# Integrated algebra 30 January 2014

Integrated algebra 30 January 2014 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
INTEGRATED ALGEBRA
Thursday, January 30, 2014 — 9:15 a.m. to 12:15 p.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

1. An example of an equation is

• (1) 2x2 – 4x + 12
• (2) |x – 6|
• (3) 4(x + 6)(x – 2)
• (4) 2x = x2 + 3
Answer: (4) 2x = x2 + 3

2. The greatest common factor of 3m2n 12mn2 is

• (1) 3n
• (2) 3m
• (3) 3mn
• (4) 3mn2

3. Jeremy is hosting a Halloween party for 80 children. He will give each child at least one candy bar. If each bag of candy contains 18 candy bars, which inequality can be used to determine how many bags, c, Jeremy will need to buy?

• (1) 18c ≥ 80
• (2) 18c ≤ 80
• (3) c18 ≥80
• (4) c18 ≤80

4. Which statement regarding biased sampling is false?

• (1) Online sampling is biased because only the people who happen to visit the web site will take the survey.
• (2) A radio call-in survey is biased because only people who feel strongly about the topic will respond.
• (3) A survey handed to every third person leaving a library is biased because everyone leaving the library was not asked to participate.
• (4) Asking for experts to take a survey is biased because they may have particular knowledge of the topic.
Answer: (3) A survey handed to every third person leaving a library is biased because everyone leaving the library was not asked to participate.

5. Which relation is not a function?

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

6. What is an equation of the line that passes through the point (- 2,- 8) and has a slope of 3?

• (1) y = 3x – 2
• (2) y = 3x – 22
• (3) y = 3x + 2
• (4) y = 3x + 22
Answer: (1) y = 3x – 2

7. A figure consists of a square and a semicircle, as shown in the diagram below.

If the length of a side of the square is 6, what is the area of the shaded region?

• (1) 36 – 3π
• (2) 36 – 4.5π
• (3) 36 – 6π
• (4) 36 – 9π

8. The box-and-whisker plot shown below represents the number of  magazine subscriptions sold by members of a club.

Which statistical measures do points B, D, and E represent,respectively?

• (1) minimum, median, maximum
• (2) first quartile, median, third quartile
• (3) first quartile, third quartile, maximum
• (4) median, third quartile, maximum
Answer: (3) first quartile, third quartile, maximum

9. What is the slope of a line represented by the equation 2y = x – 4?

• (1) 1
• (2)  ½
• (3) – 1
• (4) – ½

10. What is the solution of the system of equations below?

2x + 3y = 7
x + y = 3

• (1) (1,2)
• (2) (2,1)
• (3) (4,-1)
• (4) (4,1)

11. The graph below illustrates the number of acres used for farming in Smalltown, New York, over several years.

Using a line of best fit, approximately how many acres will be used for farming in the 5th year?

• (1) 0
• (2) 200
• (3) 300
• (4) 400

12. When 16x3 12x2 4x is divided by 4x, the quotient is

• (1) 12x2 – 8x
• (2) 12x2 – 8x + 1
• (3) 4x2 – 3x
• (4) 4x2 – 3x + 1
Answer: (4) 4x2 – 3x + 1

13. The width of a rectangle is 4 less than half the length. If ℓ represents the length, which equation could be used to find the width, w?

14. Which data can be classified as quantitative?

• (1) favorite stores at which you shop
• (2) U.S. Representatives and their home states
• (3) sales tax rate in each New York county
• (4) opinion of a freshman on the color of Paul’s shirt
Answer: (3) sales tax rate in each New York county

15. Two cubes with sides numbered 1 through 6 were rolled 20 times. Their sums are recorded in the table below.

What is the empirical probability of rolling a sum of 9?

16. What is the vertex of the graph of the equation y =3x2 + 6x + 1?

• (1) (-1,-2)
• (2) (-1,10)
• (3) (1,-2)
• (4) (1,10)

17. The length and width of a rectangle are 48 inches and 40 inches. To the nearest inch, what is the length of its diagonal?

• (1) 27
• (2) 62
• (3) 88
• (4) 90

18. Which graph represents the solution set of 2x – 5 < 3?

19. Jonathan drove to the airport to pick up his friend. A rainstorm forced him to drive at an average speed of 45 mph, reaching the airport in 3 hours. He drove back home at an average speed of 55 mph. How long, to the nearest tenth of an hour, did the trip home take him?

• (1) 2.0 hours
• (2) 2.5 hours
• (3) 2.8 hours
• (4) 3.7 hours