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(6x ^{2} – 3) = 11x^{2} – x is shown below**

Given: 2(6x^{2} – 3) = 11x^{2} – x

Step 1: 12x^{2} – 6 = 11x^{2} – 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

**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

**3. The expression 49x ^{2} – 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)

- (1) 11
- (2) 17
- (3) 27
- (4) 33

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

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

**6. In the functions f(x) = kx ^{2} 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.

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

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)

**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

**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

**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}

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

**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

**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

**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

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

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

- (1) 13
- (2) 21
- (3) 28
- (4) 36

**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

**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

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

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

**19. The zeros of the function f(x) = 2x ^{3 }+ 12x – 10x^{2 }are**

- (1) {2, 3}
- (2) {– 1, 6}
- (3) {0, 2, 3}
- (4) {0, – 1, 6}

**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

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