MATH - MATHEMATICS LEVEL 2 TEST REFERENCE INFORMATION THE...

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Unformatted text preview: MATHEMATICS LEVEL 2 TEST REFERENCE INFORMATION THE FOLLOWING INFORMATION IS FOR YOUR REFERENCE IN ANSWERING SOME OF THE QUESTTIONS IN THIS TEST. Volume of a right circular cone with radius r and height h: V= 12 πr h 3 Lateral Area of a right circular cone with circumference of the base c and slant height l: S= 1 cl 2 Volume of a sphere with radius r: V= 42 πr 3 Surface Area of a sphere with radius r: S= 4π r 2 Volume of a pyramid with base area B and height h: V= 1 Bh 3 DO NOT DETACH FROM BOOK. studysatonline.net Level 2 Test 2 1. If 2 − 2x = 6− 6 2x , then 1- 1 2x = 1 (A) − 3 (B) 1 (C) 0 (D) 2 2 5 (E) 3 ⎛1 1⎞ + ⎟= ⎝ y z⎠ 2. x ⎜ (A) (B) (C) (D) (E) x yz x y−z 2x y−z xy + xz yz 1 xy − xz Unauthorized copying or reuse of any part of this page is illegal. 2 studysatonline.net Level 2 Test 3. Figure 1 shows one cycle of the graph of the 1 function y = sin 2 x for 0 ≤ x ≤ 2π . If the minimum 2 value of the function occurs at point P, then the coordinates of P are ⎛ 3π π ⎞ ,− ⎟ 2⎠ ⎝4 (A) ⎜ ⎛ 3π 1 ⎞ ,− ⎟ 2⎠ ⎝4 Figure 1 (B) ⎜ ⎛ 3π ⎞ , −π ⎟ 2 ⎝ ⎠ (C) ⎜ ⎛ 3π ⎞ , −1 ⎟ ⎝2 ⎠ (D) ⎜ (E) (π , 0 ) 4. If P and Q are different points in a plane, the set of all points (x, y) the sum of whose distances from those two points P and Q is constant is (A) The region of two plane on one side of line (B) The exterior of a square (C) The region of the plane bounded by a parabola (D) A circle (E) An ellipse Unauthorized copying or reuse of any part of this page is illegal. 3 studysatonline.net Level 2 Test 5. If 4 x =5.2, then x = (A) 0.52 (B) 1.95 (C) 3.97 (D) 6.76 (E) 12.46 6. In Figure 2, r cos θ = (A) − x (B) − y (C) r Figure 2 (D) x − y (E) r + x 7. If f ( x ) = x − 2 x and g ( x) = 2 x2 + 1 x2 − 3 , then g ( f (6)) = (A) 0.2 (B) 1.19 (C) 1.25 (D) 3.63 (E) 4.15 Unauthorized copying or reuse of any part of this page is illegal. 4 studysatonline.net Level 2 Test 8. If a, b, and c are nonzero real numbers and if a 9b 7 c 4 = (A) a −3 , then c = 2 1 (B) 9b3c 2 1 8 4 (C) 4a (D) (E) 2 9 6 a b4 3 3 a b2 9. In the triangle in Figure 3, if OA = AB , what is the slope of segment AB ? (A) 2 (B) 2 2 (C) − 2 Figure 3 2 (D) − 2 (E) It cannot be determined from the information given. 10. Where defined, sec(5θ )icos(5θ ) = (A) 1 (B) 0 (C) –1 (D) 2 csc(4θ ) (E) 2 sec(4θ ) Unauthorized copying or reuse of any part of this page is illegal. 5 studysatonline.net Level 2 Test 11. The graph of y = f ( x) is shown in Figure 4. Which of the following could be the graph of y = f ( x) ? (A) (B) Figure 4 (C) (D) (E) Unauthorized copying or reuse of any part of this page is illegal. 6 studysatonline.net Level 2 Test 12. If 5 and –3 are both zeros of the polynomial P ( x ) , then a factor of P ( x ) is (A) x 2 − 15 (B) x 2 + 2 x − 15 (C) x 2 + 15 (D) x 2 − 2 x − 15 (E) x 2 + 2 x + 15 13. A surveyor is standing 100 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5 . How tall is the tree? (A) 138.15 (B) 197.52 (C) 298.87 (D) 300.14 (E) 312.38 14. If f ( x) = 5 x − 2 and f ( g (2)) = 13 , which of the following could be g ( x)? (A) 7 x − 11 (B) 11x + 7 (C) 11x − 7 (D) 11x + 7 (E) 7 x + 11 Unauthorized copying or reuse of any part of this page is illegal. 7 studysatonline.net Level 2 Test 15. Figure 5 shows a cube with edge of length 5 centimeters. If points A and C are midpoints of the edges of the cube, What is the perimeter of region ABCD? (A) 6.71 cm (B) 13.42 cm (C) 22.36 cm (D) 31.25 cm (A) 45.00 cm 16. An equation of line Figure 5 in Figure 6 is (A) y = x + 2 (B) y = 2x (C) y = 2x – 2 (D) y = 2x + 2 (E) y = x – 2 Figure 6 17. The mean score of 11 students in a certain geometry class was 69. When a new student enrolled, the mean increased to 71. What was the score of the new student? (A) 91 (B) 92 (C) 93 (D) 101 (E) 110 Unauthorized copying or reuse of any part of this page is illegal. 8 studysatonline.net Level 2 Test 18. If 0 < x < 2π and sin x = 0.866 , what is the value of ⎛ x⎞ cot ⎜ ⎟ ? ⎝2⎠ (A) 1.732 (B) –1.732 (C) –0.577 (D) 1 (E) -1 19. Recently 3,164 students at Woodson High School and 2,464 students at Fairfax High School took a math exam. A total of 4,221 students passed. If the same percentage of the students in each school passed, how many of the students at Woodson passed? (A) 3164 (B) 2373 (C) 5628 (D) 31643 (E) 24641 20. If f : ( x, y ) → ( x − 3 y, y ) for every pair ( x, y ) in the plane, for what points ( x, y ) is it true that ( x, y ) → ( x, y ) ? (A) The set of points ( x, y ) such that y = 0 (B) The set of points ( x, y ) such that x = 1 (C) The set of points ( x, y ) such that x = 0 (D) (1, −1) only (E) (0,0) only Unauthorized copying or reuse of any part of this page is illegal. 9 studysatonline.net Level 2 Test 21. What number must be added to each of the three numbers –1, 1, and 5 so that the resulting three numbers form a geometric sequence? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 2 22. If f ( x) = ax − bx − c for all real numbers x and if f (0) = 1 and f (1) = 1 , then a – b = (A) –1 (B) 0 (C) 1 (D) 2 (E) 3 23. If θ is the degree of the largest angle of a triangle that has sides of 10, 8, and 8, then what is sin θ ? (A) 0.78 (B) 0.84 (C) 0.98 (D) 1 (E) 1.05 Unauthorized copying or reuse of any part of this page is illegal. 10 studysatonline.net Level 2 Test 24. What is the domain of f ( x) = − x + 16 5 2 (A) x > 0 (B) x > 4 (C) −4 ≤ x ≤ 4 (D) x < 14 (E) All real numbers 25. If sin x = cot x , which of the following is a possible radian value of x ? (A) –1.00 (B) –0.71 (C) 0.71 (D) 0.81 (E) 0.91 26. Figure 7 shows a portion of the graph of y = 5 . What is the sum of the areas of the three inscribed rectangles shown? x (A) 4682 (B) 3,380 (C) 2,912 (D) 1302 (E) 625 Figure 7 Unauthorized copying or reuse of any part of this page is illegal. 11 studysatonline.net Level 2 Test −0.116 t 27. Suppose Q(t ) = cie is the equation for the amount that exists at any time t after a certain radioactive element decays, where c equals the initial amount and t is the elapsed time in years. How long will it take for the element decays to a level of 30% of the original amount? (A) 1 (B) 5 (C) 10 (D) 20 (E) 25 28. Which of the following lines are asymptotes of the graph of f ( x) = x2 − x ? x +1 I. x = − 1 II. y = x − 2 III. y = −2 (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III 29. If f ( x − 2) = x + 3 for all real numbers x, then f ( x) = (A) x − 1 (B) x + 1 (C) x + 5 (D) x − 5 (E) 2 x − 1 Unauthorized copying or reuse of any part of this page is illegal. 12 studysatonline.net Level 2 Test 30. Which of the following can be the coordinates of the center of a circle tangent to the x-axis and y-axis in the third quadrant? (A) (-2, 0) (B) (2, 0) (C) (0, 2) (D) (-2, -2) (E) (2, -2) 31. What is the range of the function defined by ⎧2 x , x > 3 ⎪ h( x ) = ⎨ 1 ? ⎪x5 , x ≤ 3 ⎩ 1 (A) y > 35 (B) y ≥ 3 1 (C) 3 5 < y < 3 (D) y ≤ 3 1 (E) y > 8 and y ≤ 35 2 32. If 5 x − 6 y + 3 = 0 and 3 y − 2 x = 0 for x ≥ 0 , then 8 x = (A) 12.06 (B) 13.19 (C) 13.54 (D) 14.72 (E) 14.91 Unauthorized copying or reuse of any part of this page is illegal. 13 studysatonline.net Level 2 Test −1 33. If f ( x) = ln x for x > 0 , then f ( x) = (A) e x (B) x 2 (C) x e (D) e x (E) ln x 34. If x1 = 1 and xn +1 =3 5 + xn , then x3 = (A) 1.68 (B) 1.72 (C) 1.89 (D) 2.13 (E) 2.65 35. Figure 8 shows a triangle inscribed in a semicircle. What is the area of the triangle in terms of θ ? (A) tan(2θ ) (B) 2π (C) 2 sin θ cos θ (D) 4 cos θ Figure 8 (E) 4 sin(2θ ) Unauthorized copying or reuse of any part of this page is illegal. 14 studysatonline.net Level 2 Test 36. A random number generator on a machine selects five integers from 1 to 20. What is the probability that all five numbers are less than or equal to 10? (A) 0.03125 (B) 0.0613 (C) 0.125 (D) 0.167 (E) 0.24 37. If the magnitudes of vectors u and v are 7 and 15, respectively, then the magnitude of vector (u − v) could NOT be (A) 7 (B) 8 (C) 11 (D) 14 (E) 18 a b 38. If (8.02) = (4.12) , what is the value of a ? b (A) –0.34 (B) 0.34 (C) 0.48 (D) 0.68 (E) 1.3 Unauthorized copying or reuse of any part of this page is illegal. 15 studysatonline.net Level 2 Test 39. If arcsin(sin θ ) = − π 2 ≤θ ≤ π 2 , then θ= 3 π (B) − 2 (C) 0 (E) 3 and − π (A) − (D) π π 3 π 2 40. The 4th term of an arithmetic sequence is 20, and the 13th term is 65. What is the 15th term? (A) 50 (B) 75 (C) 100 (D) 125 (E) 150 41. Which of the following is the equation of the line perpendicular to y = 3 x + 4 that passes through the 5 point (3, -13)? (A) y = − 5 x + 12 3 (B) y = − 5 x −8 3 (C) y = − 3 x+8 5 (D) y = 3 4 x − 14 5 5 (E) y = 3 4 x + 14 5 5 Unauthorized copying or reuse of any part of this page is illegal. 16 studysatonline.net Level 2 Test 42. For all θ , sin( −2θ ) + cos(θ ) + cos(−θ ) = (A) 0 (B) 1 (C) 2 sin θ + 2 cos θ (D) 2 cos θ (1 − sin θ ) (E) 2(sin θ − cos θ ) ⎡( n + 1)!⎤ ⎣ ⎦= 43. 2 ⎡( n − 1)!⎤ ⎣ ⎦ 2 (A) n (B) n+1 (C) n(n+1) 2 (D) n (n + 1) (E) [n(n + 1)] 2 44. The radius of the base of a right circular cone is 10 and the radius of a parallel cross section is 6. If the distance between the base and the cross section is 12, what is the height of the cone? (A) 10 (B) 12 (C) 18 (D) 24 (E) 30 Unauthorized copying or reuse of any part of this page is illegal. 17 studysatonline.net Level 2 Test 45. For the given statement, “If x = __ , then a rational number” can be true when x is x is not (A) 0 (B) 1 (C) 2 (D) 4 (E) 9 46. If f ( x) = −( x + 1) horizontally shifts 3 units left and vertically 2 units up and the resulting graph is g ( x) , 2 then what is g (−2) ? (A) -3 (B) –2 (C) –1 (D) 0 (E) 1 47. In how many distinguishable ways can you write the letters in INTERNET? (A) 5,040 (B) 7,620 (C) 10,080 (D) 20,160 (E) 40,320 Unauthorized copying or reuse of any part of this page is illegal. 18 studysatonline.net Level 2 Test 48. Which of the following sets have an element of 0 in that set? I. II. III. The set of positive rational numbers The set of positive even integers The set of natural numbers (A) None (B) I only (C) II only (D) III only (E) I, II, and III 49. What is the length of the major axis of the ellipse 2 2 whose equation is 90( x − 1) + 60( y + 3) = 1500 ? (A) 4 (B) 5 (C) 6 (D) 8 (E) 10 50. Under which of the following conditions is ab positive? a −b (A) 0 > b > a (B) a > 0 > b (C) a > b > 0 (D) b > a > 0 (E) None of the above Unauthorized copying or reuse of any part of this page is illegal. 19 ...
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