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.

**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)(x
^{2}+ 3x – 4) - (2) f(x) = (x – 2)(x
^{2}+ 3x – 4) - (3) f(x) = (x + 2)(x
^{2}+ 3x + 4) - (4) f(x) = (x – 2)(x
^{2}+ 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

**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 10
^{6})(1 – 0.31)^{7} - (2) f(t) = (9.05 x 10
^{6})(1 + 0.31)^{7} - (3) f(t) = (9.05 x 10
^{6})(1 + 0.031)^{7} - (4) f(t) = (9.05 x 10
^{6})(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)

**9. Four expressions are shown below.**

I 2(2x^{2} – 2x – 60)

II 4(x^{2} – x – 30)

III 4(x + 6)(x – 5)

IV 4x(x – 1) – 120

The expression 4x^{2} – 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

**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) = 3x ^{2} – 3x – 6 are**

- (1) – 1 and – 2
- (2) 1 and – 2
- (3) 1 and 2
- (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)

**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

- (1) – 1.75 and – 1.438
- (2) – 1.75 and 4
- (3) – 1.438 and 0
- (4) 4 and 0

**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

**20. If Lylah completes the square for f(x) = x ^{2} – 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

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