Algebra 16 June 2016 Questions Answer Keys

**The University Of The State Of New York**

Regents High School Examination

Algebra I

Thursday, June 16, 2016 — 9:15 a.m. to 12:15 p.m., only

Student Name _________________________________________________________

School Name __________________________________________________________

**1. The expression x ^{4} – 16 is equivalent to**

- (1) (x
^{2}+ 8)(x^{2}– 8) - (2) (x
^{2}– 8)(x^{2}– 8) - (3) (x
^{2}+ 4)(x^{2}– 4) - (4) (x
^{2}– 4)(x^{2}– 4)

**2. An expression of the fifth degree is written with a leading coefficient of seven and a constant of six. Which expression is correctly written for these conditions?**

- (1) 6x
^{5}+ x^{4}+ 7 - (2) 7x
^{6}– 6x^{4}+ 5 - (3) 6x
^{7}– x^{5}+ 5 - (4) 7x
^{5}+ 2x^{2}+ 6

**3. The table below shows the year and the number of households in a building that had high-speed broadband internet access**

For which interval of time was the average rate of change the smallest?

- (1) 2002 – 2004
- (2) 2003 – 2005
- (3) 2004 – 2006
- (4) 2005 – 2007

**4. The scatterplot below compares the number of bags of popcorn and the number of sodas sold at each performance of the circus over one week.**

Which conclusion can be drawn from the scatterplot?

- (1) There is a negative correlation between popcorn sales and soda sales.
- (2) There is a positive correlation between popcorn sales and soda sales.
- (3) There is no correlation between popcorn sales and soda sales.
- (4) Buying popcorn causes people to buy soda.

**5. The Celluloid Cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, which system of equations could be used to determine how many adult tickets, a, and how many child tickets, c, were sold?**

- (1) a + c = 150

10.25a + 7.75c = 1470 - (2) a + c = 1470

10.25a + 7.75c = 150 - (3) a + c = 150

7.75a + 10.25c = 1470 - (4) a + c = 1470

7.75a + 10.25c = 150

**6. The tables below show the values of four different functions for given values of x.**

Which table represents a linear function?

- (1) f(x)
- (2) g(x)
- (3) h(x)
- (4) k(x)

**7. The acidity in a swimming pool is considered normal if the average of three pH readings, p, is defined such that 7.0 < p < 7.8. If the first two readings are 7.2 and 7.6, which value for the third reading will result in an overall rating of normal?**

- (1) 6.2
- (2) 7.3
- (3) 8.6
- (4) 8.8

**8. Dan took 12.5 seconds to run the 100-meter dash. He calculated the time to be approximately**

- (1) 0.2083 minute
- (2) 750 minutes
- (3) 0.2083 hour
- (4) 0.52083 hour

**9. When 3x + 2 ≤ 5(x – 4) is solved for x, the solution is**

- (1) x ≤ 3
- (2) x ≥ 3
- (3) x ≤ – 11
- (4) x ≥ 11

**10. The expression 3(x ^{2} – 1) (x^{2} – 7x + 10) is equivalent to**

- (1) 2x
^{2}– 7x + 7 - (2) 2x
^{2}+ 7x – 13 - (3) 2x
^{2}– 7x + 9 - (4) 2x
^{2}+ 7x – 11

**11. The range of the function f(x) = x ^{2} + 2x – 8 is all real numbers**

- (1) less than or equal to – 9
- (2) greater than or equal to – 9
- (3) less than or equal to – 1
- (4) greater than or equal to – 1

**12. The zeros of the function f(x) = x ^{2} – 5x – 6 are**

- (1) – 1 and 6
- (2) 1 and – 6
- (3) 2 and – 3
- (4) – 2 and 3

**13. In a sequence, the first term is 4 and the common difference is 3. The fifth term of this sequence is**

- (1) – 11
- (2) – 8
- (3) 16
- (4) 19

**14. The growth of a certain organism can be modeled by C (t) = 10(1.029)^{24t} , where C(t) is the total number of cells after t hours. Which function is approximately equivalent to C(t)?**

- (1) C(t) = 240(.083)
^{24t} - (2) C(t) = 10(.083)
^{t} - (3) C(t) = 10(1.986)
^{t} - (4) C(t) = 240(1.986)
^{t/24}

**15. A public opinion poll was taken to explore the relationship between age and support for a candidate in an election. The results of the poll are summarized in the table below.**

What percent of the 21– 40 age group was for the candidate?

- (1) 15
- (2) 25
- (3) 40
- (4) 60

**16. Which equation and ordered pair represent the correct vertex form and vertex for j(x) = x ^{2} – 12x + 7?**

- (1) j(x) = (x – 6)
^{2}+ 43, (6,43) - (2) j(x) = (x – 6)
^{2}+ 43, (– 6,43) - (3) j(x) = (x – 6)
^{2}– 29, (6, – 29) - (4) j(x) = (x – 6)
^{2}– 29, (– 6, – 29)

**17. A student invests $500 for 3 years in a savings account that earns 4% interest per year. No further deposits or withdrawals are made during this time. Which statement does not yield the correct balance in the account at the end of 3 years?**

- (1) 500(1.04)
^{3} - (2) 500(1 – .04)
^{3} - (3) 500(1 + .04)(1 + .04)(1 + .04)
- (4) 500 + 500(.04) + 520(.04) + 540.8(.04)

**18. The line represented by the equation 4y + 2x = 33.6 shares a solution point with the line represented by the table below.**

The solution for this system is

- (1) (– 14.0, – 1.4)
- (2) (– 6.8,5.0)
- (3) (1.9,4.6)
- (4) (6.0,5.4)

**19. What is the solution of the equation 2(x + 2) ^{2} – 4 = 28?**

- (1) 6, only
- (2) 2, only
- (3) 2 and – 6
- (4) 6 and – 2

**20. The dot plot shown below represents the number of pets owned by students in a class.**

Which statement about the data is not true?

- (1) The median is 3.
- (2) The interquartile range is 2.
- (3) The mean is 3.
- (4) The data contain no outliers.

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