Algebra Regents 1

1. The expression $x^2 - 16y^2$ is equivalent to

(a) (x-4y)(x-4y)

(b) (x-4y)(x+4y)

(d)(x-8y)(x+8y)

Question 1 of 30

2. The legs of an isosceles right triangle each measures 8 centimeters. What is the length of the hypotenuse, to the nearest tenth of a centimeter?

(a) 7.3

(b) 9.1

(d) 11.3

Question 2 of 30

3. In the diagram below, the spinner is divided into 8 equal sections.
Which outcome is most likely to occur on a single spin?

(a) a prime number

(b) a perfect square

(d) a number that is a factor of 4

Question 3 of 30

4. What is 3 $\sqrt{45}$ expressed in simplest radical form?

(a) 3 $\sqrt{5}$

(b) 6 $\sqrt{5}$

(d) 27 $\sqrt{5}$

Question 4 of 30

5. A survey is being conducted to determine is dairy products such as milk and cheese should be taxed in Richmond County. Which group, when randomly surveyed, would be likely to produce the most bias?

(a) 30 drivers at a Richmond County gas station

(b) 50 dairy farmers from Richmond County

(d) 100 parents from the Richmond County High School

Question 5 of 30

6. How many different ways can you arrange the letters in the word QUICK?

(a) 5

(b) 25

(d) 120

Question 6 of 30

7. What is the slope of the line that passes through the points (-1,2) and (5,4)

(a) $\frac{1}{3}$

(b) 3

(d) -3

Question 7 of 30

8. Which set of ordered pairs represents a function?

(a) {(4,0), (5,1), (5,0)}

(b) {(0,4), (1,4), (1,5)}

(d) {(2,1), (6,2), (6,5)}

Question 8 of 30

9. A cyclist biked 27.3 miles from 6:15am to 9:00am. He then biked an additional 16.7 miles from 9:00am to 11:15pm. What was his average speed for the entire trip, in miles per hour?

19.2

8.7

8.8

22.0

Question 9 of 30

10. Which verbal expression can be represented by 3(x-7)?

(a) 7 less than 3 times x

(b) 3 multiplied by x less than 7

(d) the product of x and 3, decreased by 7

Question 10 of 30

11. Which equation represents a line parallel to the x-axis?

(a) y=x

(b) y=2

(d) x=-3

Question 11 of 30

12. Given: A = {1, 3, 5, 7}
B = {1, 2, 4, 5, 7, 8, 9}

What is the intersection of sets A and B?

(a) {1, 5, 7}

(b) {2, 4, 8, 9}

(d) {1, 2, 3, 4, 5, 6, 7, 8, 9}

Question 12 of 30

13. The value of a home purchased for $420,000 increases in value at the rate of 6% per year. What will be the value of the home in 4 years?

(a) $445,200

(b) $471,912

(d) $530,240

Question 13 of 30

14. Mary is 4 years younger than her sister and 3 years older than her brother. The sum of their ages is 37. What is Mary's age?

(a) 9

(b) 10

(d) 15

Question 14 of 30

15. What is the product of $(4 x 10^5), (1.3 x 10^2), and (5 x 10^{-3})$

expressed in scientific notation?

(a) 26 x $10^4$

(b) 2.6 x $10^5$

(d) 2.6 x $10^6$

Question 15 of 30

16. When 3x + 5y - 12 is subtracted from 3x - 2y - 8, the difference is

(a) -7y + 4

(b) -3y + 4

(d) -3y - 16

Question 16 of 30

17. A study showed that a decrease in temperature led to a decrease in crime rates. Which statement best describes the relationship?

(a) positive correlation and a causal relationship

(b) negative correlation and a causal relationship

(d) negative correlation and not a causal relationship

Question 17 of 30

18. In the right triangle ABC shown below, AB = 11.3 and BC = 9.5. Find the measure of $\angle$ A, to the nearest tenth of a degree.

(a) $32.8^{\circ}$

(b) $40.1^{\circ}$

(d) $57.2^{\circ}$

Question 18 of 30

19. Which notation describes {0, 1, 2}?

(a) {x | 0

(b) {x | 0 $\le$ x $\le$ 3, where x is an integer}

(d) {x | 0 $\le$ x<3, where x is an integer}

Question 19 of 30

20. The amount of money earned varies directly with the number of hours spent working. If Katie earns $300 working 40 hours, how much money does she earn working 50 hours?

(a) $325

(b) $350

(d) $400

Question 20 of 30

21. What is the solution of the system of equations x - 2y = 9 and x + 3y = 16?

(a) (1, 5)

(b) (5, 1)

(d) (-5, -1)

Question 21 of 30

22. What is the value of the expression -2 $x^2$ y + 5x - y when x = 3 and y = -2?

(a) - 19

(b) 49

(d) 89

Question 22 of 30

23. The data in the table below are graphed, and the slope is examined.

The rate of change represented in this table can be described as?

(a) negative

(b) positive

(d) undefined

Question 23 of 30

24. Which is an example of a quadratic function?

(a) 4x = 3 - y

(b) y = 2x + 2 $\sqrt{3}$

(d) $3^x$ + 1 = y

Question 24 of 30

25. What are the roots of the equation $3x^2$ - 27x = 0?

(a) 0 and -3

(b) 0 and 3

(d) 0 and 9

Question 25 of 30

26. Which set of data can be classified as qualitative?

(a) weights of athletes at a local gym

(b) ages of volunteers at a fundraiser

(d) blood types of donors at a blood drive

Question 26 of 30

27. Ms. Johnson is replacing the poster on the school's bulletin board. She calculated the area of the bulletin board to be 25.72 square feet. The actual area of the bulletin board is 28.03 square feet. What is the relative error in calculating the area of the bulletin board, to the nearest thousandth?

(a) 0.082

(b) 0.083

(d) 0.090

Question 27 of 30

28. Which expression represents $9x^2 - 16$ factored completely?

(a) (3x + 4)(3x - 4)

(b) (3x - 4)(3x - 4)

(d) (3x - 8)(3x - 8)

Question 28 of 30

29. A right triangle contains a $27^{\circ}$ angle whose opposite side measures 4.3 centimeters. What is the length of the hypotenuse, to the nearest hundredth of a centimeter?

(a) 4.19

(b) 9.47

(d) 8.44

Question 29 of 30

30. Tom is putting up a fence around his garden. The garden is in the shape of a semicircle and a square shown in the diagram below.

Which expression represents the length if fencing, in feet, that Tom will need?

(a) 36 + 6 $\pi$

(b) 36 + 12 $\pi$

(d) 144 + 36 $\pi$

Question 30 of 30