# Mathematics 13 August 2003

Mathematics 13 August 2003 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Wednesday, August 13, 2003 — 8:30 to 11:30 a.m., only

1. Which graph does not represent a function of x?

2. What is the value of x in the equation √5 – 2x = 3i?

• (1) 1
• (2) 7
• (3) –2
• (4) 4

3. Which graph represents the solution set of |2x – 1| < 7?

4. The strength of a medication over time is represented by the equation y = 200(1.5)–x, where x represents the number of hours since the medication was taken and y represents the number of micrograms per millimeter left in the blood. Which graph best represents this relationship?

• (1) –1
• (2)1 ⁄3 + xy
• (3) –(3 + xy)
• (4) 3 + xy

6. Which graph represents data used in a linear regression that produces a correlation coefficient closest to –1?

8. Which transformation is not an isometry?

• (1) rotation
• (2) line reflection
• (3) dilation
• (4) translation

9. A dog has a 20-foot leash attached to the corner where a garage and a fence meet, as shown in the accompanying diagram. When the dog pulls the leash tight and walks from the fence to the garage, the arc the leash makes is 55.8 feet.

What is the measure of angle θ between the garage and the fence, in radians?

• (1) 0.36
• (2) 2.79
• (3) 3.14
• (4) 160

Triangle EGC can be proved congruent to triangle FGA by

• (1) HL ≅ HL
• (2) AAA ≅ AAA
• (3) AAS ≅ AAS
• (4) SSA ≅ SSA

11. An architect commissions a contractor to produce a triangular window. The architect describes the window as ΔABC, where m∠A = 50, BC = 10 inches, and AB = 12 inches. How many distinct triangles can the contractor construct using these dimensions?

• (1) 1
• (2) 2
• (3) more than 2
• (4) 0

12. The accompanying graph shows the relationship between a person’s weight and the distance that the person must sit from the center of a seesaw to make it balanced.

Which equation best represents this graph?

• (1) y = 12x2
• (2) y = –120x
• (3) y = 2 log x
• (4) y = 120x

13. If f and g are two functions defined by f(x) = 3x + 5 and g(x) = x2 + 1, then g(f(x)) is

• (1) x2 + 3x + 6
• (2) 9x2 + 30x + 26
• (3) 3x2 + 8
• (4) 9x2 + 26
Answer: (2) 9x2 + 30x + 26

14. What is the product of 5 + √-36 and 1 – √-49 , expressed in simplest a + bi form?

• (1) –37 + 41i
• (2) 5 – 71i
• (3) 47 + 41i
• (4) 47 – 29i
• (1) csc θ
• (2) sec θ
• (3) cot θ
• (4) sin θ

17. The amount of ketchup dispensed from a machine at Hamburger Palace is normally distributed with a mean of 0.9 ounce and a standard deviation of 0.1 ounce. If the machine is used 500 times, approximately how many times will it be expected to dispense 1 or more ounces of ketchup?

• (1) 5
• (2) 16
• (3) 80
• (4) 100

18. A commercial artist plans to include an ellipse in a design and wants the length of the horizontal axis to equal 10 and the length of the vertical axis to equal 6. Which equation could represent this ellipse?

• (1) 9x2 + 25y2 = 225
• (2) 9x2 – 25y2 = 225
• (3) x2 + y2 = 100
• (4) 3y = 20x2
Answer: (1) 9x2 + 25y2 = 225

20. In the equation ax2 + 6x – 9 = 0, imaginary roots will be generated if

• (1) –1 < a < 1
• (2) a < 1, only
• (3) a > –1, only
• (4) a < –1