广东深圳耀华实验学校高二国际班上学期期末考试数学

2019 年冬季期末考试 高二国际 SAT2 数学试卷 高二国际 SAT2 数学试卷 Page 1 of 3 Section One: Multiple Choice 1. Which function is shown in the graph? A) f(x) = 2(2.3)x 2 B) f(x) = 4(2.3)x C) f(x) = 4(2.3)x + 2 D) f(x) = 5(2.3)x 3 2. Gasoline costs $1.99 per gallon. If the price per gallon increases an average of 6% per month, which function models the exponential growth of the pricing? A) f(x) = 1.06(1.99)x B) f(x) = 1.99(1.06)x C) f(x) = 1.06(1.99)x D) f(x) = 1.99 1.06x 3. Which function represents exponential growth? A) u(t) = 7.0 2 3 t B) u(t) = 7.0 3 2 t C) u(t) = 7.0(0.8)t D) u(t) = 7.0 10 9 t 4. What is the horizontal asymptote of the function y = 2(0.3)x 1 4? A) y = 4 B) y = 0.3 C) y = 2 D) y = 4 5. What is the simplified expression of 2 3 7 ? 14 x x e e A) 5 1 2 x e B) 8 1 2 x e C) D) 8 7 2 x e 6. What is the value of 2e3.2, rounded to the nearest thousandth? A) 77.967 B) 49.065 C) 0.082 D) 0.081 7. Which expression is equivalent to x? A) log x B) log 2x C) log 10 x D) log 100 x 8. What is an equivalent expression for 2 log4 3 + log4 2? A) 2 log4 6 B) log4 6 C) log4 12 D) log4 18 9. Which of the following is not equivalent to log5 8? A) ln8 ln5 B) 2 log5 4 C) 3 log5 2 D) log5 4 + log5 2 10. What is the inverse of the function y = 82x ? A) y = ln 2ln8 x B) y = 2ln ln8 x C) y = ln8 2ln x D) y = 2ln8 ln x 11. What is the solution to the equation log4 4x + 2 log4 x = 4? A) 1 B) 2 C) 3 D) 4 12. A pheasant farmer started her farm with 120 pheasants. An analysis of her records shows that her pheasant population has increased by 15% each year. The farmer wants to determine a model of pheasant population growth using an exponential function. According to her model, what will the pheasant population be in 10 years? A) 311 B) 485 C) 501 D) 1380 13. What is f(x) g(x) if f(x) = 5x3/2 and g(x) = (4x)3/2? A) x3/2 B) x3/2 C) 3x3/2 D) 3x3/2 E) (5 3 16) x3/2 14. Which expression is equal to g(f(x) if f(x) = x3 1 and g(x) = 6x2 ? A) 6x2(x3 1) B) (6x2)3 1 C) 6 216 1 x D) 6(x3 1)2 E) 32 6 (1)x 15. A store that sent you a coupon for 10% off any item has a sale for $5 off all jeans. The pair you want is $39.50. What do you pay if the 10% off must be applied after the $5 is taken off? A) $3.45 B) $19.75 C) $30.55 D) $30.72 E) $31.05 16. What is the inverse of y = 10 x 2? A) y = 11 102 x B) y = 5x C) y = 2 10 x D) y = 10(x + 2) E) y = 10(x 2) 17. What is the domain and range, respectively, of the function g(x) = 1 ? 3 x A) x 0, y 0 B) x 0, y 0 C) x 0, y 0 D) x 0, y 0 E) y 6, y 3 B) x 0.5, y 3 D) All real numbers, y 0.5 E) All real numbers, y 3 22. You deposit $500 in an account that pays 5% annual interest compounded continuously. What is the balance after 3 years? A) $578.81 B) $580.38 C) $580.74 D) $580.91 E) $580.92 23. What is the inverse of the function y = 2 ln(x 5)? A) y = ln2 x +5 B) x = ln2 y +5 C) y = 2e(x 5) D) y = e2x + 5 E) y = e0.5x + 5 24. The graph of which function is shown? A) y = log4 x B) y = log4 (x 1) + 2 C) y = log4(x + 1) + 2 D) y = log4(x 2) + 1 E) y = log4(x + 2) + 1 25. What is the solution of the equation 9x = 2 1 ? 27 x A) x = 6 5 B) x = 5 6 C) x = 1 3 D) x = 2 5 E) x = 6 26. What is (are) the solution(s) of the equation log4 4x + log4(x + 3) = 2? A)4, 1 B) 4 C) 4, 1 D) 1 E) 4 27. The graph of what exponential function passes through the points (1, 28) and (2, 112)? A) y = 4x7 B) y = 4 7x C) y = 7 4x D) y = 7x4 E) y = x11 28. A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear? A) 3/8 B) 3/7 C) 5/8 D) 3/4 E) 7/8 29. Matrix X has r rows and c columns, and matrix Y has c rows and d columns, where r, c, and d are different. Which of the following statements must be false? I. The product YX exists II. The product of XY exists and has r rows and d columns. III. The product XY exists and has c rows and c columns. A) I only B) II only C) III only D) I and II E) I and III 30. Which rule represents the nth term of the following sequence? 2 22 2,. 4 9 16 A) 2 2 n a n B) 2 2 n a n C) 2 21 n a n D) an = 2n2 E) an = 2n + 1 31. Which summation notation represents the following series? 1 + 3 + 7 + 15 + 31 A) 1 21 i i B) 5 1 21 i i C) 1 21 i i D) 5 1 21 i i E) 5 1 21 i i 32. Your schools auditorium has 20 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row, and so on. How many seats are there in all 20 rows? A) 380 B) 440 C) 780 D) 880 E) 1560 33. What is a rule for the nth term of the geometric sequence whose graph is shown? A) an = 1 1 4 2 n B) an = 1 1 4 2 n C) an = 1 1 (4) 2 n D) an = 1 1 ( 4) 2 n E) an = 1 1 2 2 n 34. You go to work for a company that pays $.01 the first day, $.02 the second day, $.04 the third day, and so on. If the daily wage keeps doubling, what will your total income be after working 15 days? A) $.15 B) $2.02 C) $32 D) $327.67 E) $32,767 2019 年冬季期末考试 高二国际 SAT2 数学试卷 高二国际 SAT2 数学试卷 Page 3 of 3 35. What is the sum of the infinite geometric series 1 1 2 3( )? 3 i t A) 9 B) 12 C) 18 D) 24 E) 50 36. Which fraction is equal to the repeating decimal 0.363636. . . ? A) 2 11 B) 4 11 C) 36 100 D) 37 101 E) 18 11 37. A pendulum is released to swing freely. On the first swing, the pendulum travels a distance of 14 inches. On each successive swing, the pendulum travels 96% of the distance of the previous swing. What is the total distance the pendulum swings? A) 14 inches B) 25 inches C) 100 inches D) 275 inches E) 350 inches 38. What are the first four terms (a1 to a4) of the sequence for which a0 = 1 and an = an 1 + 2n? A) 1, 3, 9, 27 B) 1, 1, 3, 5 C) 1, 1, 3, 7 D) 1, 1, 5, 11 E) 1, 5, 11, 19 39. What are the first three iterates x1, x2, and x3 of the function f(x) = 1 5 2 x for an initial value of x0 = 2? A) 17 ,4, 22 B) 2 ,4 ,6 C) 4 ,3 , 7 2 D) 6, 2, 4 E) 6, 2, 4 40. What is the probability that a prime number is less than 7, given that it is less than 13? A) 0.33 B) 0.4 C) 0.5 D) 0.6 E) 0.75 41. The ellipse 4x2 + 8y2 = 64 and the circle x2 + y2 = 9 intersect at points where the y coordinates are A) 2 B) 5 C) 6 D) 7 E) 10 42. If the probability that the Giants will win the NFC championship is p and if the probability that the Raiders will win the AFC championship is q, what is the probability that only one of these teams will win its respective championship? A) pq B) p+q-2pq C) | | D) 1-pq E) 2pq-p-q 43. A U.S. dollar equals 0.716 European euros, and a Japanese yen equals 0.00776 European euros. How many U.S. dollars equal a Japanese yen? A) 0.0056 B) 0.011 C) 0.71 D) 94.2 E) 179.98 44. A cylinder whose base radius is 3 is inscribed in a sphere of radius 5. What is the difference between the volume of the sphere and the volume of the cylinder? A) 88 B) 297 C) 354 D) 448 E) 1345 45. The pendulum on a clock swings through an angle of 1 radian, and the tip sweeps out an arc of 12 inches. How long is the pendulum? A) 3.8 inches B) 6 inches C) 7.6 inches D) 12 inches E) 35 inches 46. The graph of y = x4 + 11x3 + 9x2 97x + c is shown below with the window shown below it. Which of the following values could be c ? A) 2820 B) 80 C) 80 D) 250 E) 2820 47