Mathematics 19 June 2008 Questions Answer Keys

**The University of the State of New York**

REGENTS HIGH SCHOOL EXAMINATION

MATHEMATICS B

Thursday, June 19, 2008 — 1:15 to 4:15 p.m., only

Print Your Name: ______________________________________________________

Print Your School’s Name:_________________________________________________

- (1) 1
- (2) 0
- (3) 3
- (4) –3

- (1) 32
- (2) 48
- (3) 96
- (4) 192

**3. Kathy deposits $25 into an investment account with an annual rate of 5%, compounded annually. The amount in her account can be determined by the formula A = P(1 + R) ^{t}, where P is the amount deposited, R is the annual interest rate, and t is the number of years the money is invested. If she makes no other deposits or withdrawals, how much money will be in her account at the end of 15 years?**

- (1) $25.75
- (2) $43.75
- (3) $51.97
- (4) $393.97

**4. The accompanying graph shows the elevation of a certain region in New York State as a hiker travels along a trail.**

What is the domain of this function?

- (1) 1,000 ≤ x ≤ 1,500
- (2) 1,000 ≤ y ≤ 1,500
- (3) 0 ≤ x ≤ 12
- (4) 0 ≤ y ≤ 12

**5. Which relation is a function?**

- (1) x
^{2}+ y^{2}= 16 - (2) 2x
^{2}+ 6y^{2}= 1 - (3) y
^{2}= x^{2}+ 3x – 4 - (4) y = x
^{2}+ 3x – 4

**6. If f(x) = x ^{2} + 4 and g(x) x = √1 − x , what is the value of f(g(–3))?**

- (1) 2i√3
- (2) 2
- (3) 8
- (4) 13

**7. Which expression represents the sum of the sequence 3, 5, 7, 9, 11?**

**8. Which value of a does not satisfy the inequality |a| > 2a – 3?**

- (1) –1
- (2) 0
- (3) 3
- (4) –5

**9. If point (5,2) is rotated counterclockwise 90° about the origin, its image will be point**

- (1) (2,5)
- (2) (2,–5)
- (3) (–2,5)
- (4) (–5,–2)

**10. What is the sum of 5 – 3i and the conjugate of 3 + 2i?**

- (1) 2 + 5i
- (2) 2 – 5i
- (3) 8 + 5i
- (4) 8 – 5i

**12. The expression cos ^{2} 4θ + sin^{2} 4θ is equivalent to**

- (1) 1
- (2) 2
- (3) cos θ
- (4) cos 8θ

**13. The value of √ x ^{2} − 9 is a real and irrational number when x is equal to**

- (1) 5
- (2) 0
- (3) –3
- (4) 4

**14. If 2 ^{4x+1} = 8^{x+a}, which expression is equivalent to x?**

- (1) a – 1
- (2) 3a – 1
- (3)
^{a − 1}⁄_{15} - (4)
^{a − 1}⁄_{3}

**15. In 1995, the federal government paid off one-third of its debt. If the original amount of the debt was $4,920,000,000,000, which expression represents the amount that was not paid off?**

- (1) 1.64 × 10
^{4} - (2) 1.64 × 10
^{12} - (3) 3.28 × 10
^{8} - (4) 3.28 × 10
^{12}

**17. Al is standing 50 yards from a maple tree and 30 yards from an oak tree in the park. His position is shown in the accompanying diagram. If he is looking at the maple tree, he needs to turn his head 120° to look at the oak tree.**

How many yards apart are the two trees?

- (1) 58.3
- (2) 65.2
- (3) 70
- (4) 75

**18. A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet.**

What is the length of arc AC, in feet?

- (1) 63
- (2) 31
- (3) 20
- (4) 10

**19. The expression i ^{100} + i^{101} + i^{102} equals**

- (1) 1
- (2) –1
- (3) –i
- (4) i

**20. Which equation has roots whose sum is 3 and whose product is –4?**

- (1) x
+ 3x – 4 = 0^{2} - (2) x
– 3x – 4 = 0^{2} - (3) x
+ 4x – 3 = 0^{2} - (4) x
– 4x + 3 = 0^{2}

**Mathematics 19 June 2008 Questions Answers Keys**

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