# Algebra 12 August 2015

Algebra 12 August 2015 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I (Common Core)
Wednesday, August 12, 2015 — 8:30 to 11:30 a.m., only
Student Name:________________________________________________________
School Name: ________________________________________________________

1. Given the graph of the line represented by the equation  f(x) = – 2x + b, if b is increased by 4 units, the graph of the new line would be shifted 4 units

• (1) right
• (2) up
• (3) left
• (4) down

2. Rowan has \$50 in a savings jar and is putting in \$5 every week. Jonah has \$10 in his own jar and is putting in \$15 every week. Each of them plots his progress on a graph with time on the horizontal axis and amount in the jar on the vertical axis. Which statement about their graphs is true?

• (1) Rowan’s graph has a steeper slope than Jonah’s.
• (2) Rowan’s graph always lies above Jonah’s.
• (3) Jonah’s graph has a steeper slope than Rowan’s.
• (4) Jonah’s graph always lies above Rowan’s.
Answer: (3) Jonah’s graph has a steeper slope than Rowan’s.

3. To watch a varsity basketball game, spectators must buy a ticket at the door. The cost of an adult ticket is \$3.00 and the cost of a student ticket is \$1.50. If the number of adult tickets sold is represented by a and student tickets sold by s, which expression represents the amount of money collected at the door from the ticket sales?

• (1) 4.50as
• (2) 4.50(a + s)
• (3) (3.00a)(1.50s)
• (4) 3.00a + 1.50s

4. The graph of f(x) is shown below.

Which function could represent the graph of f(x)?

• (1) f(x) = (x + 2)(x2 + 3x – 4)
• (2) f(x) = (x – 2)(x2 + 3x – 4)
• (3) f(x) = (x + 2)(x2 + 3x + 4)
• (4) f(x) = (x – 2)(x2 + 3x + 4)
Answer: (1) f(x) = (x + 2)(x2 + 3x – 4)

5. The cost of a pack of chewing gum in a vending machine is \$0.75. The cost of a bottle of juice in the same machine is \$1.25. Julia has \$22.00 to spend on chewing gum and bottles of juice for her team and she must buy seven packs of chewing gum. If b represents the number of bottles of juice, which inequality represents the maximum number of bottles she can buy?

• (1) 0.75b + 1.25(7) ≥ 22
• (2) 0.75b + 1.25(7) ≤ 22
• (3) 0.75(7) + 1.25b ≥ 22
• (4) 0.75(7) + 1.25b ≤ 22
Answer: (4) 0.75(7) + 1.25b ≤ 22

6. Which graph represents the solution of y ≤ x + 3 and y ≥ – 2x – 2?

7. The country of Benin in West Africa has a population of 9.05 million people. The population is growing at a rate of 3.1% each year. Which function can be used to find the population 7 years from now?

• (1) f(t) = (9.05 x 106)(1 – 0.31)7
• (2) f(t) = (9.05 x 106)(1 + 0.31)7
• (3) f(t) = (9.05 x 106)(1 + 0.031)7
• (4) f(t) = (9.05 x 106)(1 – 0.031)7
Answer: (3) f(t) = (9.05 x 106)(1 + 0.031)7

8. A typical cell phone plan has a fixed base fee that includes a certain  amount of data and an overage charge for data use beyond the plan. A cell phone plan charges a base fee of \$62 and an overage charge of \$30 per gigabyte of data that exceed 2 gigabytes. If C represents the cost and g represents the total number of gigabytes of data, which equation could represent this plan when more than 2 gigabytes are used?

• (1) C = 30 + 62(2 – g)
• (2) C = 30 + 62(g – 2)
• (3) C = 62 +30(2 – g)
• (4) C = 62 + 30(g – 2)
Answer: (4) C = 62 + 30(g – 2)

9. Four expressions are shown below.

I     2(2x2 – 2x – 60)
II      4(x2 – x – 30)
III     4(x + 6)(x – 5)
IV     4x(x – 1) – 120

The expression 4x2 – 4x – 120 is equivalent to

• (1) I and II, only
• (2) II and IV, only
• (3) I, II, and IV
• (4) II, III, and IV
Answer: (3) I, II, and IV

10. Last week, a candle store received \$355.60 for selling 20 candles. Small candles sell for \$10.98 and large candles sell for \$27.98. How many large candles did the store sell?

• (1) 6
• (2) 8
• (3) 10
• (4) 12

11. Which representations are functions?

• (1) I and II
• (2) II and IV
• (3) III, only
• (4) IV, only
• (1) 1
• (2) – 2
• (3) – 1
• (4) – 13/3

13. The zeros of the function f(x) = 3x2 – 3x – 6 are

• (1) – 1 and – 2
• (2) 1 and – 2
• (3) 1 and 2
• (4) – 1 and 2
Answer: (4) – 1 and 2

14. Which recursively defined function has a first term equal to 10 and a common difference of 4?

• (1) f(1) = 10   f(x) = f(x – 1) + 4
• (2) f(1) = 4  f(x) = f(x – 1) + 10
• (3) f(1) = 10  f(x) = 4f(x – 1)
• (4) f(1) = 4  f(x) = 10f(x – 1)
Answer: (1) f(1) = 10   f(x) = f(x – 1) + 4

15. Firing a piece of pottery in a kiln takes place at different temperatures for different amounts of time. The graph below shows the temperatures in a kiln while firing a piece of pottery after the kiln is preheated to 200ºF.

During which time interval did the temperature in the kiln show the greatest average rate of change?

• (1) 0 to 1 hour
• (2) 1 hour to 1.5 hours
• (3) 2.5 hours to 5 hours
• (4) 5 hours to 8 hours
Answer: (1) 0 to 1 hour
• (1) – 1.75 and – 1.438
• (2) – 1.75 and 4
• (3) – 1.438 and 0
• (4) 4 and 0
Answer: (2) – 1.75 and 4

18. Alicia has invented a new app for smart phones that two companies  are interested in purchasing for a 2-year contract.
Company A is offering her \$10,000 for the first month and will increase the amount each month by \$5000.
Company B is offering \$500 for the first month and will double their payment each month from the previous month.
Monthly payments are made at the end of each month. For which monthly payment will company B’s payment first exceed company A’s payment?

• (1) 6
• (2) 7
• (3) 8
• (4) 9

19. The two sets of data below represent the number of runs scored by two different youth baseball teams over the course of a season.

Team A: 4, 8, 5, 12, 3, 9, 5, 2
Team B: 5, 9, 11, 4, 6, 11, 2, 7

Which set of statements about the mean and standard deviation is true?

• (1) mean A < mean B
standard deviation A > standard deviation B
• (2) mean A > mean B
standard deviation A< standard deviation B
• (3) mean A < mean B
standard deviation A < standard deviation B
• (4) mean A > mean B
standard deviation A > standard deviation B
Answer: (1) mean A < mean B
standard deviation A > standard deviation B

20. If Lylah completes the square for f(x) = x2 – 12x + 7 in order to find the minimum, she must write f(x) in the general form f(x) = (x – a)2 + b. What is the value of a for f(x)?

• (1) 6
• (2) – 6
• (3) 12
• (4) – 12