A1© 2014 College Board. All rights reserved. SpringBoard Algebra 1, Unit 1 Practice

1. Answers may vary. The year increases by 7 each time the occurrence number increases by 1.

2. 1949, 1956, 1963, 1970, …; the common difference is 7.

3. C

4. Answers may vary. A typical person lives to about 70 years old; the comet would be visible about 7 times during this time.

5. 1998

6.

Figure 4 Figure 5 Figure 6

Figure Number Number of Pennies

1 12 33 64 105 156 21

7.

8. 1, 3, 6, 10, 15, 21, …; no; consecutive terms do not differ by the same amount.

9. a. n Emilio’s Expression

1 22 63 124 205 306 42

Emilio’s expression does not give the correct number of pennies in each figure.

b. Emilio’s expression gives values that are twice the number of pennies in each figure. Therefore, divide Emilio’s expression by 2 (or multiply

by 12

) to find the correct expression; ( )+n n 12

,

or 12

n(n 1 1), or n2

(n 1 1).

10. C

11. Figure 13; Figure 13 contains ( )13 142

5 91 pennies,

so you will have 9 pennies left over. Figure 14

requires ( )14 152

5 105 pennies, which is more than

you have.

12. a. 2 1 0.50m

b. 2 1 0.50m 5 7.50; 11 miles

20

25

15

10

5

1 2 3 4 5 6 7 8 9 10

y

x

Figure Number

Num

ber o

f Pen

nies

Answers to Algebra 1 Unit 1 Practice

A2© 2014 College Board. All rights reserved. SpringBoard Algebra 1, Unit 1 Practice

13. a. When m . 10, the fare is reduced by $1. The expression becomes 2 1 0.50m 2 1, or 1 1 0.50m.

b. Yes; based on the answer to Item 12b, a non-discounted cab fare of $7.50 corresponds to a trip of 11 miles. Therefore, Lupe must have traveled at least 11 miles.

c. 13 miles

14. D

15. 19 years old

16. Answers will vary; 5x 2 1 5 3(x 1 2)

17. B

18. a. 3x 2 7 5 x 2 2

3x 2 x 2 7 5 x 2 x 2 2

2x 2 7 5 22

2x 2 7 1 7 5 22 1 7

2x 5 5

x22

5 52

x 5 52

b. 3x 2 7 5 x 2 2

3x 2 7 1 7 5 x 2 2 1 7

3x 5 x 1 5

3x 2 x 5 x 2 x 1 5

2x 5 5

x22

5 52

x 5 52

c. Both Alex and Danny are correct. Either method leads to the correct solution.

d. Yes; for example, you could begin by adding 2 to both sides.

3x 2 7 5 x 2 2

3x 2 7 1 2 5 x 2 2 1 2

3x 2 5 5 x

3x 2 x 2 5 5 x 2 x

2x 2 5 5 0

2x 2 5 1 5 5 0 1 5

2x 5 5

x22

5 52

x 5 52

19. 25 hours per week

20. Answers will vary. Students may mention several factors, such as the amount of money Jordan wants to earn, the number of hours she is willing and/or able to work per week, and the type of work environment that Jordan prefers. To earn the most money, Jordan should choose the job with the neighbor if she plans to work fewer than 25 hours per week; she should choose the job at the mall if she plans to work more than 25 hours per week.

21. C

22. 1

23. a. 18x 2 3

b. 43 units

A3© 2014 College Board. All rights reserved. SpringBoard Algebra 1, Unit 1 Practice

24. x 2 5 5 2(4x 2 3) Original equation

x 2 5 5 8x 2 6 Distributive Property

x 2 x 2 5 5 8x 2 x 2 6 Subtraction Property of Equality

25 5 7x 2 6 Combine like terms.

25 1 6 5 7x 2 6 1 6 Addition Property of Equality

1 5 7x Combine like terms.

17

5 x77

Division Property of Equality

17

5 x Solution

25. The solution is correct.

5(a 1 5) 2 3 5 3(2 2 a) Original equation

5a 1 25 2 3 5 6 2 3a Distributive Property

5a 1 22 5 6 2 3a Combine like terms.

5a 1 3a 1 22 5 6 2 3a 1 3a Addition Property of Equality

8a 1 22 5 6 Combine like terms.

8a 1 22 2 6 5 6 2 6 Subtraction Property of Equality

8a 1 16 5 0 Combine like terms.

8a 1 16 2 16 5 0 2 16 Subtraction Property of Equality

8a 5 216 Combine like terms.

a88

52168

Division Property of Equality

a 5 22 Solution

26. Tatiana solved the equation correctly, but her result of 0 5 0 indicates that the equation has infinitely many solutions, not just x 5 0.

27. B

28. All values of b except 2; explanation may vary. The value of 3x 2 2 cannot be equal to the value of 3x minus a number other than 2.

29. a. Equations may vary but should be equivalent to 4x 1 2m 5 2(x 1 12) 1 2(x 1 3).

b. Simplifying the right side of the equation gives 4x 1 2m 5 4x 1 30. Therefore, the equation will have infinitely many solutions if 2m 5 30, or if m 5 15.

c. All values of m except 15; the value of 4x 1 30 cannot be equal to the value of 4x added to a number other than 30. Therefore, if m fi 15, then 2m fi 30 and the equation has no solutions.

d. No value of m; based on the answers to parts b and c, if m 5 15, there are infinitely many solutions, and if m fi 15, there are no solutions. There are no other options for the value of m, so this equation can never have exactly one solution.

30. h 5 VB3

31. Solve the formula for F to get F 5 95

C 1 32.

32. Paris; its average temperature is 57.2° F. All of the other cities’ average temperatures fall outside of Igor’s preferred temperature range.

33. D

34. No; a appears on both sides of the equation.

35. D

A4© 2014 College Board. All rights reserved. SpringBoard Algebra 1, Unit 1 Practice

36. E . 92; U # 60

37. No; explanations may vary. 94 . 60, but 94 is a grade of E.

38. Answers will vary. All numbers greater than or equal to 2 are solutions of the inequality.

39. 4 1 3x # 15; x # 113

, or 323

2 31 4 50

The solutions represent the possible numbers of pounds of grapes that Kelli can buy.

40. B

41. Lavan is correct; x 5 210 would result in all of the sides having negative lengths, which is impossible. If x 5 1, all of the sides have positive lengths.

42. Answers will vary; x 5 2 would result in two of the sides having negative lengths, which is impossible.

43. 0 # x , 4

44. C

45. Conjunctions; each stock value was greater than or equal to the low price and less than or equal to the high price. Inequalities using and are conjunctions.

46. Answers may vary. According to Kevin’s inequality, the value of Century stock was as low as $30 and as high as $67. Neither of these statements is correct.

47. 2 31 4 52524 232221 0

|x 2 (21)| 5 3, or |x 1 1| 5 3

48. D

49. No; counterexamples will vary. If x 5 6 and z 5 1, then |z 2 x| 5 |1 2 6| 5 |25| 5 5, while |z| 2 |x| 5 |1| 2 |6| 5 1 2 6 5 25.

50. You need to know whether the melting point of radon is above or below 0° C.

51. A

52. Oxygen, nitrogen, and iodine

53. |c 2 2300| # 700, which results in the range 1600 # c # 3000

1600 1800 2000 2200 2400 2600 2800 3000

54. Answers will vary; |x 2 1.5| # 3.5

55. Answers will vary; |x 1 2| , 26