Algebra 16 August 2017

Algebra 16 August 2017 Questions Answer Keys

The University Of The State Of New York
Regents High School Examination
Algebra I
Wednesday, August 16, 2017 — 8:30 to 11:30 a.m., only
Student Name _________________________________________________________
School Name __________________________________________________________

1. A part of Jennifer’s work to solve the equation 2(6x2 – 3) = 11x2 – x is shown below

Given: 2(6x2 – 3) = 11x2 – x
Step 1: 12x2 – 6 = 11x2 – x

Which property justifies her first step?

  • (1) identity property of multiplication
  • (2) multiplication property of equality
  • (3) commutative property of multiplication
  • (4) distributive property of multiplication over subtraction
Answer: (4) distributive property of multiplication over subtraction 

2. Which value of x results in equal outputs for j(x) = 3x – 2 and b(x) = |x + 2|?

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

3. The expression 49x2 – 36 is equivalent to

  • (1) (7x – 6)2
  • (2) (24.5x – 18)2
  • (3) (7x – 6)(7x + 6)
  • (4) (24.5x – 18)(24.5x + 18)
Answer: (3) (7x – 6)(7x + 6) 
  • (1) 11
  • (2) 17
  • (3) 27
  • (4) 33
Answer: (3) 27 

5. The graph below models the height of a remote-control helicopter over 20 seconds during flight.

Algebra 16 August 2017

Over which interval does the helicopter have the slowest average rate of change?

  • (1) 0 to 5 seconds
  • (2) 5 to 10 seconds
  • (3) 10 to 15 seconds
  • (4) 15 to 20 seconds
Answer: (2) 5 to 10 seconds 

6. In the functions f(x) = kx2 and g(x) = |kx|, k is a positive integer.

If k is replaced by 1/2, which statement about these new functions is true?

  • (1) The graphs of both f(x) and g(x) become wider.
  • (2) The graph of f(x) becomes narrower and the graph of g(x) shifts left.
  • (3) The graphs of both f(x) and g(x) shift vertically.
  • (4) The graph of f(x) shifts left and the graph of g(x) becomes wider.
Answer: (1) The graphs of both f(x) and g(x) become wider. 

7. Wenona sketched the polynomial P(x) as shown on the axes below.

Algebra 16 August 2017

Which equation could represent P(x)?

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

8. Which situation does not describe a causal relationship?

  • (1) The higher the volume on a radio, the louder the sound will be.
  • (2) The faster a student types a research paper, the more pages the research paper will have.
  • (3) The shorter the time a car remains running, the less gasoline it will use.
  • (4) The slower the pace of a runner, the longer it will take the runner to finish the race
Answer: (2) The faster a student types a research paper, the more pages the research paper will have. 

9. A plumber has a set fee for a house call and charges by the hour for repairs. The total cost of her services can be modeled by c(t) 125t + 95.

Which statements about this function are true?

I. A house call fee costs $95.
II. The plumber charges $125 per hour.
III. The number of hours the job takes is represented by t.

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

10. What is the domain of the relation shown below?

{(4,2),(1,1),(0,0),(1,– 1),(4,– 2)}

  • (1) {0, 1, 4}
  • (2) {– 2, – 1, 0, 1, 2}
  • (3) {– 2, – 1, 0, 1, 2, 4}
  • (4) {– 2, – 1, 0, 0, 1, 1, 1, 2, 4, 4}
Answer: (1) {0, 1, 4} 

11. What is the solution to the inequality 2 + 4/9x ≥ 4 + x?

Algebra 16 August 2017
Answer: (1) 1 

12. Konnor wants to burn 250 Calories while exercising for 45 minutes at the gym. On the treadmill, he can burn 6 Cal/min. On the stationary bike, he can burn 5 Cal/min.

If t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of Calories that Konnor can burn on the stationary bike?

  • (1) b
  • (2) 5b
  • (3) 45 – b
  • (4) 250 – 5b
Answer: (2) 5b 

13. Which value of x satisfies the equation 5/6 (3/8 – x) 16?

  • (1) –19.575
  • (2) –18.825
  • (3) –16.3125
  • (4) –15.6875
Answer: (2) –18.825 

14. If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?

  • (1) p(t) = 3(100)t
  • (2) p(t) =100(3)t
  • (3) p(t) = 3t + 100
  • (4) p(t) = 100t + 3
Answer: (2) p(t) =100(3)t 

15. A sequence of blocks is shown in the diagram below

Algebra 16 August 2017

This sequence can be defined by the recursive function a1 = 1 and an = an – 1 + n. Assuming the pattern continues, how many blocks will there be when n = 7?

  • (1) 13
  • (2) 21
  • (3) 28
  • (4) 36
Answer: (3) 28 

16. Mario’s $15,000 car depreciates in value at a rate of 19% per year. The value, V, after t years can be modeled by the function V 15,000(0.81)t . Which function is equivalent to the original function?

  • (1) V = 15,000(0.9)9t
  • (2) V = 15,000(0.9)2t
  • (3) V = 15,000(0.9) t/9
  • (4) V = 15,000(0.9) t/2
Answer: (2) V = 15,000(0.9)2t 

17. The highest possible grade for a book report is 100. The teacher deducts 10 points for each day the report is late.

Which kind of function describes this situation?

  • (1) linear
  • (2) quadratic
  • (3) exponential growth
  • (4) exponential decay
Answer: (1) linear 

18. The function h(x), which is graphed below, and the function g(x) = 2|x + 4| – 3 are given.

Algebra 16 August 2017

Which statements about these functions are true?

I. g(x) has a lower minimum value than h(x).
II. For all values of x, h(x) < g(x)
III. For any value of x, g(x) ≠ h(x).

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

19. The zeros of the function f(x) = 2x3 + 12x – 10x2 are

  • (1) {2, 3}
  • (2) {– 1, 6}
  • (3) {0, 2, 3}
  • (4) {0, – 1, 6}
Answer: (3) {0, 2, 3}

20. How many of the equations listed below represent the line passing through the points (2,3) and (4, – 7)?

5x + y = 13
y + 7 = – 5(x – 4)
y = – 5x + 13
y – 7 = 5(x – 4)

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

 

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