[PDF] SAT Mathematics Level 2 Practice Test 14.pdf | Plain Text

# 21 1 1. Which of the following could not be domain of фߚ− ߇? (A) 2 (B) 3 (C) 4 (D) ࡮ (E) ߇஼ 2. There are $0.25, $0.1, and $1 coins. If the number of each coin is the same, how many coins are needed to make total of $27? (A) Ϲϸ (B) 20 (C) 25 (D) 30 (E) 40 3. W hich of the following equations represents the graph ? (A) ߛ ි ʇߚʇ− Ϲ (B) ߛ ි ʇߚ+ Ϲʇ (C) ߛ ි ʇߚ− Ϲʇ (D) ʇߛʇි ߚ− Ϲ (E) ʇߛʇි ʇߚʇ+ Ϲ 4. Which of the following could be the condition that log x (x – 2) is defined? (A) x > 0 and x ≠ 1 (B) x = 1 (C) x > 0 (D) x < 2 (E) x > 2

# 21 2 5. If Ͻ౱௄஻ි ߍ, then x is (A) ߎߑ߉ ிߍ− Ϲ (B) Ϲ− ౥౨ౠ ி ౥౨ౠ౤ (C) ஻ ౥౨ౠ ி− ߎߑ߉ߍ (D) Ϲ− ߎߑ߉ ிߍ (E) ߎߑ߉ ౤Ͻ 6. What is the range of csc x? (A) (−с ɧϹ] ɧ[Ϲɧс ) (B) [−ϹɧϹ] (C) (−Ϲɧс ) (D) (с ɧ−с ) (E) (−с ɧϹ) 7. In the following matrix system, if x = –1, then y = ? [Ϻ ϸ Ϲ ϻ] + [ϸ ϻ Ϻ ߚ] = ෪Ϻ ϻ ϻ ߛ෮ (A) 0 (B) 2 (C) 5 (D) 7 (E) 8 8. If (x – 1)2 + (y + 1 )2 = 0, what is the value of x + y? (A) –2 (B) –1 (C) 0 (D) 1 (E) 2

# 21 3 9. Above is the graph of y = f(x) . Which of the following could be the graph of y = –f(x –k)? (k is positive real value) (A) (B) (C) (D) (E)

# 21 4 10. In a plane, what is the set that is formed by a fixed point and points with constant distance? (A) Two parallel lines (B) Circle with constant radius (C) Parallel line (D) Many lines (E) A circle with a radius 1 11. If f(x) = 5 – 2x and f(g(x)) = 1, then what is g(x) = ? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 12. The 7 th term of Ϲɧ஻ ஽ɧ஻ ௃ɧ஻ ஼ு ɧɫ is (A) ஻ ஽ (B) ஻ ூ஻ (C) ϻ௅஽ (D) (஻ ஽) ீ (E) (஻ ஽) ு 13. If f(x) = 3 x2 and g(x) = 3( x – 2)2, which of the following is true ? (A) Range of f(x) and g(x) are different (B) f(x) and g(x) has common one solution (C) If f(x ) shifted left 2 units on the x-axis, it is same as g(x) (D) Domain of f(x) and g(x) is {ߚ ʇ ߚ > ϸ} (E) x value of the vertex of both f(x) and g(x) are identical

# 21 5 14. Parabola y = x 2 + 2x + 10 has no real solution because (A) its y-intercept is a positive number (B) its vertex is above the x-axis and the graph is concave upward (C) the graph is concave downward (D) its vertex is above the x-axis (E) its maximum value is a positive number 15 . ߅ߑߕࡦ + ċėě (࡮+ ࡦ)+ ěđĖ (−ࡦ)+ ċėě (஽ಝ ஼ + ࡦ) = (A) ߅ߑߕࡦ (B) 0 (C) ߕߋߐࡦ (D) Ϻ߅ߑߕࡦ (E) −Ϻ߅ߑߕࡦ 1 ʇ 23 2 ʇ 33 3 ʇ 45 2 ʇ 3 means 23 16. In the stem plot above, what is the median? (A) ϹϺ (B) 13 (C) 23 (D) 34 (E) 35 17. The vertical asymptote does not exist in the expression ஽౱௅౤ ౱௄ி. What is the value of k? (A) ʈϹϽ (B) ʈϽ (C) ʈϻ (D) ϻ (E) 5

# 21 6 18. If k is a positive integer, kt > 0 and 8k + 2 t = 27, what is the sum of all possible of t? (A) 0 (B) 11 (C) 14 (D) 16.5 (E) None of these 19. The function f has the property th at f(–s) = f(s) for all numbers s. Which of the following is true for the graph of y = f(x) in the xy -plane ? (A) A vertical line (B) A line with slope 1 (C) A circle with center (0, 0) (D) A semicircle with center (0, 0) (E) A parabola symmetric about the y-axis 20. There is a pair of black, white, green, and blue socks in the box. If a sock is randomly picked, at least how many socks should be picked in order to pick a pair with the same color ? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 21. If the volume of the cube is ߃஽, what is the surface area of the cube? (A) ߃஼ (B) ϼ߃஼ (C) Ͼ߃஼ (D) ϹϺ ߃஼ (E) ϹЀ ߃஼

# 21 7 22. It was reported that 50% of the students of a certain high school lived within 5 miles of its school and 30% of those lived in an apartment. If a student of this school is selected at random, what is the probability that he lives in an apartment within 5 miles of the school? (A) 0.15 (B) 0.2 (C) 0.25 (D) 0.3 (E) 0.35 23. A math teacher assumes that the number of students in Calculus class is between 15 and 19. If x is the number of students, which of the following represents all possible values of x? (A) |x – 17| < 2 (B) |x + 17| < 2 (C) |x – 17| > 2 (D) |x + 17| > 2 (E) |x – 17| = 2 24. If f(x) = 2 x – 3, g(x) = –x + 3, and h(x) = 3 x – 2, then what is f(x) ? (A) 2g(x) – h(x) + 1 (B) g(x) – 2h(x) + 2 (C) g(x) + h(x) (D) g(x) + h(x) – 2 (E) g(x) + h(x) – 4 25. If the 10 th term of an arithmetic sequence is 50, and the 28 th term is 140, what is the first term of the sequence? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7

# 21 8 26. If f(x) = kx and f(f(x)) = 4 x, then what is the value of k? (A) None of these (B) –2 (C) 0 (D) 2 (E) ±2 27. At a party every parti cipant shook hands with each other only once. Thirty -six hand shak es were exchanged at this party. How many people were at this party ? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 28. If ౱ ౲௄౱ි Ϻ is true, then what is the value of ౲ ౱௅౲? (A) – 1 (B) – ஼ ஽ (C) ஼ ஽ (D) − ஻ ஽ (E) 1

# 21 9 29. In the complex plane above, if z = 1 – i what is the point that shows –iz +3. (A) A (B) B (C) C (D) D (E) E 30. The standard deviation for four numbers, a, b, c, d is 0.1. If each number is increased by 2, which of the following is true? (A) Standard deviation will be increased by 2 (B) Standard deviation will be decreased by 2 (C) Standard deviation will be 0.1 (D) We don’t have enough information. (E) Standard deviation will be just a little bit bigger than 0.1 31. If M is the midpoint of the line segment BC of хީުޫ , which is consisted of 3 points A(0, 3), B(2, 1), and C(4, 2), then what is the coordinate of the point that divides line segment AM by 2:1? (A) (1, 2) (B) (2, 2) (C) (3, 1) (D) (3, 2) (E) (4, 1)

# 21 10 32. If f(x) – f(y) = f(౱ ౲), then f(x) = (A) ϻ౱ (B) ߚ஼ (C) lnx (D) ஻ ౱ (E) фߚ 33. Solve ஻ ౬ౢ౧ ಴ಕ− Ϲ= (A) ߅ߑߖ ஼ࡦ (B) ߕ߇߅ ஼ࡦ (C) ߕߋߐ ஼ࡦ (D) ʈ߅ߕ߅ ஼ࡦ (E) −ߖ߃ߐ ஼ࡦ 34. Mason has a newspaper route for which he collects t dollars each day. From this amount he pays out ౭ ி dollars per day for the cost of the papers, and he saves the rest of the money. In terms of t, how many days will it take Mason to save $1,200. (A) ஻ɧி஺஺ ౭ (B) ౭ ஻ɧி஺஺ (C) ౭ ஻ɧ஺஺஺ (D) ஻ɧ஺஺஺ ౭ (E) 1,500 t

# 21 11 35. In the figure below, what is the area of хީުޫ ? (A) 4.02 (B) 4.89 (C) 5.46 (D) 5.97 (E) 7.21 36. The area of the base of a pyramid is Ϻ× Ϻ and the altitude is фϻ. What is the dihedral angle between base and lateral side of this pyramid? (A) 15º (B) 30º (C) 45º (D) 60º (E) 90º 37. A wire is 11 feet long. How many ways can the wire be cut into more than one piece so that the length of each piece is a prime number? (A) Ϻ (B) 3 (C) 4 (D) 5 (E) 6

# 21 12 38. When of the following satisfies “If ߃ > ߄ɧ߈(߃)< ߈(߄)?” (A) ߛ ි ߚ஽+ Ϻ (B) y = ln x (C) ߛ ි ߇౱ (D) ߛ ි −ߚி+ Ϲ (E) ߛ ි −ߚ஼+ ߚ 39. What does (1, ಝ ீ) equal to? (A) (1, ಝ ஽) (B) (1, ு ீ࡮) (C) (–1, − ி ீ࡮) (D) (–1, ஻஽ ீ࡮) (E) (–1, − ஻஻ ீ࡮) 40. What is the period of ʇϺěđĖ (࡮ߚ )ċėě (࡮ߚ )ʇ? (A) ϸ (B) ஻ ஼ (C) Ϲ (D) ஽ ஼ (E) 2

# 21 13 41. A dog’s lifetime is represented as g(x) and a human’s life as f(x). If x represents the year, the following equation is true. g(x) = 8 x f(x) = –0.015 x4 + 0.31 x3 – 0.017 x2 + 5 x + 13 Which of the following is true? I. If a dog is 4 years old, a human is 15 -17 years old. II. If a dog is older than 10, a human is older than 18. III. If a human is 20 years old, a dog is 3 years old. (A) None (B) I only (C) II only (D) I and II (E) II and III 42. In the figure above in the sector form OST, length of the minor arc ޻޼๨ is ஼ ஽࡮. What is the length of the chord ޻޼ ? (A) 2.07 (B) 3.68 (C) 4.26 (D) 5.17 (E) 6.27

# 21 14 43. What is true statement about the two spheres whose equations is ߚ஼+ ߛ஼+ ߜ஼ි Ϲ and ߚ஼+ ߛ஼+ ߜ஼ි Ё (A) Two spheres meet (B) Two spheres are externally tangent (C) Two spheres meet and two points are formed (D) The two spheres meet and a circle is formed (E) The two spheres do not meet 44. If f(x) = ߇஼౱+ Ϻ, then ߈௅஻(߇)? (A) 0.165 (B) –0.165 (C) –0.235 (D) 0.561 (E) –0.561 45. An autobike begins on a level road directly towa rd a building that is 150 feet t all. How far does the car travel during the time that the angle of elevation from the autobike to the top of the building changes from 27º to 36º ? (A) 43ft (B) 55ft (C) 71ft (D) 88ft (E) 97ft 46. The price of a house in 1990 was $111,250 and the value increased at same rate annually. If the price was doubled by year 2010, what is the percentage of the value increased annually? (A) 2.7% (B) 3.5% (C) 3.9% (D) 4.2% (E) 4.9%

# 21 15 47. In the figure below, what is the area of the trapezoid? (A) 30 (B) 60 (C) 100 (D) 120 (E) 240 48. For ߚ஼+ ߄ߚ + ߅ි ϸ, b and c are real numbers. If a root of a function is 1 + i, which of the following is the value of b? (A) –2 (B) 0 (C) 2 (D) 4 (E) None of the above 49. As the figure, triangle PQR is inscribed inside the circle. If ٧P = 105º and ٧R = 45º, what is the radius of this circle? (A) 1 (B) фϺ (C) фϻ (D) 2 (E) фϽ

# 21 16 50. When a tennis ball is thrown into the lake, it sinks into the water, and then rises back to the surface. If the depth of the surface of the lake is 0 and the depth the tennis ball sinks in to the lake for t seconds is d(t) , when the equation is d(t) = 2 t2 – 7t + 6, how long would t take for the tennis ball to float back to the surface of the lake? (A) 0.5 (B) 1.5 (C) 2 (D) 2.5 (E) 3

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