Math III (H) – K Jones Name: _______________________ (2pts)Test – Rational Expressions, Functions, and Equations

Section I – Fill in The Blank (1pt each)Directions: Use the word bank below to correctly complete each sentence. No word is used more than once. Spelling counts

Word Bank

approximateasymptotes

cancelledcongruentdifferenceextraneous

factors

FOILholes

horizontalinterceptproductquotientsimplify

solutionsum

variablevertical

XY

zeroes

- One of the most striking differences in solving rational equations compared to most other

types of equations is that you have to remember to check for ____________________

solutions. This anomaly is a side effect of multiplying an equation by a

____________________ expression.

- When it comes to simplifying a rational expression the first step is to

_____________________ the numerator and denominator to determine if there are any

commons factors that can be “___________________________”.

- The vertical _____________________ and holes of a rational function are determined by

the ____________________ of the denominator.

- If the degree of the numerator is less than the degree of the denominator the

___________________ asymptote will be at y = 0. If the degrees of numerator and

denominator are equal than the horizontal asymptote is at y = k, where k is the

_____________________ of the coefficients of the leading terms.

- For all functions to find the ________________ intercept(s) you set the function equal to

zero and to find the _________________ intercept you “plug in” zero and evaluate.

Section II – ACT (3pts each)Directions: Clearly circle your answer choice. Make sure to read questions carefully.

1. Which of the following is equivalent to 6x− x−4x+5 ?

a. −x2−10x−30x2+5 x

b. −x2+10 x+30x2+5 x

c. −x2+10 x−305 x−x2

d. −x2−10x+30x2−5 x

e. −x2−10x−30x2+5 x

2. If f ( x )=x3+2 x and g ( x )=5−2x what does g (f (2 ) ) equal?

a. -29

b. -19

c. -15

d. 3

e. 12

3. A cube with edges ½ inch long is shown below. What is the length, in inches, of a diagonal that runs from one corner of the cube to the opposite?

a.14

b.34

c.32

d. √22

e. √32

4. Each side of the smaller square in the figure below is x inches long, and each of the larger square is c inches longer than a side of the smaller square. The area of the larger square is how many square inches greater than the area of the smaller square?

a. c2

b. xc

c. 4c

d. (x + c)2

e. 2xc + c2

5. In the standard (x, y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?

a. (3, -7)

b. (4, -8)

c. (5, -1)

d. (8, -3)

e. (9, -3)

Section III – Graphing (10pts each)Directions: Sketch the graph of each function. Clearly label all asymptotes and make sure holes are drawn clearly.

1. f ( x )= 4 x+46−2x

2. f ( x )= 4 x+8x3+5x2+6 x

3. f ( x )=6 x2−21 x−12x2+x−20

Section IV – Operations (7pts each)Directions: Simplify each expression. Box or circle your final answer.

1. 4−x2

x2−3x−10

2.6

2x3−8 x÷ 3 x−6x3+2 x2−8 x

3.xx+3

+ 2x2+4 x+3

4.x

x2−4 x−12− x+1x3−36 x

Section V – Solving Equations (5ptes each)Directions: Solve each equation. Box or circle your final answer.

1.2 x−42x2+3

= x+8x2−6

2.2x−1

−2x=1

3.3x+3

+ 2x+2

= 2x+1

Section VII Extra Credit (1pt each)

1. Finish this iconic song lyric:“In west Philadelphia born and raised,the ____________________ is whereI spent most of my days.”

a. School yardb. Play yardc. Play groundd. Amish country e. Playground

2. Rick Astley is never going to what? (Clearly circle your answer)

a. Give you upb. Let you downc. Make you cryd. Hurt youe. All of the above

3. This question could be worth absolute free points. You have a choice to make, would you rather earn 1 point or 3 points for this question? The catch is that if 10%, or more, of the class chooses 3 points then no one will earn any points on this question. The results will remain 100% anonymous. Which do you choose?

a. 1 extra credit pointb. 3 extra credit points

4. Five students are left alone with 72 holiday cookies. James ate 10, Lily ate 24, Percy ate 6, and Rubeus ate 40. How many cookies did the fifth student eat?

a. There is not enough information to answer this question.b. Uh, why were those students left alone with that many cookies?c. 40? Seriously, Rubeus?d. I can only think about Harry Potter, sorry.

Math III (H) – K Jones Name: _______________________ (2pts)Test – Rational Expressions, Functions, and Equations

Section I – Fill in The Blank (1pt each)Directions: Use the word bank below to correctly complete each sentence. No word is used more than once. Spelling counts

Word Bank

approximateasymptotes

cancelledcongruentdifferenceextraneous

factors

FOILholes

horizontalinterceptproductquotientsimplify

solutionsum

variablevertical

XY

zeroes

- One of the most striking differences in solving rational equations compared to most other

types of equations is that you have to remember to check for ____________________

solutions. This anomaly is a side effect of multiplying an equation by a

____________________ expression.

- When it comes to simplifying a rational expression the first step is to

_____________________ the numerator and denominator to determine if there are any

commons factors that can be “___________________________”.

- The vertical _____________________ and holes of a rational function are determined by

the ____________________ of the denominator.

- If the degree of the numerator is less than the degree of the denominator the

___________________ asymptote will be at y = 0. If the degrees of numerator and

denominator are equal than the horizontal asymptote is at y = k, where k is the

_____________________ of the coefficients of the leading terms.

- For all functions to find the ________________ intercept(s) you set the function equal to

zero and to find the _________________ intercept you “plug in” zero and evaluate.

Section II – ACT (3pts each)Directions: Clearly circle your answer choice. Make sure to read questions carefully.

6. Which of the following is equivalent to 6x− x−4x+5 ?

a. −x2−10x−30x2+5 x

b. −x2−10x+30x2−5 x

c. −x2+10 x+30x2+5 x

d. −x2+10 x−305 x−x2

e. −x2−10x−30x2+5 x

7. If f ( x )=x3+2 x and g ( x )=5−2x what does g (f (2 ) ) equal?

a. -29

b. -19

c. -15

d. 3

e. 12

8. A cube with edges ½ inch long is shown below. What is the length, in inches, of a diagonal that runs from one corner of the cube to the opposite?

a.14

b.34

c. √22

d. √32

e.32

9. Each side of the smaller square in the figure below is x inches long, and each of the larger square is c inches longer than a side of the smaller square. The area of the larger square is how many square inches greater than the area of the smaller square?

a. c2

b. (x + c)2

c. 2xc + c2

d. xc

e. 4c

10. In the standard (x, y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?

a. (3, -7)

b. (4, -8)

c. (5, -1)

d. (8, -3)

e. (9, -3)

Section III – Graphing (10pts each)Directions: Sketch the graph of each function. Clearly label all asymptotes and make sure holes are drawn clearly.

4. f ( x )=6 x−66−2 x

5. f ( x )= 4 x−8x3−5 x2+6 x

6. f ( x )=6 x2+21x−12x2−x−20

Section IV – Operations (7pts each)Directions: Simplify each expression. Box or circle your final answer.

5. 9−x2

x2−4 x+3

6.6

2x3−8 x÷ 3 x−6x3+2 x2−8 x

7.xx−2

+ 2x2+x−6

8.x

x2+4 x−12− x+1x3−36x

Section V – Solving Equations (5ptes each)Directions: Solve each equation. Box or circle your final answer.

4.2 x−42x2+3

= x+8x2−6

5.1x+4

−1x=1

6.2x+2

+ 1x+1

= 6x+3

Section VII Extra Credit (1pt each)

5. Finish this iconic song lyric:“In west Philadelphia born and raised,the ____________________ is whereI spent most of my days.”

a. School yardb. Play yardc. Play groundd. Amish country e. Playground

6. Rick Astley is never going to what? (Clearly circle your answer)

a. Give you upb. Let you downc. Make you cryd. Hurt youe. All of the above

7. This question could be worth absolute free points. You have a choice to make, would you rather earn 1 point or 3 points for this question? The catch is that if 10%, or more, of the class chooses 3 points then no one will earn any points on this question. The results will remain 100% anonymous. Which do you choose?

a. 1 extra credit pointb. 3 extra credit points

8. Five students are left alone with 72 holiday cookies. James ate 10, Lily ate 24, Percy ate 6, and Rubeus ate 40. How many cookies did the fifth student eat?

a. There is not enough information to answer this question.b. Uh, why were those students left alone with that many cookies?c. 40? Seriously, Rubeus?d. I can only think about Harry Potter, sorry.

Math III (H) – K Jones Name: _______________________ (2pts)Test – Rational Expressions, Functions, and Equations

Section I – Fill in The Blank (1pt each)Directions: Use the word bank below to correctly complete each sentence. No word is used more than once. Spelling counts

Word Bank

approximateasymptotes

cancelledcongruentdifferenceextraneous

factors

FOILholes

horizontalinterceptproductquotientsimplify

solutionsum

variablevertical

XY

zeroes

- One of the most striking differences in solving rational equations compared to most other

types of equations is that you have to remember to check for ____________________

solutions. This anomaly is a side effect of multiplying an equation by a

____________________ expression.

- When it comes to simplifying a rational expression the first step is to

_____________________ the numerator and denominator to determine if there are any

commons factors that can be “___________________________”.

- The vertical _____________________ and holes of a rational function are determined by

the ____________________ of the denominator.

- If the degree of the numerator is less than the degree of the denominator the

___________________ asymptote will be at y = 0. If the degrees of numerator and

denominator are equal than the horizontal asymptote is at y = k, where k is the

_____________________ of the coefficients of the leading terms.

- For all functions to find the ________________ intercept(s) you set the function equal to

zero and to find the _________________ intercept you “plug in” zero and evaluate.

Section II – ACT (3pts each)Directions: Clearly circle your answer choice. Make sure to read questions carefully.

11. Which of the following is equivalent to 6x− x−4x+5 ?

a. −x2+10 x−305 x−x2

b. −x2−10x−30x2+5 x

c. −x2−10x+30x2−5 x

d. −x2−10x−30x2+5 x

e. −x2+10 x+30x2+5 x

12. If f ( x )=x3+2 x and g ( x )=5−2x what does g (f (2 ) ) equal?

a. -29

b. -19

c. -15

d. 3

e. 12

13. A cube with edges ½ inch long is shown below. What is the length, in inches, of a diagonal that runs from one corner of the cube to the opposite?

a. √22

b. √32

c.14

d.34

e.32

14. Each side of the smaller square in the figure below is x inches long, and each of the larger square is c inches longer than a side of the smaller square. The area of the larger square is how many square inches greater than the area of the smaller square?

a. xc

b. c2

c. (x + c)2

d. 2xc + c2

e. 4c

15. In the standard (x, y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?

a. (3, -7)

b. (4, -8)

c. (5, -1)

d. (8, -3)

e. (9, -3)

Section III – Graphing (10pts each)Directions: Sketch the graph of each function. Clearly label all asymptotes and make sure holes are drawn clearly.

7. f ( x )=6 x−66−3 x

8. f ( x )= 4 x−24x3−4 x2−12x

9. f ( x )= 4 x2+14 x−8x2−x−20

Section IV – Operations (7pts each)Directions: Simplify each expression. Box or circle your final answer.

9. 16−x2

x2−3 x−4

10.6

2x3−8 x÷ 3 x−6x3+2 x2−8 x

11.xx+3

+ 2x2+x−6

12.x

x2+4 x−12− x−2x3−36x

Section V – Solving Equations (5ptes each)Directions: Solve each equation. Box or circle your final answer.

7.2 x−42x2+3

= x+8x2−6

8.1x−4

−1x=1

9.2x+3

+ 1x−1

= 22 x−6

Section VII Extra Credit (1pt each)

9. Finish this iconic song lyric:“In west Philadelphia born and raised,the ____________________ is whereI spent most of my days.”

a. School yardb. Play yardc. Play groundd. Amish country e. Playground

10. Rick Astley is never going to what? (Clearly circle your answer)

a. Give you upb. Let you downc. Make you cryd. Hurt youe. All of the above

11. This question could be worth absolute free points. You have a choice to make, would you rather earn 1 point or 3 points for this question? The catch is that if 10%, or more, of the class chooses 3 points then no one will earn any points on this question. The results will remain 100% anonymous. Which do you choose?

a. 1 extra credit pointb. 3 extra credit points

12. Five students are left alone with 72 holiday cookies. James ate 10, Lily ate 24, Percy ate 6, and Rubeus ate 40. How many cookies did the fifth student eat?

a. There is not enough information to answer this question.b. Uh, why were those students left alone with that many cookies?c. 40? Seriously, Rubeus?d. I can only think about Harry Potter, sorry.