Algebra 1 Final Exam

Question 1 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. Select one: a. 200 feet b. 140 feet c. 80 feet d. 20 feet e. 10 feet Question 2 How much must be invested today at 10%, compounded continuously, to be worth $271,000 in 10 years? Pick the closest answer. [Use e = 2.71] Select one: a. $250,000 b. $100,000 c. $10,000 d. $1,000 e. No amount will be enough Question 3 If f(x) = 3x +2 and g(x) = x -4, (f/g)(4) is: Select one: a. Undened b. 0 c. 14 d. (3, 2, 4) e. None of these Question 4 The half-life of carbon 14 is 5,730 years. its original carbon 14? Select one: a. 7,500 years b. 7,000 years c. 6,500 years d. 6,000 years e. Less than 6,000 years Approximately , how old is a bone that has 70% of Question 5 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 Question 6 4 3 2 What are the possible rational roots of f(x) = 3x – x + x – x + 5? Select one: a. {±1, ±5} b. {±1/3, ±5/3} c. {±1, ±1/3, ±5, ±5/3} d. {1, 1/5, 3, 3/5} e. {1, 1/3, 5, 5/3} Question 7 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. Select one: a. 20 feet b. 50 feet c. 1,400 feet d. 140 feet e. 1,000 feet Question 8 On a circle of radius 2, center (0, 0), nd the x and y coordinates at angle 270 degrees (or π in radian measure). Select one: a. (2, –2) b. (2, 0) c. (0, –2) d. (0, 2) e. (2, 2) Question 9 On a circle of radius 4 nd the x and y coordinates at angle 180 degrees (or π in radian measure). Select one: a. (0, 4) b. (4, 0) c. (4, 4) d. (-4, 0) e. (2, 2) Question 10 What is the exact value of sin (22.5 degrees)? Select one: a. .383 b. sqrt (2) c. sqrt (2 – sqrt(2)) / 2 d. sqrt ((2 + sqrt (2)) / 4) e. Impossible Question 11 What is (2, - π/6) in rectangular coordinates? Select one: a. 0 b. (sqrt 3, 1) c. (sqrt 3, -1) d. – 1 / (sqrt (2) + sqrt (6)) e. Impossible Question 12 What is the period of y = 3cos (8x + π/2) + 5? Select one: a. 2π b. π c. π/2 d. π/3 e. π/4 Question 13 If I invest $10,000 at 5% compounded monthly, how much will I have in 8 years? Choose the closest answer. Select one: a. $5,000 b. $10,000 c. $15,000 d. $20,000 e. $25, 000 Question 14 What is the equation of the line passing through (1, –4) and parallel to y = –x + 1? Select one: 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 15 What is the polar representation of z = – 4i? Select one: a. –4cis (–π/4) b. –4cis (π/4) c. 4cis (–π/2) d. 4cis (π) e. None of these Question 16 x Solve for x: (1/3) = 81 Select one: a. 4 b. –2 c. 3 d. –4 e. None of these Question 17 If f(x) = 3x + 2 and g(x) = x – 4, (g/f)(1) is: Select one: a. Undened b. –3/5 c. –5/3 d. 3/5 e. 5/3 Question 18 What is the equation of the line passing through (-1, 4) and parallel to y = 2x + 1? Select one: a. y = 2x + 6 b. y = 2x + 1 c. y = 2x d. No such line exists e. None of these Question 19 What is the polar representation of z = 6i? Select one: a. 6 cis i b. 6 cis π c. π cis 6 d. 6 cis (π/2) e. 36 Question 20 What is the equation of a line through (-1, 4) and (-2, 7)? Select one: a. y = 3x + 1 b. y = -3x + 1 c. y = -3x + 7 d. y = 3x + 7 e. None of these