# Mathematics 13 August 2002

Mathematics 13 August 2002 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Tuesday, August 13, 2002 — 8:30 to 11:30 a.m., only

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1. Which fraction represents the probability of obtaining exactly eight heads in ten tosses of a fair coin?

• (1) 45/1,024
• (2) 64/1,024
• (3) 90/1,024
• (4) 180/1,024
Answer: (1) 45/1,024

2. In a New York City high school, a survey revealed the mean amount of cola consumed each week was 12 bottles and the standard deviation was 2.8 bottles. Assuming the survey represents a normal distribution, how many bottles of cola per week will approximately 68.2% of the students drink?

• (1) 6.4 to 12
• (2) 6.4 to 17.6
• (3) 9.2 to 14.8
• (4) 12 to 20.4
Answer: (3) 9.2 to 14.8

3. What is the solution of the inequality |x + 3| ≤ 5?

• (1) –8 ≤ x ≤ 2
• (2) –2 ≤ x ≤ 8
• (3) x ≤ –8 or x ≥ 2
• (4) x ≤ –2 or x ≥ 8
Answer: (1) –8 ≤ x ≤ 2

4. What is the domain of f(x) = 2x?

• (1) all integers
• (2) all real numbers
• (3) x ≥ 0
• (4) x ≤ 0
Answer: (2) all real numbers

5. A function is defined by the equation y = 5x – 5. Which equation defines the inverse of this function?

• (1) y = 1/5x – 5
• (2) y = 5x + 5
• (3) x = 1/5y – 5
• ­(4) x = 5y – 5
Answer: (4) x = 5y – 5

6. An architect is designing a building to include an arch in the shape of a semi-ellipse (half an ellipse), such that the width of the arch is 20 feet and the height of the arch is 8 feet, as shown in the accompanying diagram. Which equation models this arch? Answer: (1)

7. To balance a seesaw, the distance, in feet, a person is from the fulcrum is inversely proportional to the person’s weight, in pounds. Bill, who weighs 150 pounds, is sitting 4 feet away from the fulcrum. If Dan weighs 120 pounds, how far from the fulcrum should he sit to balance the seesaw?

• (1) 4.5 ft
• (2) 3.5 ft
• (3) 3 ft
• (4) 5 ft
Answer: (4) 5 ft

8. What is the last term in the expansion of (x + 2y)5?

• (1) y5
• (2) 2y5
• (3) 10y5
• (4) 32y5
Answer: (4) 32y

9. In the equation logx 4 + logx 9 = 2, x is equal to

• (1) √13
• (2) 6
• (3) 6.5
• (4) 18
Answer: (2) 6

10. Which expression represents the sum of 1/√13 and 1/√2? Answer: (1)

11. Which equation has imaginary roots?

• (1) x2 – 1 = 0
• (2) x2 – 2 = 0
• (3) x2 + x + 1 = 0
• (4) x2 – x – 1 = 0
Answer: (3) x2 + x + 1 = 0

12. If log k = c log v + log p, k equal

• (1) vcp
• (2) (vp)c
• (3) vc + p
• (4) cv + p
Answer: (1) vcp • (1) 24
• (2) 14
• (3) 6
• (4) 4
Answer: (2) 14

14. In the accompanying diagram of Δ ABC, m∠A = 30, m∠C = 50, and AC = 13. What is the length of side to the nearest tenth?

• (1) 6.6
• (2) 10.1
• (3) 11.5
• (4) 12.0
Answer: (2) 10.1

15. Expressed in simplest form, i16 + i6 – 2i5 + i13 is equivalent to

• (1) 1
• (2) –1
• (3) i
• (4) –i
Answer: (4) –i

16. If point (a,b) lies on the graph y = f(x), the graph y = f–1(x) must contain point

• (1) (b,a)
• (2) (a,0)
• (3) (0,b)
• (4) (–a,–b)
Answer: (1) (b,a)

17. If the sum of the roots of x2 + 3x – 5 = 0 is added to the product of its roots, the result is

• (1) 15
• (2) –15
• (3) –2
• (4) –8
Answer: (4) –8 • (1) 1
• (2) √3
• (3) 3
• (4) 1/3√3
Answer: (3) 3

19. The accompanying graph represents the figure I. Which graph represents after a transformation defined by ry = x° R90°? Answer: (3) Answer: (2) x/

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