Algebra 13 June 2017

Algebra 13 June 2017 Questions Answer Keys

The University Of The State Of New York
Regents High School Examination
Algebra I
Tuesday, June 13, 2017 — 1:15 to 4:15 p.m., only
Student Name _________________________________________________________
School Name __________________________________________________________

1. To keep track of his profits, the owner of a carnival booth decided to model his ticket sales on a graph. He found that his profits only declined when he sold between 10 and 40 tickets. Which graph could represent his profits?

Algebra 13 June 2017
Answer: (3) 

2. The formula for the surface area of a right rectangular prism is A = 2lw + 2hw + 2lh, where l, w, and h represent the length, width, and height, respectively. Which term of this formula is not dependent on the height?

  • (1) A
  • (2) 2lw
  • (3) 2hw
  • (4) 2lh
Answer: (2) 2lw 

3. Which graph represents y = √x – 2 ?

Algebra 13 June 2017
Answer: (4) 

4. A student plotted the data from a sleep study as shown in the graph below.

Algebra 13 June 2017

The student used the equation of the line y = – 0.09x + 9.24 to model the data. What does the rate of change represent in terms of these data?

  • (1) The average number of hours of sleep per day increases 0.09 hour per year of age.
  • (2) The average number of hours of sleep per day decreases 0.09 hour per year of age.
  • (3) The average number of hours of sleep per day increases 9.24 hours per year of age.
  • (4) The average number of hours of sleep per day decreases 9.24 hours per year of age.
Answer: (2) The average number of hours of sleep per day decreases 0.09 hour per year of age. 

5. Lynn, Jude, and Anne were given the function f(x) = – 2x2 + 32, and they were asked to find f(3). Lynn’s answer was 14, Jude’s answer was 4, and Anne’s answer was ± 4. Who is correct?

  • (1) Lynn, only
  • (2) Jude, only
  • (3) Anne, only
  • (4) Both Lynn and Jude
Answer: (1) Lynn, only 

6. Which expression is equivalent to 16x4 – 64?

  • (1) (4x2 – 8)2
  • (2) (8x2 – 32) 2
  • (3) (4x2 + 8)(4x2 – 8)
  • (4) (8x2 + 32)(8x2 – 32)
Answer: (3) (4x2 + 8)(4x2 – 8) 

7. Vinny collects population data, P(h), about a specific strain of bacteria over time in hours, h, as shown in the graph below

Algebra 13 June 2017

Which equation represents the graph of P(h)?

  • (1) P(h) = 4(2)h
  • (2) P(h) = 46/5 h + 6/5
  • (3) P(h) = 3h2 + 0.2h + 4.2
  • (4) P(h) = 2/3 h3 – h2 + 3h + 4
Answer: (1) P(h) = 4(2)h 

8. What is the solution to the system of equations below?

y = 2x + 8
3(– 2x + y) = 12

  • (1) no solution
  • (2) infinite solutions
  • (3) (– 1,6)
  • (4) (1/2, 9)
Answer: (1) no solution 

9. A mapping is shown in the diagram below.

Algebra 13 June 2017

This mapping is

  • (1) a function, because Feb has two outputs, 28 and 29
  • (2) a function, because two inputs, Jan and Mar, result in the output 31
  • (3) not a function, because Feb has two outputs, 28 and 29
  • (4) not a function, because two inputs, Jan and Mar, result in the output 31
Answer: (3) not a function, because Feb has two outputs, 28 and 29 

10. Which polynomial function has zeros at – 3, 0, and 4?

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

11. Jordan works for a landscape company during his summer vacation. He is paid $12 per hour for mowing lawns and $14 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $250 this week. If m represents the number of hours mowing lawns and g represents the number of hours planting gardens, which system of inequalities could be used to represent the given conditions?

  • (1) m + g ≤ 40
    12m + 14g ≥ 250
  • (2) m + g ≥ 40
    12m + 14g ≤ 250
  • (3) m + g ≤ 40
    12m + 14g ≤ 250
  • (4) m + g ≥ 40
    12m + 14g ≤ 250
Answer: (1) m + g ≤ 40
12m + 14g ≥ 250 

12. Anne invested $1000 in an account with a 1.3% annual interest rate. She made no deposits or withdrawals on the account for 2 years. If interest was compounded annually, which equation represents the balance in the account after the 2 years?

  • (1) A = 1000(1 – 0.013)2
  • (2) A = 1000(1 + 0.013)2
  • (3) A = 1000(1 – 1.3)2
  • (4) A = 1000(1 + 1.3)2
Answer: (2) A = 1000(1 + 0.013)2 

13. Which value would be a solution for x in the inequality 47 – 4x < 7?

  • (1) – 13
  • (2) –10
  • (3) 10
  • (4) 11
Answer: (4) 11 

14. Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the correlation coefficient to determine the strength of the linear fit.

Which correlation coefficient represents the strongest linear relationship?

  • (1) 0.9
  • (2) 0.5
  • (3) – 0.3
  • (4) – 0.8
Answer: (1) 0.9 

15. The heights, in inches, of 12 students are listed below

61, 67, 72, 62, 65, 59, 60, 79, 60, 61, 64, 63

Which statement best describes the spread of these data?

  • (1) The set of data is evenly spread.
  • (2) The median of the data is 59.5.
  • (3) The set of data is skewed because 59 is the only value below 60.
  • (4) 79 is an outlier, which would affect the standard deviation of these data.
Answer: (4) 79 is an outlier, which would affect the standard deviation of these data. 

16. The graph of a quadratic function is shown below.

Algebra 13 June 2017

An equation that represents the function could be

  • (1) q(x) = 1/2 (x + 15)2 – 25
  • (2) q(x) = – 1/2 (x + 15)2 – 25
  • (3) q(x) = 1/2 (x –15)2 + 25
  • (4) q(x) = – 1/2 (x – 15)2 + 25
Answer: (4) q(x) = – 1/2 (x – 15)2 + 25

17. Which statement is true about the quadratic functions g(x), shown in the table below, and f(x) =  (x – 3)2 + 2 ?

Algebra 13 June 2017
  • (1) They have the same vertex.
  • (2) They have the same zeros.
  • (3) They have the same axis of symmetry.
  • (4) They intersect at two points.
Answer: (3) They have the same axis of symmetry. 

18. Given the function f(n) defined by the following:

f(1) = 2
f(n) = – 5f(n 1) + 2

Which set could represent the range of the function?

  • (1) {2, 4, 6, 8,…}
  • (2) {2, – 8, 42, – 208,…}
  • (3) {– 8, 42, – 208, 1042,…}
  • (4) {– 10, 50, – 250, 1250,…}
Answer: (2) {2, – 8, 42, – 208,…}

19. An equation is given below.

4(x 7) = 0.3(x + 2) + 2.11

The solution to the equation is

  • (1) 8.3
  • (2) 8.7
  • (3) 3
  • (4) – 3
Answer: (1) 8.3

20. A construction worker needs to move 120 ft 3 of dirt by using a wheelbarrow. One wheelbarrow load holds 8 ft3 of dirt and each load takes him 10 minutes to complete. One correct way to figure out the number of hours he would need to complete this job is

Algebra 13 June 2017
Answer: (4) 

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