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Math I I Unit 4 Test Review

Multiple Choice

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

Solve the following system of equations by graphing.

1. > ' = 1 1 J - 6 y = ^6x + \\ a. ( -1 ,5 ) c. (5 ,1) b. (1 ,7) d. (1 ,5)

2. 2>' + 8x = 58 y-5x = \\ a. (2,21) c. (4 ,20) b. (21,2) d. (1 ,21)

3. j ^ - 3 x - 8

a. ( -5 ,1 ) c. ( 1 , - 3 ) b. ( - 1 , - 5 ) d. ( 1 , - 5 )

Solve each system of equations by using substitution.

4. 8x + 7 ^ = 1 8 3;c - 5>' = 22 a. ( -2 ,4 ) c. ( 4 , - 2 ) b. ( 3 , - 2 ) d. (4 ,0)

5. 3r + 3.y = 9 3r-6 .s=18 a. (4 , -0 .5) c. ( 4 , - 1 ) b. (5.5,3) d. ( 2 , - 1 )

6. y=x + l

ix-Ay = Q a. (1 ,2) c. (2 ,1) b. (0, 1) d. ( - 1 , 0)

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7. -9 = x-3y

-2x + 6~6y a. (3, 4) b. infinitely many solutions

c. ( -9 ,0 ) d. ( -3 ,2 )

Solve each system of equations by using elimination.

3p + 9q = 6 5p -5q = 30 a. ( 6 , - 1 ) c. (5,0.5) b. (3.75,2) d. ( 5 , - 1 )

9. 6a + 6b = l2 6a-5b = n a. (1 ,0) c. (3 , -0 .5) b. (2 ,0) d. (2,0.25)

10. 4p + 4q = 4 4p-4q = 2?, a. ( 5 , - 3 ) c. ( 4 , - 3 ) b. (2.75,4) d. (4 , -1 .5)

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Solve the system of inequalities by graphing.

11. x>2 y>% a.

14--

12--

10--

( I I I I I I I I I

-8 -6 -4 -2 _2

~4

-6

C.

I I I I I I I I I >

4 6 8 10 12 X

( I I I I I I I I I I

-10 -8 -6 -4 -2 ^ t

-4

"6

I I I I I I I I I )

8 10 X

b. I 4 - -

12--

10--

8--

6--

44-

< I I I I I I I I I I I

-10 -8 -6 -4 -2 + 1 4 6 8 10 -2 -

-4--

-6--

-8--

d. 14--

12--

10--

8

6

4

I ! I I I I I I ) < I I I I I I I I I

-8 -6 -4 -2

y

I I I I I I I I I )

2 4 6 $ 10 12 -r

12. 2x = 2y-6

y = —x-\ a. no solution b. one

13. 2x = 2> ' -6

y = x-2 a. no solution b. one

c. two d. infinitely many

c. two d. infinitely many

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Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

14. y^-x + 5

y = 6x-2 a. no solution c. infinitely many

b. one solution; (4, 1) d. one solution; ( 1 , 4)

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15. - 4 x + 7 = 2

a. no solution c, one solution; ( - 2 , - 1 )

b. one solution; ( - 1 , - 2 ) d. infinitely many

16. At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina bought 9 CDs and spent atotal of $114.00. How many $12.00 CDs did she purchase? a. 9 c. 5 b. 6 d. 3

Use elimination to solve the system of equations.

17. - 2 A - - 1 0 ^ = 1 0

- 3 A + 10;; = -10 a. (0 ,1) c. ( - 20 , -5 ) b. (20,5) d. ( 0 , - 1 )

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18. -4x + 2y = -2

4x + 6y=l0 a. ( -2 ,3 ) c. ( - 1 , - 1 ) b. (1 ,1) d. ( 2 , - 3 )

19. The cost of 3 large candles and 5 small candles is $6.40. The cost o f 4 large candles and 6 small candles is $7.50. Which pair o f equations can be used to determine, /, the cost o f a large candle, and s, the cost o f a small candle? a. 3?+5.^ = 6.4 c. 3?+5^ = 6.4

4r + 6.y = 7.5 t + s = 7.5 h. t + s = 6A d. 5t + 3s = 6A

At + 6s ^1.5 6 + 45 = 7.5

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Solve the system of inequalities by graphing.

20. yi^-x + A

yy-'Tx-A

a.

b.

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a. X = 7 b. x = 0

23. y = 3x-6

a. X = 2 b, X = 7

c. X = - 2 d. X = - 7

c. d.

x = - 4 x = 3

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24. State the excluded values for the rational expression. 2 f l - l Q

a'-9 a. 3 c. - 3 ,3 b. - 5 , 5 d. 5

25. State the excluded values for each rational expression. 4 a - 4

fl' - 2 a - 1 5 a. 1 c. 3,-5 b. - 1 , 1 d. - 3 , 5

26. Simplify the expression. State the excluded values o f the variables.

a" + 16a+ 63 a + 1

a. a + 7; - 9 b. a + 9;7 c. a + 9 ; -7 d. a + 7; 9

Find the product and simplify.

U 6d' 27- , ,

6d 9b

9

8*1 •2

9b'

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(x-3) ix-l)(x + 7)

{x + 4)(x + 7)' ( x - 3 )

ix^3){x-\)(x + 7) a.

b.

c.

d.

ix + 4)(x + 7)(x-3)

x - \ x + 4 x + 4 x - \ ( x - 3 ) ( x - l )

(x + 4 ) ( x - 3 )

29. Find tlie quotient.

5a' 2a

8^ 8k' 4

a.

b.

c.

d.

IQq

64k'

2 5a k

5a"'k

40a'k 16

30. Find the quotient.

(r + 3) ( r + 3) ( r - 2 ) ( r + 4) ' ( r - 8 ) ( r + 4)

(r + 3)^

( r - 2 ) ( r - 8 ) ( r + 4)^

(r + 3 ) ( r - 8 ) ( r + 4)

( r - 2 ) ( r + 4)(r + 3)

r - 8

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31.

Find the quotient,

b' +?,b + l b + \

1 a. — + — +

b.

A +1 A+1 A -

h c. b + \ d. h + 1

32. Find the sum. - 7 / 9 /

a. / c. 2

33. Find the sum. ly-5 4>' + 8

4y + 4~^ 4y + 4

ny + 3

8j + 8

3>'- 13

^- 4j; + 4

c. 11> + 3

1 ly + 3

4y + 4

34. Find the difference. 3r _ 2r 5 " 5

I r Ir

^- T " ^

b. I r d. I

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35. Find the difference. 14ffl _ -16

7m + 8 ~ 7/77 + 8 14777- 16 14»7+16

^' 7777 + 8 7/77+8

b, 2 d. I 36. Find the sum.

+ •

a.

/ - 6 / - 5

1 6 / - 88

1 6 / - 88

1 6 / - 88

( / - 6 ) ( / - 5 )

1 6 / - 88

37. Find the sum. b 1

+ -4b+ 1 16Z?+28 & + 7

a.

d.

20Z) + 35

b 4 /) + 7 4Z) + 7

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38. Find the difference. 4 _ 2

g-5 g-6 2 g - 1 4

2 g - 1 4

( g - 5 )

2 g - 1 4

( g - 5 ) ( g - 6 )

2 g - 1 4

( g - 6 )

a.

b.

c.

d.

39. Find the difference. m 6

3m-6'^ 9m- 18 m-6 I

\2m-2A 3 m , m-6

" ^ • 3 ^ • 3 ^ 7 = 6

Essay

40. The total height o f a building, b, and the antenna tower on top o f it, is 425 feet. The difference in heights o f the building and the antenna tower is 324 feet. The following system o f equations represents the situation. ^ + ? = 425

b-t = 32A

a. Explain how to use elimination to solve a system of equations. b. hiclude a step-by-step solution to find the height of the antenna tower.

41. Explain the difference between the solution to a system o f equations and a system o f inequalities. Use the following two systems to explain your answer.

y = 2x-A

y = -3x + 1

and

y <2x'-4

y > -3x + 1

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Math I I Unit 4 Test Review Answer Section

M U L T I P L E C H O I C E

1. D 2. A 3. D 4. C 5. C 6. A 7. D 8. D 9. B

10. C 11. C 12. B 13. A 14. D 15. B 16. B 17. D 18. B 19. A 20. C 21. A 22. A 23. A 24. C 25. D 26. C 27. D 28. B 29. C 30. C 31. D 32. A 33. D 34. A 35. B 36. C 37. B 38. C

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39. C

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E S S A Y

40. a, Sample answer: Elimination can be used to solve height problems i f the coefficients of one variable are the same or are additive inverses. The two equations in the system o f equations are added or subtracted so that one of the variables is eliminated. You then solve for the remaining variable. This number is substituted into one o f the original equations, and that equation is solved for the other variable,

b. The following steps can be used to find the height of the antenna tower.

b + t 425 lYrite the equation in column form and add. {+)b-t^ 324

2b = 749 The tvartable is eliminated.

2b 2

749 2

Divide each side by 2.

b = 374.5 Simplfy.

b + t^ 425 First equation

374.5+ r = 425 Z) = 374.5

374.5 + ^ - 374.5 = 425 - 374.5 Subtract 374.5from each side

= 50.5 Simplify. The height of the antenna tower is 50.5 feet.

Eliminate one variable by adding the two equations. Solve for b and then substitute that value into one of the equations to find the value o f /.

Assessment Rubric Level 3 Superior * Shows thorough understanding o f concepts. *Uses appropriate strategies. *Computation is correct. *Written explanation is exemplary. *Diagram/table/chart is accurate (as applicable). *Goes beyond requirements o f problem.

Level 2 Satisfactory *Shows understanding of concepts. *Uses appropriate strategies. ^Computation is mostly correct. *Written explanation is effective. *Diagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements o f problem.

Level 1 Nearly Satisfactory *Shows understanding of most concepts. *May not use appropriate strategies. *Computation is mostly correct. *Written explanation is satisfactory. *Diagram/table/chart is mostly accurate (as applicable).

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* Satisfies most of the requirements o f problem.

Level 0 Unsatisfactory

* Shows little or no understanding of the concept. *May not use appropriate strategies. *Computation is incorrect. *Written explanation is not satisfactory. *Diagram/table/chart is not accurate (as applicable). *Does not satisfy requirements o f problem.

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41. The solution to a system o f equations is usually a point. The solution can be obtained in one of three ways: graphing, substitution, or elimination. The point (1,-2) is the solution to the above system of equations.

In contrast, the solution to a system of inequalities must be obtained by graphing. The solution is a set of points common to both inequalities. When graphing an inequality, use a solid line to include the points on the line in the solution (for < and >), and a dotted line i f the points on the line are not included in the solution (for < and >). After graphing both inequalities, the area where the shaded areas overlap is the solution. This graph shows the solution to the system o f inequalities shown above.

Assessment Rubric Level 3 Superior *Shows thorough understanding o f concepts. *Uses appropriate strategies. *Computation is correct. ""Written explanation is exemplary. *Diagram/table/chart is accurate (as applicable). *Goes beyond requirements o f problem.

Level 2 Satisfactory *Shows understanding o f concepts. *Uses appropriate strategies. *Computation is mostly correct. ^Written explanation is effective. *Diagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements o f problem.

Level 1 Nearly Satisfactory * Shows understanding o f most concepts. *May not use appropriate strategies. *Computation is mostly correct. *Written explanation is satisfactory. *Diagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem.

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