Mathematics 26 January 2010

Mathematics 26 January 2010 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Tuesday, January 26, 2010 — 9:15 a.m. to 12:15 p.m., only

1. If √x- 4 = 7, what is the value of x?

• (1) 11
• (2) 18
• (3) 45
• (4) 53

2. The coordinates of ABC are A(1,1), B(2,3), and C(3,1). If ΔA′B′C′ is the result of the transformation D2 º ry-axis , then A′B′C′ is

• (1) similar to ΔABC
• (2) congruent to ΔABC
• (3) a right triangle
• (4) an equilateral triangle

3. What is the value of

• (1) 10
• (2) 13
• (3) 30
• (4) 60

4. An equation of a parabola that has x = −2 as its axis of symmetry is

• (1) y = x2 − 4x + 1
• (2) y = x2 − 2x + 3
• (3) y = 2x2 + 8x − 3
• (4) y = 2x2 + 4x − 7
Answer: (3) y = 2x2 + 8x − 3

5. What is the solution set for the equation ⎟3 − 2x⎟ = 5?

• (1) {−1,4}
• (2) {1,−4}
• (3) {−1}
• (4) {4}

6. A central angle of  15 radians intercepts an arc whose degree measure is

• (1) 48
• (2) 72
• (3) 96
• (4) 15

7. If cos 2θ = 1, a value of θ is

• (1) 45°
• (2) 90°
• (3) 180°
• (4) 270°

8. If cos x = −0.7 and csc x > 0, the terminal side of angle x is located in Quadrant

• (1) I
• (2) II
• (3) III
• (4) IV

9. The graph of the equation xy = 12 is best described as

• (1) a circle
• (2) two lines
• (3) an ellipse
• (4) a hyperbola

10. The image of function f(x) is found by mapping each point on the function (x,y) to the point (y,x). This image is a reflection of f(x) in

• (1) the x-axis
• (2) the y-axis
• (3) the line whose equation is y = x
• (4) the line whose equation is y = −x
Answer: (3) the line whose equation is y = x

11. What is the inverse of the function y = 3x − 2?

12. Which equation represents the circle whose center is (3,−1) and whose radius is √6 ?

• (1) (x + 3)² + (y − 1)² = 36
• (2) (x − 3)² + (y + 1)² = 36
• (3) (x + 3)² + (y − 1)² = 6
• (4) (x − 3)² + (y + 1)² = 6
Answer: (4) (x − 3)² + (y + 1)² = 6

13. Which expression is equivalent to

14. If log x = 3 log a − log b, then x is equal to

15. Which expression is equivalent to b in the equation

16. In the binomial expansion of (x + y)8, what is the coefficient of the termcontaining x3y5?

• (1) 15
• (2) 28
• (3) 56
• (4) 70

17. If R is inversely proportional to A, and R = 4 when A = 100, what is the value of R when A = 250?

• (1) 0.625
• (2) 1.6
• (3) 10
• (4) 6,250

18. If m∠A = 35, b = 3, and a = 4, how many different triangles can be constructed?

• (1) No triangles can be constructed.
• (2) two triangles
• (3) one right triangle, only
• (4) one obtuse triangle, only
Answer: (4) one obtuse triangle, only

19. In a right triangle where one of the angles measures 30°, what is the ratio of the length of the side opposite the 30° angle to the length of the side opposite the 90° angle?

• (1) 1:√2
• (2) 1:2
• (3) 1:3
• (4) 1:√3

20. If zero is the value of the discriminant of the equation ax2 + bx + c = 0, which graph best represents y = ax2 + bx + c?