry Review 29. A fountain is located between two trees. Each tree has a height of 60 feet. The angles of elevation from the base of the fountain to the top of each tree are 64° and 48° as shown below.

32. Right triangle XYZ is shown below.

What is the horizontal distance between the two trees (rounded to the nearest foot)?

A. 40 ft B. 83 ft C. 147 ft D. 190 ft 30. Katherine wants to prove that the measures of the interior angles of a triangle have a sum of 180°. She draws a triangle and extends one of the sides through a vertex. She then draws a line through this vertex that is parallel to the opposite side, as shown in the diagram below. Which of the following statements must be true and could be used as part of Katherine's proof?

Enter the ratio equivalent to tan(X). tan(X) =______ 33. A student is riding a bicycle and sees a traffic light that is 50 feet away. The vertical distance between the traffic light and the student is 14 feet. The student also notices a helicopter at an angle of elevation of 82°. The helicopter is directly above the traffic light. A diagram of the situation is shown below.

Select all that apply. A. m∠1 = m∠5 B. m∠2 = m∠4 C. m∠3 = m∠4 + m∠5 D. m∠3 + m∠4 + m∠5= 180° E. m∠1 + m∠2 + m∠4+ m∠5 = 180° 31. Jorge is standing at a horizontal distance of 25 feet away from a building. His eye level is 5.5 feet above the ground and looking up he notices a window washer on the side of the building at an angle of elevation of 65°. How high is the window washer above the ground? Round your answer to the nearest tenth of a foot? Feet=______

To the nearest tenth of a foot, what is the vertical distance between the student and the helicopter? Feet= _____

Why Couldn't the *o

Elephants Go Swimming Together?

Give the measure of each numbered angle. Find your answer in the Code Key and notice the letter next to it. Write this letter in the box containing the number of the angle. (Assume that lines in each figure that do not intersect are parallel.)

4

4

Sec Math II SAGE Review Algebra Assessment ID: ib.327049

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