Math 1201 Final Exam (question and answers with verified answers GRADE A+)

The graph of y = 4sin (3x + 2) + 1 has amplitude of: a. 0 b. 1 c. 2 d. 3 e. 4 - e. 4 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 - c. sqrt (2 - sqrt(2)) / 2 Solve for x: (1/2)x = 16 a. -4 b. -2 c. 2 d. 4 e. None of these - a. -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 - d. 140 feet 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 - a. Undefined What is the vertex of f(x) = x2 + 3x + 2? a. 7 b. (0, 2) c. (-3/2, -1/4) d. -3/2 e. None of these - c. (-3/2, -1/4) 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 - a. (2, 1) 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 - c. $15,000 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 - c. $40,000 What, approximately, is log2 32? Choose the closest answer. a. 1 b. 2 c. 3 d. 5 e. None of these - d. 5 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 - b. y = -3x + 1 What is the exact value of sin (120 degrees)? a. 1⁄2 b. .866 c. √3/2 d. -1/2 e. None of these - c. √3/2 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 - d. 6cis (π/2) 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 - a. y = 2x + 6 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 - d. 3,000 years 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) - d. (-4, 0) 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} - e. {+-1, +-2, +-4, +-8} What is the period of y = 3cos (8x + π/2) + 5? a. 2π b. π c. π/2 d. π/3 e. π/4 - e. π/4 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 - b. (1, -sqrt 3) 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 - d. (1, 2, 3) What is the period of y = 3cos ( 4x + π/2) + 5? a. π/4 b. π/2 c. π d. 2π e. -π - b. π/2 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 - c. 4cis (-π/2) 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 - d. x + y + 3 = 0 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 e. Impossible - b. sqrt (2 - sqrt(3)) / 2 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 - a. 200 feet 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 - b. -3/5 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 - b. (-2, -2) What is the vertex of f(x) = x + 3x + 2? Select one: a. 7 b. (0, 2) c. (-3/2, -1/4) d. -3/2 e. None of these - c. (-3/2, -1/4) 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 - c. (sqrt 3, -1) 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 - d. $100,000