Algebra 1 Semester 2 Instructional Materialspapachan.weebly.com/uploads/1/1/1/1/11111363/s2...Jan...

Algebra 1 Semester 2 Instructional Materials 2013-2014

Updated 1/29/14

2013-2014

Algebra 1 Semester 2

Instructional Materials for the WCSD Math Common Finals

The Instructional Materials are for student and teacher use and are aligned

to the Math Common Final blueprint for this course. When used as test

practice, success on the Instructional Materials does not guarantee success

on the district math common final.

Students can use these Instructional Materials to become familiar with the

format and language used on the district common finals. Familiarity with

standards vocabulary and interaction with the types of problems included

in the Instructional Materials can result in less anxiety on the part of the

students.

Teachers can use the Instructional Materials in conjunction with the course

guides to ensure that instruction and content is aligned with what will be

assessed. The Instructional Materials are not representative of the depth

or full range of learning that should occur in the classroom


Updated 1/29/14

Multiple Choice: Identify the choice that best completes the statement or answers the question.

1. You invited friends over to your house to watch a movie. You let each person decide if they

wanted to snack on popcorn, which cost $2.50 per person, or candy, which cost $1.75 per

person. You spent $17.75 to buy snacks for 8 people. Write a system of equations that you

could use to determine how many people chose popcorn (𝑝) and how many chose candy (𝑐).

A. 𝑓(𝑥) = {

2.50𝑝 + 1.75𝑐 = 8𝑝 + 𝑐 = 17.75

C. 𝑓(𝑥) = {17.75 − 2.5𝑝 = 817.75 − 1.5𝑐 = 8

B. 𝑓(𝑥) = {2.50𝑝 + 8𝑝 = 17.751.75𝑐 + 8𝑐 = 17.75

D. 𝑓(𝑥) = {2.50𝑝 + 1.75𝑐 = 17.75

𝑝 + 𝑐 = 8

2. Two different families bought general admission tickets for a Reno Aces baseball game.

One family paid $70 for 6 adults and 2 children. The other family paid $59 for 3 adults and

4 children. How much does an adult ticket cost?

A. $8 C. $11.67

B. $9 D. $19.67

3. Which system of inequalities models the graph below?

A. {𝑦 <

1

3𝑥 − 1

2𝑥 + 4𝑦 > 8

B. {𝑦 < −

1

3𝑥 − 1

2𝑥 − 4𝑦 > 8

C. {𝑦 > −

1

3𝑥 − 1

2𝑥 − 4𝑦 < 8

D. {𝑦 >

1

3𝑥 − 1

2𝑥 + 4𝑦 < 8


Updated 1/29/14

4. Jesse wants to plant peach and apple trees in his backyard. He can fit at most 9 trees. Each

peach tree costs $60, and each apple tree costs $75. If he only has $600 to spend, make a

graph showing the number of each kind of tree that he can buy.

A.

C.

B.

D.

5. Which piecewise function is represented by the graph?

A. 𝑓(𝑥) = {2𝑥 − 3, 𝑥 < 13𝑥 − 5, 𝑥 > 1

B. 𝑓(𝑥) = {2𝑥 + 3, 𝑥 ≤ 13𝑥 − 5, 𝑥 > 1

C. 𝑓(𝑥) = {2𝑥 + 3, 𝑥 ≥ 13𝑥 − 5, 𝑥 > 1

D. 𝑓(𝑥) = {2𝑥 − 3, 𝑥 < 13𝑥 − 5, 𝑥 ≥ 1


Updated 1/29/14

6. Which graph represents the piecewise function?

𝑓(𝑥) = {1

2𝑥 − 1, 𝑥 ≥ 2

2, 𝑥 < 2

A.

C.

B.

D.

7. The value of −√68 is between which two integers?

A. −9 and −8 C. −8 and −7

B. 8 and 9 D. 7 and 8

8. The value of √903

is between which two integers?

A. 4 and 5 C. 5 and 6

B. 6 and 7 D. 9 and 10

9. What is the simplified form of √48 ∙ √54 ?

A. 6√162 C. 18√32

B. 36√2 D. 2√1296


Updated 1/29/14

10. What is the simplified form of 4√5 ∙ (8√2 − √3) ?

A. 32√10 − 4√15 C. 12√7 − 4√8

B. 32√10 − 12√3 D. 8√10 − 4√3

11. What is the simplified form of (4𝑔−3ℎ4)−3 ?

A.

−12𝑔6

ℎ12 C.

12𝑔9

ℎ

B. −64𝑔9

ℎ12 D.

𝑔9

64ℎ12

12. What is the simplified form of (−3𝑐1

2) (2𝑐15

2 𝑑−8) ?

A.

−6𝑐8

𝑑8 C.

−5𝑐7

𝑑8

B. 6𝑑8

𝑐8 D. −6𝑐𝑑

13. What is the simplified form of 36𝑚−4𝑛6

4𝑚𝑛−2𝑝−4 ? (Assume that 𝑚 ≠ 0, 𝑛 ≠ 0, and 𝑝 ≠ 0)

A.

9𝑛4𝑝4

𝑚3 C.

9𝑛8𝑝4

𝑚5

B. 9𝑛8

𝑚5𝑝4 D.

9𝑚5

𝑛8𝑝4


Updated 1/29/14

14. Which of the following graphs represent 𝑦 = |𝑥| − 2 ?

A.

C.

B.

D.

15. Reflect the graph of 𝑓(𝑥) = |𝑥| over the x-axis and translate the function one (1) unit up.

Which of the following is the function after the translation?

A. 𝑓(𝑥) = |𝑥| − 1 C. 𝑓(𝑥) = |𝑥| + 1

B. 𝑓(𝑥) = |𝑥 + 1| D. 𝑓(𝑥) = −|𝑥| + 1

16. Which of the following is the solution for x in the equation 2|𝑥 + 3| + 6 = 10 ?

A. 𝑥 = −5 C. 𝑥 = 1

B. 𝑥 = −5 and 𝑥 = −1 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

17. Which of the following is the solution for x in the equation −3|𝑥 + 4| = 6 ?

A. 𝑥 = −6 C. 𝑥 = −2

B. 𝑥 = −6 and 𝑥 = −2 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛


Updated 1/29/14

18. If 𝑓(𝑥) = 2|𝑥 + 3| − 4 and 𝑔(𝑥) =1

2𝑥 + 5, use the tables below find the x-value(s) where

𝑓(𝑥) = 𝑔(𝑥).

𝑓(𝑥) = 2|𝑥 + 3| − 4

𝑥 𝑓(𝑥) −7 4 −6 2 −5 0 −4 −2 −3 −4 −2 −2 −1 0 0 2 1 4 2 6 3 8 4 10

𝑔(𝑥) =1

2𝑥 + 5

𝑥 𝑔(𝑥) −7 1.5 −6 2 −5 2.5 −4 3 −3 3.5 −2 4 −1 4.5 0 5 1 5.5 2 6 3 6.5 4 7

A. 𝑥 = 2, 4, 6 C. 𝑥 = −6, 2

B. 𝑥 = 2, 6 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

19. Which graph below models the solutions to the equation −3|𝑥 + 2| + 4 = −2 ?

A.

C.

B.

D.


Updated 1/29/14

20. Given the equation and graph of 𝑦 = −𝑥2 − 1, what is the domain and range?

A. Domain: 𝑎𝑙𝑙 𝑅𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠

Range: 𝑦 ≥ 1

B. Domain: 𝑎𝑙𝑙 𝑅𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠

Range: 𝑦 ≤ −1

C. Domain: 𝑎𝑙𝑙 𝑅𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠

Range: 𝑦 ≤ 1

D. Domain: −1 ≤ 𝑥 ≤ 1

Range: 𝑦 ≤ −1

21. Which of the following quadratic functions represents the function graphed below?

A. 𝑦 =

1

2𝑥2 − 5

B. 𝑦 = 2𝑥2 − 5

C. 𝑦 = 2(𝑥 + 5)2

D. 𝑦 = 2(𝑥 − 5)2


Updated 1/29/14

22. Which of the following graphs represent 𝑦 = 𝑥2 − 4?

A.

C.

B.

D.

23. Translate the graph of 𝑓(𝑥) = 𝑥2 four (4) units to the left, three (3) units up and stretch the

graph by a factor of 2. Which of the following is the function after the transformations?

A. 𝑓(𝑥) =

1

2(𝑥 + 4)2 + 3 C. 𝑓(𝑥) = 2(𝑥 + 4)2 + 3

B. 𝑓(𝑥) =1

2(𝑥 − 3)2 − 4 D. 𝑓(𝑥) = 2(𝑥 − 3)2 − 4

24. Which of the following quadratic functions represents the function graphed?

A. 𝑦 = (𝑥 − 1)2 + 3

B. 𝑦 = −(𝑥 + 3)2 + 1

C. 𝑦 = −(𝑥 + 1)2 + 3

D. 𝑦 = −(𝑥 − 1)2 + 3


Updated 1/29/14

25. Which of the following is the vertex for 𝑦 = −4(𝑥 − 5)2 + 2 ?

A. (25, 2) C. (−5, 2)

B. (−20, 2) D. (5, 2)

26. What is the y-intercept of the graph of 𝑦 = 2(𝑥 − 1)2 + 3 ?

A. (1, 3) C. (0, 3)

B. (0, 5) D. (2, 1)

27. Given the graph of 𝑦 = 𝑥2, what is the solution for x after the transformation down four (4)

units and left three (3) units?

A. 𝑥 = −2, 𝑥 = 2

B. 𝑥 = 3

C. 𝑥 = −5, 𝑥 = −1

D. 𝑥 = −4, 𝑥 = 3

28. Which of the following are the x-intercepts for 𝑦 = (𝑥 + 2)2 − 16

A. (−6, 0), (2, 0) C. (−6, 0), (−2, 0)

B. (−2, 0), (16, 0) D. (2, 0), (−16, 0)

29. Solve for x in 16𝑥2 − 49 = 0 .

A. 𝑥 = ±

49

16 C. 𝑥 =

16

49

B. 𝑥 = ±7

4 D. 𝑥 =

7

4

30. What is the product of the binomials: (𝑟 − 8)(𝑟 + 5) ?

A. 𝑟2 − 40 C. 𝑟 − 3

B. 𝑟2 + 13𝑟 − 40 D. 𝑟2 − 3𝑟 − 40


Updated 1/29/14

31. What is the simplified form of (𝑏 + 7)2 ?

A. 𝑏2 + 14𝑏 + 49 C. 𝑏2 + 49𝑏 + 49

B. 𝑏2 + 49 D. 𝑏 + 49

32. The polynomial 𝑥2 + 11𝑥 + 30 is factorable. One factor is (𝑥 + 6), what is the other

factor?

A. (𝑥 + 1) C. (𝑥 − 5)

B. (𝑥 + 3) D. (𝑥 + 5)

33. Which of the following is a factor of 3𝑥2 − 12 ?

A. (𝑥 + 12) C. (𝑥 − 2)

B. (𝑥 − 4) D. (𝑥 + 4)

34. Which of the following is a factor of 2𝑥2 + 7𝑥 − 30 ?

A. (𝑥 − 5) C. (𝑥 − 12)

B. (𝑥 + 6) D. (𝑥 − 6)

35. What is the solution to 𝑥2 + 8𝑥 = 84 ?

A. 𝑥 = −12, 𝑥 = 7 C. 𝑥 = −14, 𝑥 = 6

B. 𝑥 = 14, 𝑥 = −6 D. 𝑥 = −12, 𝑥 = 4

36. Using the quadratic formula, what is the solution to ℎ2 + 9ℎ − 4 = 0 ?

A. ℎ =−9 − √65

2, ℎ =

−9 + √65

2 C. ℎ =

9 − √97

2, ℎ =

9 + √97

2

B. ℎ =9 − √65

2, ℎ =

9 + √65

2 D. ℎ =

−9 − √97

2, ℎ =

−9 + √97

2


Updated 1/29/14

37. Which of the following is a solution to 2𝑥2 + 14𝑥 = 18

A. 𝑥 =7 ± √85

2 C. 𝑥 =

−7 ± √85

2

B. 𝑥 =−7 ± √13

2 D. 𝑥 =

14 ± √340

4

38. Which of the following is the vertex form for 𝑦 = 𝑥2 + 4𝑥 + 7 ?

A. 𝑦 = (𝑥 + 2)2 + 3 C. 𝑦 = (𝑥 + 2)2 + 7

B. 𝑦 = (𝑥 − 2)2 + 4 D. 𝑦 = (𝑥 − 2)2 + 3

39. What is the y-intercept of the graph of 𝑦 = 𝑥2 + 9𝑥 + 15 ?

A. (0, 9) C. (0, 15)

B. (9, 15) D. (0, −15)

40. What is the vertex of the function 𝑓(𝑥) = −2𝑥2 + 8𝑥 − 9 ?

A. (−4, −73) C. (−2, −33)

B. (4, −9) D. (2, −1)

41. The graph of ℎ(𝑥) = −𝑥2 + 10𝑥 − 16 models the height of one of the arches at the

entrance of a parking structure. If the domain of this function is 𝑥 ≥ 0, what is the range?

A. ℎ(𝑥) ≤ 5 C. ℎ(𝑥) ≤ 9

B. ℎ(𝑥) ≤ 8 D. ℎ(𝑥) ≤ 10

42. Which of the following best describes the data in the table?

𝑥 1 2 3 4

𝑦 3 9 27 81

A. Exponential with a growth rate of 3

B. Linear with a rate of change of 6

C. Quadratic with a second difference of 12

D. none of the above


Updated 1/29/14

43. Since the year 2001 the population of community A grows exponentially as illustrated in

the table. The exponential rate of growth is 1.3. What is are the units for the rate of growth

in the table?

𝑦𝑒𝑎𝑟 2001 2002 2003 2004 2005 2006 𝑝𝑒𝑜𝑝𝑙𝑒 1200 1560 2028 2636.4 3427.32 4455.52

A. people per year

B. years per people

C. years

D. people

44. Determine which of the following equations represent exponential growth or decay.

Equation 1 Equation 2 Equation 3 Equation 4

𝑦 = 1.5−𝑥

𝑦 = 0.8𝑥

𝑦 = 0.5−𝑥

𝑦 = 2.7𝑥

A. Equation 1: Decay

Equation 2: Decay

Equation 3: Growth

Equation 4: Growth

C. Equation 1: Decay

Equation 2: Growth

Equation 3: Growth

Equation 4: Decay

B. Equation 1: Growth

Equation 2: Growth

Equation 3: Decay

Equation 4: Decay

D. Equation 1: Growth

Equation 2: Decay

Equation 3: Decay

Equation 4: Growth

45. Which of the following functions is modeled in the table?

𝑥 1 2 3 4 5

𝑦 3 12 27 48 75

A. Exponential C. Quadratic

B. Linear D. none of the above

46. What is the solution for x in 4𝑥 = 64 ?

A. 𝑥 = 16 C. 𝑥 = 3

B. 𝑥 = 4 D. 𝑥 = 2


Updated 1/29/14

47. What is the solution for x in 52𝑥−9 = 125 ?

A. 𝑥 = 6 C. 𝑥 = 5

B. 𝑥 = 4 D. 𝑥 = 3

48. What is the solution to the system graphed?

A. (2, 4)

B. (4, 2)

C. (1, 2)

D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

49. What is the solution for x in the system?

{𝑦 = 8

𝑦 = 2𝑥

A. 𝑥 =

1

3 C. 𝑥 = 1

B. 𝑥 =1

2 D. 𝑥 = 3

50. What is the solution for x in the system?

{3 = 32𝑦

𝑦 = 𝑥 + 1

A. 𝑥 = −1 C. 𝑥 =

1

2

B. 𝑥 = −1

2 D. 𝑥 = 2


Updated 1/29/14

Algebra 1 Semester 2 Instructional Material Answers

1. D 11. D 21. B 31. A 41. C

2. B 12. A 22. A 32. D 42. A

3. C 13. C 23. C 33. C 43. A

4. A 14. D 24. D 34. B 44. A

5. B 15. D 25. D 35. C 45. C

6. C 16. B 26. B 36. D 46. C

7. A 17. D 27. C 37. C 47. A

8. A 18. C 28. A 38. A 48. A

9. B 19. A 29. B 39. C 49. D

10. A 20. B 30. D 40. D 50. B

Algebra 1 Semester 2 Instructional Materialspapachan.weebly.com/uploads/1/1/1/1/11111363/s2...Jan...

Documents

Transcript of Algebra 1 Semester 2 Instructional Materialspapachan.weebly.com/uploads/1/1/1/1/11111363/s2...Jan...