MATH 1201 Array Final Exam.

MATH 1201 FINAL EXAM Question 1 The graph of y = 4sin (3x + 2) + 1 has amplitude of: a. 0 b. 1 c. 2 d. 3 e. 4 Question 2 What is the exact value of sin (22.5 degrees)? a. .383 b. sqrt (2) c. sqrt (2 – sqrt(2)) / 2 d. sqrt ((2 + sqrt (2)) / 4) e. Impossible Question 3 Solve for x: (1/2)x = 16 a. -4 b. -2 c. 2 d. 4 e. None of these Question 4 If an ant is 50 feet away from a tree growing straight up, and the ant has to look up at an angle of 70 degrees to see the top of the tree, how tall is the tree? Select the closest answer. a. 20 feet b. 50 feet c. 100 feet d. 140 feet e. 1,000 feet Question 5 If f(x) = 3x +2 and g(x) = x -4, (f/g)(4) is: a. Undefined b. 0 c. 14 d. (3, 2, 4) e. None of these Question 6 What is the vertex of f(x) = x2 + 3x + 2? a. 7 b. (0, 2) c. (-3/2, -1/4) lOMoARcPSD|6749068 d. -3/2 e. None of these Question 7 Solve the system: 2x + 3y = 7, 3x - 5y = 1 a. (2, 1) b. (1, 2) c. (0, 0) d. There is no solution e. None of these Question 8 If I invest $10,000 at 5% compounded monthly, how much will I have in 8 years? Choose the closest answer. a. $5,000 b. $10,000 c. $15,000 d. $20,000 e. $25, 000 Question 9 How much must be invested today at 8%, compounded continuously, to be worth $100,000 in 12 years? Pick the closest answer. a. $250,000 b. $100 c. $40,000 d. $4,000 e. No amount will be enough Question 10 What, approximately, is log2 32? Choose the closest answer. a. 1 b. 2 c. 3 d. 5 e. None of these Question 11 What is the equation of a line through (-1, 4) and (-2, 7)? a. y = 3x + 1 b. y = -3x + 1 c. y = -3x + 7 d. y = 3x + 7 e. None of these Question 12 What is the exact value of sin (120 degrees)? a. 1⁄2 b. .866lOMoARcPSD|6749068 c. √3/2 d. -1/2 e. None of these Question 13 What is the polar representation of z = 6i? a. 6cis i b. 6 cis π c. π cis 6 d. 6cis (π/2) e. 36 Question 14 What the equation of the line passing through (-1, 4) and parallel to y = 2x + 1? a. y = 2x + 6 b. y = 2x + 1 c. y = 2x d. No such line exists e. None of these Question 15 The half-life of carbon 14 is 5,730 years. How old is a bone that has 70% of its original carbon 14? a. 500 years b. 1,000 years c. 4,000 years d. 3,000 years e. None of these Question 16 On a circle of radius 4 find the x and y coordinates at angle 180 degrees (or π in radian measure). a. (0, 4) b. (4, 0) c. (4, 4) d. (-4, 0) e. (2, 2) Question 17 What are the possible rational roots of f(x) = x4 -7x + 8? a. {8} b. {+-1, +-2, +-7, +-8} c. {+-1, +-2,+-8} d. {+-1, +-8} e. {+-1, +-2, +-4, +-8} Question 18 What is the period of y = 3cos (8x + π/2) + 5? a. 2π b. π c. π/2 lOMoARcPSD|6749068 d. π/3 e. π/4 Question 19 What is 2cis(–π/3) in rectangular coordinates? a. (–1, –sqrt 3) b. (1, –sqrt 3) c. (1, sqrt 3) d. (–1, sqrt 3) e. Impossible Question 20 Solve the system: x + y + z = 6, 2x – y + z = 3, x + y – z = 0 a. (0, 0, 6) b. (3, 2, 1) c. 1 d. (1, 2, 3) e. None of these Question 21 What is the period of y = 3cos ( 4x + π/2) + 5? a. π/4 b. π/2 c. π d. 2π e. –π Question 22 What is the polar representation of z = –4i? a. –4cis (–π/4) b. –4cis (π/4) c. 4cis (–π/2) d. 4cis (π) e. None of these Question 23 What is the equation of the line passing through (1, –4) and parallel to y = –x + 1? a. –x + y + 3 = 0 b. x – y + 3 = 0 c. x + y – 3 = 0 d. x + y + 3 = 0 e. None of these Question 24 What is the exact value of sin (15 degrees)? a. .380 b. sqrt (2 – sqrt(3)) / 2 c. sqrt (2 + sqrt (3)) / 2 d. .350 lOMoARcPSD|6749068 e. Impossible Question 25 If an ant is 100 feet away from a tree growing straight up, and the ant has to look up at an angle of 68 degrees to see the top of the tree, how tall is the tree? Select the closest answer. a. 200 feet b. 140 feet c. 80 feet d. 20 feet e. 10 feet Question 25.1 If f(x) = 3x + 2 and g(x) = x – 4, (g/f)(1) is: a. Undefined b. –3/5 c. –5/3 d. 3/5 e. 5/3 Question 26 What is the vertex of f(x) = x 2 + 4x + 2? a. (2, 2) b. (–2, –2) c. (–π2, 2) d. (2, –2) e. None of these Question 27 What is (2, - π/6) in rectangular coordinates? a. 0 b. (sqrt 3, 1) c. (sqrt 3, -1) d. –1 / (sqrt (2) + sqrt (6)) e. Impossible Question 28 How much must be invested today at 10 %, compounded continuously, to be worth $165,000 in 5 years? Pick the closest answer. [Use e = 2.71] a. $150,000 b. $130,000 c. $110,000 d. $100,000 e. No amount will be enough Question 29 What are the possible rational roots of f(x) = 3x 4 – x 3 + x 2 – x + 5? a. {±1, ±5} b. {±1/3, ±5/3} c. {±1, ±1/3, ±5, ±5/3} lOMoARcPSD|6749068 d. {1, 1/5, 3, 3/5} e. {1, 1/3, 5, 5/3} Question 30 The graph of y = –2 sin (x – 2) + 1 has amplitude of: a. 0 b. 1 c. 2 d. 3 e. 4 Question 31 The half-life of carbon 14 is 5,730 years. Approximately, how old is a bone that has 70% of its original carbon 14? a. 7,500 years b. 7,000 years c. 6,500 years d. 6,000 years e. Less than 6,000 years