chapter 5 test - algebra 2 honors /ib-myp - ms....

Name: ______________________ Class: _________________ Date: _________ ID: A

1

Chapter 5 Test - Algebra 2 Honors /IB-MYP

Essay

Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to

include all relevant drawings and justify your answers. You may show your solution in more than

one way or investigate beyond the requirements of the problem.

1. Mr. Moseley asked the students in his Algebra class to work in groups to solve (x – 3)2 = 25, stating that each

student in the first group to solve the equation correctly would earn five bonus points on the next quiz.

Mi-Ling’s group solved the equation using the Square Root Property. Emilia’s group used the Quadratic

Formula to find the solutions. In which group would you prefer to be? Explain your reasoning.

4pts

2. The next day, Mr. Moseley had his students work in pairs to review for their chapter exam. He asked each

student to write a practice problem for his or her partner. Len wrote the following problem for his partner,

Jocelyn: Write an equation for the parabola whose vertex is (–3, –4), that passes through (–1, 0), and opens

down.

a. Jocelyn had trouble solving Len’s problem. Explain why.

b. How would you change Len’s problem?

c. Make the change you suggested in part b and complete the problem.

4pts

Name: ______________________ ID: A

2

3. a. Write a quadratic function in vertex form whose maximum value is 8.

b. Write a quadratic function that transforms the graph of your function from part a so that it is shifted

horizontally. Explain the change you made and describe the transformation that results from this change.

4pts

Short Answer

Graph the quadratic inequality.

4. y < 2x2- 6x + 10 Points (All lables includes vertex and axis and roots with coordinates 2 pt, correct parabolla

graph 3pt, correct line type solid/broken 1pt, correct shade 2pt)

Name: ______________________ ID: A

3

Multiple Choice

Identify the choice that best completes the statement or answers the question.

5. Consider the quadratic function f x( ) = -2x2+ 2x + 2. Find the y-intercept and the equation of the axis of

symmetry.

a. The y-intercept is –2.

The equation of the axis of symmetry is x = -1

2.

b. The y-intercept is 1

2.

The equation of the axis of symmetry is x = 2.

c. The y-intercept is + 2.

The equation of the axis of symmetry is x = 1

2.

d. The y-intercept is -1

2.

The equation of the axis of symmetry is x = –2.

Name: ______________________ ID: A

4

6. Graph the quadratic function f(x) = -2x2+ 2x + 2.

a. c.

b. d.

Determine whether the given function has a maximum or a minimum value. Then, find the maximum or

minimum value of the function.

7. f(x) = x2- 2x + 2

a. The function has a maximum value. The maximum value of the function is 1.

b. The function has a maximum value. The maximum value of the function is 5.

c. The function has a minimum value. The minimum value of the function is 1.

d. The function has a minimum value. The minimum value of the function is 5.

Name: ______________________ ID: A

5

8. f(x) = -x2+ 2x + 7

a. The function has a minimum value. The minimum value of the function is 8.

b. The function has a minimum value. The minimum value of the function is 4.

c. The function has a maximum value. The maximum value of the function is 4.

d. The function has a maximum value. The maximum value of the function is 8.

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which

the roots are located.

9. -x2+ 4x = 0

a.

The solution set is 0, 4ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ.

c.

The solution set is -4, 0ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ.

b.

The solution set is -4 0{ }.

d.

The solution set is 2, 4ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ.

Name: ______________________ ID: A

6

10. x2+ 4x + 2 = 0

a.

One solution is between 3 and 4, while

the other solution is between 0 and 1.

c.

One solution is between –3 and 0, while

the other solution is between –4 and –1.

b.

One solution is between –3 and –1,

while the other solution is between 0

and –4.

d.

One solution is between –3 and –4,

while the other solution is between 0

and –1.

Name: ______________________ ID: A

7

Write a quadratic equation with the given roots. Write the equation in the form ax2+ bx + c = 0, where a, b,

and c are integers.

11. -5

4 and 8

a. 4x2- 27x - 40 = 0 c. x

2- 27x - 40 = 0

b. 4x2+ 27x + 40 = 0 d. x

2- 27x + 40 = 0

Solve the equation by factoring.

12. 2x2+ 3x - 14 = 0

a. {–4, -7

2} c. {–4, 7}

b. {-7

2, 2} d. {2, 7}

Simplify.

13. 245

64

a.7 5

8c.

5

8

b.49

8d.

7 7

8

14. (2i)(-3i)(4i)

a. -24 c. 24i

b. -24i d. 24

15. i7

a. -i c. i

b. 1 d. -1

16. -4 + 4i( ) (-3 - 3i)

a. 16 + 12i c. 24 + 0i

b. 12 + 0i - 12i2

d. 12 + 0i + 12

17. 3

6 + 7i

a.18

85+

21

85i c.

18

13+

21

13i

b.6

85-

7

85i d.

18

85-

21

85i

Name: ______________________ ID: A

8

Solve the equation by using the Square Root Property.

18. 16x2- 48x + 36 = 49

a. {3

2} c. {-

13

4,

1

4}

b. {3

2, 7} d. {-

1

4,

13

4}

19. 100x2- 80x + 16 = 9

a. {1

10,

7

10} c. {

2

5}

b. {-7

10, -

1

10} d. {

2

5, 3}

Solve the equation by completing the square.

20. x2+ 2x - 3 = 0

a. -3, 1ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ c. -6, 1

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

b. -6, 2ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ d. -1, 3

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

Find the exact solution of the following quadratic equation by using the Quadratic Formula.

21. x2- 8x = 20

a. -10, 2ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ c. -4, 20

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

b. 20, 28ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ d. -2, 10

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

22. -x2+ 3x + 7 = 0

a.3 - 37

-2,

3 + 37

-2

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔ

¸

˝

˛


c.-3 - -19

-2,-3 + -19

-2

Ï

Ì

Ó


¸

˝

˛


b.-3 - 12

-2,-3 + 12

-2

Ï

Ì

Ó


¸

˝

˛


d.-3 - 37

-2,-3 + 37

-2

Ï

Ì

Ó


¸

˝

˛


Name: ______________________ ID: A

9

Find the value of the discriminant. Then describe the number and type of roots for the equation.

23. -x2- 14x + 2 = 0

a. The discriminant is 196. Because the discriminant is greater than 0 and is a perfect

square, the two roots are real and rational.

b. The discriminant is –204. Because the discriminant is less than 0, the two roots are

complex.

c. The discriminant is 204. Because the discriminant is greater than 0 and is not a

perfect square, the two roots are real and irrational.

d. The discriminant is –188. Because the discriminant is less than 0, the two roots are

complex.

Write the following quadratic function in vertex form. Then, identify the axis of symmetry.

24. y = -3x2+ 48x

a. The vertex form of the function is y = 3 x + 8( )2+ 192.

The equation of the axis of symmetry is x = -192.

b. The vertex form of the function is y = x + 192( )2+ 8.

The equation of the axis of symmetry is x = -8.

c. The vertex form of the function is y = -3 x - 8( )2+ 192.


d. The vertex form of the function is y = -3 x + 8( )2+ 192.


25. Write an equation for the parabola whose vertex is at 2, 6ÊËÁÁ

ˆ¯̃̃ and which passes through 4, - 1Ê

ËÁÁˆ¯̃̃.

a. y = x + 2( )2- 6 c. y = -1.75 x - 2( )

2+ 6

b. y = 1.75 x - 2( )2+ 6 d. y = -1.75 x + 2( )

2- 6

ID: A

1

Chapter 5 Test - Algebra 2 Honors /IB-MYP

Answer Section

ESSAY

1. ANS:

Student responses should indicate that using the Square Root Property, as Mi-Ling’s group did, would take less

time than the other method since the equation is already set up as a perfect square set equal to a constant. To

solve using the other method, the binomial would need to be expanded and the constant on the right brought

to the left side of the equal sign.

PTS: 4

2. ANS:

a. Jocelyn had trouble because the problem is impossible. No such parabola exists.

b. Student responses will vary. One of the three conditions must be omitted or modified. Sample answer:

“...that passes through (–1, –12).”

c. Answers will vary and depend on the answer for part b. For example, for the sample answer in part b above,

a possible equation is: y = –2(x + 3)2 – 4.

PTS: 4

3. ANS:

a. Answer must be of the form y = a(x – h)2 + 8 where h is any real number and a < 0.

b. Answers must be of the form y = a[x – (h + n)]2 + 8 where h and a represent the same values as in part

a. The student choice is for the value of n. The student should indicate that the graph will shift to the left n

units if his or her value of n is negative, but will shift the graph to the right n units if the chosen value of n

is positive.

PTS: 4

ID: A

2

SHORT ANSWER

4. ANS:

Graph the related quadratic equation. Since the inequality symbol is <, the parabola should be dashed. Test a

point (x1, y

1) inside the parabola. If (x

1, y

1) is the solution of the inequality, shade the region inside the

parabola. If (x1, y

1) is not a solution, shade the region outside the parabola.

PTS: 4 DIF: Advanced REF: Lesson 5-8

OBJ: 5-8.1 Graph quadratic inequalities in two variables. STA: MA.912.A.4.1.1 | MA.912.A.10.3

TOP: Graph quadratic inequalities in two variables.

KEY: Quadratic Inequalities | Graph Quadratic Inequalities

MULTIPLE CHOICE

5. ANS: C

For the quadratic equation ax2+ bx + c, the y-intercept is c and the equation of axis of

symmetry is x =-b

2a.

Feedback

A Did you check the signs?

B Did you interchange the y-intercept and the x-coordinate of the vertex?

C Correct!

D Did you use the correct formulas for the y-intercept and the x-coordinate of the

vertex?

PTS: 4 DIF: Average REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.

STA: MA.912.A.2.6 | MA.912.A.7.6 | MA.912.A.10.3 TOP: Graph quadratic functions.

KEY: Quadratic Functions | Graph Quadratic Functions

ID: A

3

6. ANS: B

First, choose integer values for x. Then evaluate the function for each x value. Graph the resulting coordinate

pairs and connect the points with a smooth curve.

Feedback

A Graph ordered pairs that satisfy the function.

B Correct!

C Did you plot the graph correctly?

D When the coefficient of x2 is less than 0, the graphs opens down.

PTS: 4 DIF: Advanced REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.

STA: MA.912.A.2.6 | MA.912.A.7.6 | MA.912.A.10.3 TOP: Graph quadratic functions.

KEY: Quadratic Functions | Graph Quadratic Functions

7. ANS: C

The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the

function.

Feedback

A The coefficient of x2 is greater than zero.

B The graph of this function opens up.

C Correct!

D What is the value of the y-coordinate of the vertex?

PTS: 4 DIF: Average REF: Lesson 5-1

OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.

STA: MA.912.A.2.6 | MA.912.A.7.6 | MA.912.A.10.3

TOP: Find and interpret the maximum and minimum values of a quadratic function.

KEY: Maximum Values | Minimum Values | Quadratic Functions

8. ANS: D

The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the

function.

Feedback

A The graph of the function opens down.

B The coefficient of x2 is less than zero.

C What is the value of the y-coordinate of the vertex?

D Correct!


OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.

STA: MA.912.A.2.6 | MA.912.A.7.6 | MA.912.A.10.3

TOP: Find and interpret the maximum and minimum values of a quadratic function.

KEY: Maximum Values | Minimum Values | Quadratic Functions

ID: A

4

9. ANS: A

The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic

equation because f(x) = 0 at those points.

Feedback

A Correct!

B The zeros of the function are the solutions of the related equation.

C What are the x-intercepts of the graph?

D Find the zeros of the function, not the vertex.


OBJ: 5-2.1 Solve quadratic equations by graphing. STA: MA.912.A.7.6 | MA.912.A.7.10

TOP: Solve quadratic equations by graphing.

KEY: Quadratic Equations | Solve Quadratic Equations

10. ANS: D

When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers

between which the roots are located.

Feedback

A Is the coefficient of x2 less than zero?

B Did you graph the function correctly?

C When the coefficient of x2 is greater than 0, the graph opens up.

D Correct!


OBJ: 5-2.2 Estimate solutions of quadratic equations by graphing.

STA: MA.912.A.7.6 | MA.912.A.7.10 TOP: Estimate solutions of quadratic equations by graphing.

KEY: Quadratic Equations | Solve Quadratic Equations

11. ANS: A

A quadratic equation with roots p and q can be written as (x - p)(x - q) = 0, which can be further simplified.

Feedback

A Correct!

B Did you check the signs of the coefficients?

C Did you calculate the coefficients correctly?

D Did you verify the answer by substituting the values?


OBJ: 5-3.1 Write quadratic equations in intercept form. STA: MA.912.A.4.3 | MA.912.A.10.3

TOP: Write quadratic equations in intercept form.

KEY: Quadratic Equations | Roots of Quadratic Equations

ID: A

5

12. ANS: B

For any real numbers a and b, if ab = 0, then either a = 0, b = 0, or both a and b are equal to zero.

Feedback

A Did you use the Zero Product Property correctly?

B Correct!

C Did you factor the binomial correctly?



OBJ: 5-3.2 Solve quadratic equations by factoring. STA: MA.912.A.4.3 | MA.912.A.10.3

TOP: Solve quadratic equations by factoring.

KEY: Quadratic Equations | Solve Quadratic Equations | Factoring

13. ANS: A

a

b=

a

b

Feedback

A Correct!

B Check the numerator.

C Check the square root of the numerator.

D Check your calculation.

PTS: 4 DIF: Average REF: Lesson 5-4 OBJ: 5-4.1 Find square roots.

STA: MA.912.A.1.6 TOP: Find square roots.

14. ANS: C

Multiply the real numbers and imaginary numbers separately.

Feedback

A Check your calculation.

B Check the sign.

C Correct!

D Multiply the imaginary numbers again.


OBJ: 5-4.2 Perform operations with pure imaginary numbers.

STA: MA.912.A.1.6 TOP: Perform operations with pure imaginary numbers.

ID: A

6

15. ANS: A

Multiply the real numbers and imaginary numbers separately.

Feedback

A Check your calculation.

B Check the sign.

C Correct!

D Compute again.


OBJ: 5-4.2 Perform operations with pure imaginary numbers.

STA: MA.912.A.1.6 TOP: Perform operations with pure imaginary numbers.

16. ANS: C

Use the FOIL method to multiply the complex numbers and use the formula i2= -1. Combine the real parts

and then the imaginary parts of the two numbers.

Feedback

A Use the FOIL method to find the product.

B Use the value of i2.

C Correct!

D Combine the real parts.


OBJ: 5-4.4 Perform multiplication operations with complex numbers.

STA: MA.912.A.1.6 TOP: Perform multiplication operations with complex numbers.

KEY: Complex Numbers | Multiply Complex Numbers

17. ANS: D

Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL

method and the difference of squares to simplify the given expression.

Feedback

A Multiply the numerator with the conjugate of the denominator.

B Have you multiplied the constant in the numerator with its conjugate of the

denominator?

C Did you multiply the conjugates correctly in the denominator?

D Correct!


OBJ: 5-4.5 Perform division operations with complex numbers.

STA: MA.912.A.1.6 TOP: Perform division operations with complex numbers.

KEY: Complex Numbers | Divide Complex Numbers

ID: A

7

18. ANS: D

For any real number n, if x2= n, then x = ± n .

Feedback

A Did you use the Square Root Property correctly?

B Did you verify the answer by substituting the values?

C Did you factor the perfect square trinomial correctly?

D Correct!


OBJ: 5-5.1 Solve quadratic equations by using the Square Root Property.

STA: MA.912.A.7.3 | MA.912.A.7.5 TOP: Solve quadratic equations by using the Square Root Property.

KEY: Quadratic Equations | Solve Quadratic Equations | Square Root Property

19. ANS: A

For any real number n, if x2= n, then x = ± n .

Feedback

A Correct!

B Did you factor the perfect square trinomial correctly?

C Did you use the Square Root Property correctly?



OBJ: 5-5.1 Solve quadratic equations by using the Square Root Property.

STA: MA.912.A.7.3 | MA.912.A.7.5 TOP: Solve quadratic equations by using the Square Root Property.

KEY: Quadratic Equations | Solve Quadratic Equations | Square Root Property

20. ANS: A

To complete the square for any quadratic expression of the form x2+ bx, find half of b, and square the result.

Then, add the result to x2+ bx.

Feedback

A Correct!

B Did you make the quadratic expression a perfect square?

C Did you verify the answer by substituting the values?

D Did you check the signs of the roots?


OBJ: 5-5.2 Solve quadratic equations by completing the square.

STA: MA.912.A.7.3 | MA.912.A.7.5 TOP: Solve quadratic equations by completing the square.

KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square

ID: A

8

21. ANS: D

The solution of a quadratic equation of the form ax2+ bx + c = 0, where a ! 0, is obtained by using the formula

x =-b ± b

2- 4ac

2a.

Feedback

A Did you check the signs of the solution?

B Did you use the correct formula?

C Did you substitute the values of a, b, and c correctly in the formula?

D Correct!


OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula.

STA: MA.912.A.7.4 | MA.912.A.7.5 | MA.912.A.10.3

TOP: Solve quadratic equations by using the Quadratic Formula.

KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula

22. ANS: D

The solution of a quadratic equation of the form ax2+ bx + c = 0, where a ! 0, is obtained by using the formula

x =-b ± b

2- 4ac

2a.

Feedback

A Did you substitute the values of a, b, and c correctly in the formula?

B Did you evaluate the discriminant correctly?

C Did you use the correct formula?

D Correct!


OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula.

STA: MA.912.A.7.4 | MA.912.A.7.5 | MA.912.A.10.3

TOP: Solve quadratic equations by using the Quadratic Formula.

KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula

ID: A

9

23. ANS: C

If b2- 4ac > 0 and b

2- 4ac is a perfect square, then the roots are rational.

If b2- 4ac > 0 and b

2- 4ac is not a perfect square, then the roots are real and irrational.

Feedback

A Did you use the correct formula for the discriminant?

B Did you check the sign of the answer?

C Correct!

D Did you use the correct order of operations while evaluating the discriminant?

PTS: 4 DIF: Basic REF: Lesson 5-6

OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.

STA: MA.912.A.7.4 | MA.912.A.7.5 | MA.912.A.10.3

TOP: Use the discriminant to determine the number and types of roots of a quadratic equation.

KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates

24. ANS: C

The vertex form of a quadratic function is y = a(x - h)2+ k.

The equation of the axis of symmetry of a parabola is x = h.

Feedback

A Did you use the correct equation of the axis of symmetry?

B Did you check the x-coordinate of the vertex?

C Correct!

D Did you identify the coordinates of the vertex correctly?

PTS: 4 DIF: Basic REF: Lesson 5-7

OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.

STA: MA.912.A.2.10 TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k.

KEY: Quadratic Functions | Axis of Symmetry

25. ANS: C

If the vertex and another point on the graph of a parabola are known, the equation of the parabola can be

written in vertex form.

Feedback

A Did you substitute correctly in the vertex form of the equation?

B Did you find the correct coefficient values?

C Correct!

D Did you check the signs of the coefficients?


OBJ: 5-7.2 Write a quadratic function in the form y = a(x - h)^2 + k.

STA: MA.912.A.2.10 TOP: Write a quadratic function in the form y = a(x – h)^2 + k.

KEY: Quadratic Functions

chapter 5 test - algebra 2 honors /ib-myp - ms....

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