# Algebra 23 January 2018

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 12x2 – 7x = 6 – 2(x2 – 1), Evan wrote 12x2 – 7x = 6 – 2x2 + 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
Answer: (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.
Answer: (3) V(x) 5 4(1.35) x, and it grows.

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
Answer: (1) 3.50H + 2.50P = 43
H + P = 14

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
Answer: (2) a function because it passes 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
Answer: (1) linear

6. Which ordered pair would not be a solution to y 5 x3 – x?

• (1) (–4, –60)
• (2) (–2, –6)
• (3) (–3, –24)
• (4) (–1, –2)
Answer: (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
Answer: (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
Answer: (3) irrational because one factor is irrational

9. Which expression is equivalent to y4 – 100?

• (1) (y2 – 10)2
• (2) (y2 – 50)2
• (3) (y2 + 10)(y2 – 10)
• (4) (y2 + 50)(y2 – 50)
Answer: (3) (y2 + 10)(y2 – 10)

10. The graphs of y = x2 – 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)
Answer: (3) (0.38, –2.85) and (2.62, 3.85)

11. The expression –4.9t2 + 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
Answer: (2) 2

12. If the domain of the function f(x) 5 2x2 – 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}
Answer: (3) {0, 10, 42}

13. Which polynomial is twice the sum of 4x2 – x + 1 and –6x2 + x – 4?

• (1) –2x2 – 3
• (2) –4x2 – 3
• (3) –4x2 – 6
• (4) –2x2 + x – 5
Answer: (3) –4×2 – 6

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
Answer: (1) 1 and 7

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.
Answer: (2) Multiply equation B by 3 and add the result to equation A.

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.
Answer: (1) The mode is the best measure of central tendency for the data.

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
Answer: (2) 1, 2

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) a1 = 3
an 5 an – 1 + 2
• (4) a1 = 1
an 5 an – 1 + 2
Answer: (3) a1 = 3
an 5 an – 1 + 2

19. If the original function f(x) = 2x2 – 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) 2x2 + 2
• (4) 2x2 – 2
Answer: (2) 2(x + 3)2 – 1

20. First consider the system of equations y= – 1/ x + 1 and y = x – 5.
Then consider the system of inequalities y > – 1/ 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.
Answer: (3) The system of inequalities has more solutions.

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