Algebra 1 Semester 2 Instructional Materialswalshmathsite.weebly.com/uploads/2/1/7/0/21709994/...Algebra 1 Semester 2 Instructional Materials 2014-2015 Updated 1/28/15 11. A moving

Algebra 1 Semester 2 Instructional Materials 2014-2015

Updated 1/28/15

2014-2015

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 1/28/15

1. Which of the following graphs represents 𝑦 = |𝑥| − 2 ?

A.

C.

B.

D.

2. Reflect the graph of 𝑓(𝑥) = |𝑥| over the x-axis and translate the function one 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

3. 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, 𝑥 = −1 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

4. 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 1/28/15

5. 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

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

A.

C.

B.

D.


Updated 1/28/15

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

A.

−12𝑔6

ℎ12 C.

12𝑔9

ℎ

B. −64𝑔9

ℎ12 D.

𝑔9

64ℎ12

8. Let 𝑓(𝑥) = −3𝑐1/2 and 𝑔(𝑥) = 2𝑐15/2𝑑−8. Find ℎ(𝑥) = 𝑓(𝑥) ∙ 𝑔(𝑥).

A. ℎ(𝑥) =

−6𝑐8

𝑑8 C. ℎ(𝑥) =

−5𝑐7

𝑑8

B. ℎ(𝑥) =6𝑑8

𝑐8 D. ℎ(𝑥) = −6𝑐𝑑

9. 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

10. Simplify: √18

42

A. √21

7 C. 3

B. √63

7 D. √3


Updated 1/28/15

11. A moving company sells boxes for packing items. The large box has a volume of

6𝑥3 + 2𝑥2 + 3 cubic units. The medium box has a volume of 2𝑥3 + 8𝑥 − 5 cubic units. A

customer purchases two large boxes and one medium box. What is the total volume of the

purchased boxes?

A. 14𝑥6 + 12𝑥3 + 1 cubic units C. 14𝑥3 + 2𝑥2 + 8𝑥 − 2 cubic units

B. 14𝑥6 + 4𝑥2 + 8𝑥 + 1 cubic units D. 14𝑥3 + 4𝑥2 + 8𝑥 + 1 cubic units

12. 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

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

A. 𝑏2 + 14𝑏 + 49 C. 𝑏2 + 49𝑏 + 49

B. 𝑏2 + 49 D. 𝑏 + 49

14. 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)

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

A. (𝑥 + 12) C. (𝑥 − 2)

B. (𝑥 − 4) D. (𝑥 + 4)

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

A. (𝑥 − 5) C. (𝑥 − 12)

B. (𝑥 + 6) D. (𝑥 − 6)


Updated 1/28/15

17. 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

18. Solve for x in 16𝑥2 − 49 = 0 .

A. 𝑥 = ±

49

16 C. 𝑥 =

16

49

B. 𝑥 = ±7

4 D. 𝑥 =

7

4

19. The height (ℎ), in feet, of a person jumping off a diving platform can be modeled by the

equation ℎ = −16𝑡2 + 4𝑡 + 6 where 𝑡 represents the time in seconds the person is in the air.

After how many seconds does the person jumping off the platform enter the water?

A. −

1

2 𝑠𝑒𝑐𝑜𝑛𝑑 C.

4

3 𝑠𝑒𝑐𝑜𝑛𝑑𝑠

B. 3

4 𝑠𝑒𝑐𝑜𝑛𝑑 D. 2 𝑠𝑒𝑐𝑜𝑛𝑑𝑠

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


Updated 1/28/15

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

A. 𝑦 =

1

2𝑥2 − 5

B. 𝑦 = 2𝑥2 − 5

C. 𝑦 =1

2(𝑥 + 5)2

D. 𝑦 = 2(𝑥 − 5)2

22. Which of the following graphs represents 𝑓(𝑥) = (𝑥 − 4)2 ?

A.

C.

B.

D.


Updated 1/28/15

23. Translate the graph of 𝑓(𝑥) = 𝑥2 four units to the left, three 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 − 4)2 + 3 D. 𝑓(𝑥) = 2(𝑥 − 4)2 + 3

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

A. 𝑦 = −(𝑥 − 3)2 − 1

B. 𝑦 = −(𝑥 + 3)2 − 1

C. 𝑦 = −(𝑥 + 1)2 − 3

D. 𝑦 = −(𝑥 − 1)2 − 3

25. Which of the following is the vertex for 𝑓(𝑥) = −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. (0, 1)


Updated 1/28/15

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

units and left three 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. 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

30. 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

31. Which of the following is the vertex form for 𝑓(𝑥) = 𝑥2 + 4𝑥 + 7 ?

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

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


Updated 1/28/15

32. 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)

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

A. (−4, −73) C. (−2, −33)

B. (4, −9) D. (2, −1)

34. Before a truck can drive through a tunnel, it must be determined if the load can fit safely

through the tunnel. The parabola 𝑓(𝑥) = −1

4(𝑥 − 8)2 + 16 models the curve of the tunnel.

If a truckload is 12 𝑓𝑒𝑒𝑡 high what is the maximum width it could be?

A. 4 𝑓𝑒𝑒𝑡

B. 8 𝑓𝑒𝑒𝑡

C. 12 𝑓𝑒𝑒𝑡

D. 16 𝑓𝑒𝑒𝑡

35. 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 1/28/15

36. 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 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

37. 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: Growth

Equation 2: Growth

Equation 3: Decay

Equation 4: Decay

C. Equation 1: Decay

Equation 2: Growth

Equation 3: Growth

Equation 4: Decay

B. Equation 1: Decay

Equation 2: Decay

Equation 3: Growth

Equation 4: Growth

D. Equation 1: Growth

Equation 2: Decay

Equation 3: Decay

Equation 4: Growth

38. If 𝑓(𝑥) = 3 ∙ 4𝑥 and 𝑔(𝑥) = 3 ∙ 2𝑥, compare the functions and determine which of the

following statements is correct.

A. The x-intercept of 𝑓(𝑥) is greater than the x-intercept of 𝑔(𝑥).

B. The y-intercept of 𝑓(𝑥) is greater than the y-intercept of 𝑔(𝑥).

C. The functions increase at the same rate.

D. The functions have the same y-intercept.


Updated 1/28/15

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

A. 𝑥 = 16 C. 𝑥 = 3

B. 𝑥 = 4 D. 𝑥 = 2

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

A. 𝑥 = 6 C. 𝑥 = 5

B. 𝑥 = 4 D. 𝑥 = 3

41. What is the solution to the system graphed?

A. (2, 4)

B. (4, 2)

C. (1, 2)

D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

42.

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


Updated 1/28/15

43. Which of the following represents the function 𝑓(𝑥) = 3 ∙ 2𝑥 − 5 ?

A.

C.

B.

D.

44. Write a recursive formula for the sequence below, assuming 𝑓(1) is the first term in the

sequence:

3, −6, 12, −24, 48 …

A. 𝑓(1) = −6 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ (−2), for 𝑛 ≥ 2

B. 𝑓(1) = −2 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ 3, for 𝑛 ≥ 2

C. 𝑓(1) = 3 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ (−2), for 𝑛 ≥ 2

D. 𝑓(1) = 3 and 𝑓(𝑛) = 𝑓(𝑛 − 1) − 9, for 𝑛 ≥ 2

45. Write an explicit formula for the geometric sequence given 𝑎3 = 1 and 𝑎5 = 0.25. Assume

the common ratio is positive.

A. 𝑎𝑛 = 8(0.25)𝑛−1 C. 𝑎𝑛 = 0.5(4)𝑛−1

B. 𝑎𝑛 = 4(0.5)𝑛−1 D. 𝑎𝑛 = 0.25(8)𝑛−1


Updated 1/28/15

46. A supervisor at a factory is testing the company’s packaging machines for accuracy. The

machines are labeled X, Y, and Z. The company standard for packaging a product is that

each bag should contain 6 to 10 𝑜𝑢𝑛𝑐𝑒𝑠. The supervisor randomly chose 10 bags from

each machine and recorded the results in the table below. Based on the dot plots below,

which statement is correct?

A. Machine X is both the most consistent and the most accurate.

B. Machine X and Y are equally consistent, but Machine Y is the most accurate.

C. Machine Z is both the most consistent and the most accurate.

D. Machine Z is the most consistent, but Machine Y is the most accurate.

47. A fast food chain took a random survey of some of their stores to find the average number

of sodas they sell per day. The data collected is given below. Which measure of central

tendency best represents the data? Justify your answer.

{165, 142, 153, 160, 135, 140, 155, 30, 162, 157}

A. The mean would be best because there is an outlier.

B. The mean would be best because there is not an outlier.

C. The median would be best because there is an outlier.

D. The median would be best because there is not an outlier.

48. The two-way frequency table shows all of the grades for males and females in a science

class. If the females were to have the same percent of B’s as the males, how many more

females would need to get a B in the class?

A. 2

A B C D F

Females 6 3 4 2 1

Males 3 6 1 0 2

B. 3

C. 4

D. 5


Updated 1/28/15

49. Use the table below to help determine which function has the greatest value as x gets larger

and larger.

𝑥 𝑓(𝑥) = 𝑥 + 3 𝑔(𝑥) = 3𝑥 ℎ(𝑥) = 𝑥3 𝑖(𝑥) = 3𝑥

3

4

5

6

A. 𝑓(𝑥) has the greatest value as x gets larger and larger.

B. 𝑔(𝑥) has the greatest value as x gets larger and larger.

C. ℎ(𝑥) has the greatest value as x gets larger and larger.

D. 𝑖(𝑥) has the greatest value as x gets larger and larger.

50. The maximum height reached by a bouncing ball is given by ℎ(𝑥) = 10(0.75)𝑥 where h is

measured in feet and x is the bounce number. Describe the domain of this function and

what it means when 𝑥 = 0.

A. The domain is all real numbers. When the bounce number 𝑥 = 0, the height h of the

ball is 10 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and

bounces.

B. The domain is all real numbers. When the bounce number 𝑥 = 0, the height h of the

ball is 7.5 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and

bounces.

C. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the

bounce number x and does not have units. When 𝑥 = 0 the height h of the ball is

10 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and

bounces.

D. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the

bounce number x and does not have units. When 𝑥 = 0 the height h of the ball is

7.5 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and

bounces.


Updated 1/28/15

Algebra 1 S2 Instructional Material Answers 2014-2015

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

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

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

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

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

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

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

8. A 18. B 28. A 38. D 48. D

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

10. A 20. C 30. C 40. A 50. C

Documents

Algebra 1 Semester 2 Instructional Materialswalshmathsite.weebly.com/uploads/2/1/7/0/21709994/...Algebra 1 Semester 2 Instructional Materials 2014-2015 Updated 1/28/15 11. A moving