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}

**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

**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

**4. What is the domain of f(x) = 2 _{x}?**

- (1) all integers
- (2) all real numbers
- (3) x ≥ 0
- (4) x ≤ 0

**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

**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?

**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

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

- (1) y
^{5} - (2) 2y
^{5} - (3) 10y
^{5} - (4) 32y
^{5}

**9. In the equation log _{x} 4 + log_{x} 9 = 2, x is equal to**

- (1) √13
- (2) 6
- (3) 6.5
- (4) 18

**10. Which expression represents the sum of ^{1}/_{√13} and ^{1}/_{√2}?**

**11. Which equation has imaginary roots?**

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

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

- (1) v
^{c}p - (2) (vp)
^{c} - (3) v
^{c}+ p - (4) cv + p

- (1) 24
- (2) 14
- (3) 6
- (4) 4

**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

**15. Expressed in simplest form, i^{16} + i^{6} – 2i^{5} + i^{13} is equivalent to**

- (1) 1
- (2) –1
- (3) i
- (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)

**17. If the sum of the roots of x ^{2} + 3x – 5 = 0 is added to the product of its roots, the result is**

- (1) 15
- (2) –15
- (3) –2
- (4) –8

- (1) 1
- (2) √3
- (3) 3
- (4)
^{1}/_{3}_{√3}

**19. The accompanying graph represents the figure I.**

Which graph represents after a transformation defined by r_{y = x}° R_{90°}?

**Mathematics 13 August 2002 Questions Answers Keys**

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