Algebra 23 January 2018 Questions Answer Keys

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

Regents High School Examination

Algebra I

Tuesday, January 23, 2018 — 1:15 to 4:15 p.m., only

Student Name _________________________________________________________

School Name __________________________________________________________

**1. When solving the equation 12x ^{2} – 7x = 6 – 2(x^{2} – 1), Evan wrote 12x^{2} – 7x = 6 – 2x^{2} + 2 as his first step. Which property justifies this step?**

- (1) subtraction property of equality
- (2) multiplication property of equality
- (3) associative property of multiplication
- (4) distributive property of multiplication over subtraction

**2. Jill invests $400 in a savings bond. The value of the bond, V(x), in hundreds of dollars after x years is illustrated in the table below.**

Which equation and statement illustrate the approximate value of the bond in hundreds of dollars over time in years?

- (1) V(x) 5 4(0.65)
^{x}, and it grows. - (2) V(x) 5 4(0.65)
^{ x}, and it decays. - (3) V(x) 5 4(1.35) x, and it grows.
- (4) V(x) 5 4(1.35)
^{ x}, and it decays.

**3. Alicia purchased H half-gallons of ice cream for $3.50 each and P packages of ice cream cones for $2.50 each. She purchased 14 items and spent $43. Which system of equations could be used to determine how many of each item Alicia purchased?**

- (1) 3.50H + 2.50P = 43

H + P = 14 - (2) 3.50P + 2.50H = 43

P + H = 14 - (3) 3.50H + 2.50P = 14

H + P = 43 - (4) 3.50P + 2.50H = 14

P + H = 43

** 4. A relation is graphed on the set of axes below.**

Based on this graph, the relation is

- (1) a function because it passes the horizontal line test
- (2) a function because it passes the vertical line test
- (3) not a function because it fails the horizontal line test
- (4) not a function because it fails the vertical line test

**5 Ian is saving up to buy a new baseball glove. Every month he puts $10 into a jar. Which type of function best models the total amount of money in the jar after a given number of months?**

- (1) linear
- (2) exponential
- (3) quadratic
- (4) square root

**6. Which ordered pair would not be a solution to y 5 x ^{3} – x?**

- (1) (–4, –60)
- (2) (–2, –6)
- (3) (–3, –24)
- (4) (–1, –2)

**7. Last weekend, Emma sold lemonade at a yard sale. The function P(c) = .50c – 9.96 represented the profit, P(c), Emma earned selling c cups of lemonade. Sales were strong, so she raised the price for this weekend by 25 cents per cup. Which function represents her profit for this weekend?**

- (1) P(c) = .25c – 9.96
- (2) P(c) = .50c – 9.71
- (3) P(c) = .50c – 10.21
- (4) P(c) = .75c – 9.96

**8. The product of √576 and √684 is**

- (1) irrational because both factors are irrational
- (2) rational because both factors are rational
- (3) irrational because one factor is irrational
- (4) rational because one factor is rational

**9. Which expression is equivalent to y ^{4} – 100?**

- (1) (y
^{2}– 10)^{2} - (2) (y
^{2}– 50)^{2} - (3) (y
^{2}+ 10)(y^{2}– 10) - (4) (y
^{2}+ 50)(y^{2}– 50)

**10. The graphs of y = x ^{2} – 3 and y = 3x – 4 intersect at approximately**

- (1) (0.38, –2.85), only
- (2) (2.62, 3.85), only
- (3) (0.38, –2.85) and (2.62, 3.85)
- (4) (0.38, –2.85) and (3.85, 2.62)

**11. The expression –4.9t ^{2} + 50t + 2 represents the height, in meters, of a toy rocket t seconds after launch. The initial height of the rocket, in meters, is**

- (1) 0
- (2) 2
- (3) 4.9
- (4) 50

**12. If the domain of the function f(x) 5 2x ^{2} – 8 is {–2, 3, 5}, then the range is**

- (1) {–16, 4, 92}
- (2) {–16, 10, 42}
- (3) {0, 10, 42}
- (4) {0, 4, 92}

**13. Which polynomial is twice the sum of 4x ^{2} – x + 1 and –6x^{2} + x – 4?**

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

**14. What are the solutions to the equation 3(x – 4) ^{2} = 27?**

- (1) 1 and 7
- (2) –1 and –7
- (3) 4 ± √24
- (4) – 4 ± √24

**15. A system of equations is shown below.**

Equation A: 5x + 9y = 12

Equation B: 4x – 3y = 8

Which method eliminates one of the variables?

- (1) Multiply equation A by –
^{1}/_{3}and add the result to equation B. - (2) Multiply equation B by 3 and add the result to equation A.
- (3) Multiply equation A by 2 and equation B by –6 and add the results together.
- (4) Multiply equation B by 5 and equation A by 4 and add the results together.

**16. The 15 members of the French Club sold candy bars to help fund their trip to Quebec. The table below shows the number of candy bars each member sold.**

When referring to the data, which statement is false?

- (1) The mode is the best measure of central tendency for the data.
- (2) The data have two outliers.
- (3) The median is 53.
- (4) The range is 120.

**17. Given the set {x| – 2 ≤ x ≤ 2, where x is an integer}, what is the solution of –2(x – 5) < 10?**

- (1) 0, 1, 2
- (2) 1, 2
- (3) –2, –1, 0
- (4) –2, –1

**18. If the pattern below continues, which equation(s) is a recursive formula that represents the number of squares in this sequence?**

- (1) y = 2x + 1
- (2) y = 2x + 3
- (3) a
_{1}= 3

a_{n}5 a_{n}– 1 + 2 - (4) a
_{1}= 1

a_{n}5 a_{n}– 1 + 2

**19. If the original function f(x) = 2x ^{2} – 1 is shifted to the left 3 units to make the function g(x), which expression would represent g(x)?**

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

**20. First consider the system of equations y= – ^{1}/_{2 } x + 1 and y = x – 5.**

**Then consider the system of inequalities y > –**

^{1}/_{2 }x + 1 and y < x – 5.When comparing the number of solutions in each of these systems, which statement is true?

- (1) Both systems have an infinite number of solutions.
- (2) The system of equations has more solutions.
- (3) The system of inequalities has more solutions.
- (4) Both systems have only one solution.

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