# Integrated Algebra 22 January 2013

Integrated Algebra 22 January 2013 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Integrated Algebra
Tuesday, January 22, 2013 — 9:15 a.m. to 12:15 p.m., only

Student Name: ______________________________________________________

School Name: _______________________________________________________

1. The number of hours spent on math homework during one week and the math exam grades for eleven students in Ms. Smith’s algebra class are plotted below.

Based on the plotted data, what is the correlation between the time spent on homework and the exam grade?

• (1) positive
• (2) negative
• (3) no correlation
• (4) cannot be determined

2. A car uses one gallon of gasoline for every 20 miles it travels. If a gallon of gasoline costs \$3.98, how much will the gas cost, to the nearest dollar, to travel 180 miles?

• (1) 9
• (2) 36
• (3) 45
• (4) 80

3. If Angelina’s weekly allowance is d dollars, which expression represents her allowance, in dollars, for x weeks?

• (1) dx
• (2) 7dx
• (3) x + 7d
• (4) d/x

4. What is the solution of the system of equations shown in the graph below?

• (1) (1,0) and (–3,0)
• (2) (0,–3) and (0,–1)
• (3) (–1,–2)
• (4) (–2,–1)

5. The solution of the equation 5 – 2x = 4x – 7 is

• (1) 1
• (2) 2
• (3) –2
• (4) –6

6. The expression 100n2 – 1 is equivalent to

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

7. In right triangle ABC shown below, what is the value of cos A?

• (1) 12/20
• (2) 16/20
• (3) 20/12
• (4) 20/16

8. A bag contains five green gumdrops and six red gumdrops. If Kim pulls a green gumdrop out of the bag and eats it, what is the probability that the next gumdrop she pulls out will be red?

• (1) 5/11
• (2) 5/10
• (3) 6/11
• (4) 6/10

9. Which graph represents a function?

10. The current population of a town is 10,000. If the population, P, increases by 20% each year, which equation could be used to find the population after t years?

• (1) P = 10,000(0.2)t
• (2) P = 10,000(0.8)t
• (3) P = 10,000(1.2)t
• (4) P = 10,000(1.8)t
Answer: (3) P = 10,000(1.2)

11. Which verbal expression is represented by 2(x + 4)?

• (1) twice the sum of a number and four
• (2) the sum of two times a number and four
• (3) two times the difference of a number and four
• (4) twice the product of a number and four
Answer: (1) twice the sum of a number and four

12. How many cubes with 5-inch sides will completely fill a cube that is 10 inches on a side?

• (1) 50
• (2) 25
• (3) 8
• (4) 4

13. A school newspaper will survey students about the quality of the school’s lunch program. Which method will create the least biased results?

• (1) Twenty-five vegetarians are randomly surveyed.
• (2) Twenty-five students are randomly chosen from each grade level.
• (3) Students who dislike the school’s lunch program are chosen to complete the survey.
• (4) A booth is set up in the cafeteria for the students to voluntarily complete the survey.
Answer: (2) Twenty-five students are randomly chosen from each grade level.

14. The vertex of the parabola y = x2 + 8x + 10 lies in Quadrant

• (1) I
• (2) II
• (3) III
• (4) IV

15. In the figure below, ABCD is a square and semicircle O has a radius of 6.

What is the area of the figure?

• (1) 36 + 6π
• (2) 36 + 18π
• (3) 144 + 18π
• (4) 144 + 36π
Answer: (3) 144 + 18π

16. What is 24x2y6 – 16x6y2 + 4xy2 divided by 4xy2?

• (1) 6xy4 – 4x5
• (2) 6xy4 – 4x5 + 1
• (3) 6x2y3 – 4x6y
• (4) 6x2y3 – 4x6y + 1
Answer: (2) 6xy4 – 4x5 + 1

17. Which expression can be used to change 75 kilometers per hour to meters per minute?

• (1) 75 km/1 hr × 1 km/1,000 hr × 1 hr/60 min
• (2) 75 km/1 hr × 1 km/1,000 hr × 60 min/1 hr
• (3) 75 km/1 hr × 1,000 m/1 km × 1 hr/60 min
• (4) 75 km/1 hr × 1,000 m/1 km × 60 min/1 hr
Answer: (3) 75 km/1 hr × 1,000 m/1 km × 1 hr/60 min

18. The inequality 2 ≤ x ≤ 3 can be written as

• (1) (–2, 3)
• (2) [–2, 3)
• (3) (–2, 3]
• (4) [–2, 3]
Answer: (4) [–2, 3]
• (1) 2 × 104
• (2) 2 × 1010
• (3) 2 × 10–4
• (4) 2 × 10–10
Answer: (3) 2 × 10–4

20. The roots of the equation x2 – 14x + 48 = 0 are

• (1) –6 and –8
• (2) –6 and 8
• (3) 6 and –8
• (4) 6 and 8
Answer: (4) 6 and 8

Integrated Algebra 22 January 2013 Questions Answers Keys

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