Q1.) The probability Ben will guess an answer on a test correctly is 60%. What’s the probability he guesses the correct answer to problem number one OR problem number 2? (Assume guessing both correctly is acceptable).
Q2.) A weighted coin has a 3/5 probability of landing heads. What is the probability of flipping the same result three flips in a row?
Q3.) Simplify completely:
Q4.) Find the sum:
5𝑥+3
10𝑥 2 −8𝑥
(𝑥+1)(𝑥+5)
4𝑥
+
2 𝑥+1
(Hint: Find a common denominator!!)
3
Q5.) Simplify: √27𝑎 3 𝑏 6 𝑐 15
Q6.) A point is 25 units from the center of a circle with a radius of 7 units. How long is the tangent segment from the point to the circle?
Q7.) What is the surface area of a sphere with a 6 cm radius?
Q8.) What is the volume of a sphere with a 6 cm radius?
Q9.) If 4y = 5x, what is the ratio of x to y?
Q10.) The dimensions of a rectangle are increased by 40% and then decreased by 20%. The new area is what percent greater than the original area?
Draw each angle in standard position:
1.) 50⁰ 2.) 330⁰ 3.) 270⁰ 4.) -135⁰ 5.)
5𝜋
4
6.)
2𝜋
3
7.) 700⁰
Give the angle between 0 and 360⁰ (or 0 and 2𝜋 if given in radians) co-terminal to the given angle:
9.) 540⁰ 10.) -100⁰ 11.) 1050⁰ 12.) -850⁰ 13.)
12𝜋
5
8.)
13𝜋
14.)
6
13𝜋
4
Convert each degree measure to radians and each radian measure to degrees.
15.) 60⁰ 16.) 240⁰ 17.) 315⁰ 18.) 𝜋
2
19.)
3𝜋
4
22.) 225⁰ 23.)
2𝜋
9
24.)
17𝜋
6
25.) 570⁰ 26.)
5𝜋
3
20.)
2𝜋
12
21.) 660⁰
27.) 9 radians (NOT 9 𝜋 radians!)
Give a positive AND negative angle co-terminal to each angle. Keep degree measures in degrees and radians in radians.
28.) 40⁰ 29.) 225⁰ 30.) 𝜋
4
31.)
11𝜋
6
32.) Calculate the area of a sector of a circle with an angle measuring
7𝜋
6
radians if the radius is 9 cm.
33.) What is the length of an arc of a circle with a radius of 8 ft if it intercepts a central angle measuring
7𝜋
4
radians?
34.) Angular velocity is defined by the equation 𝜔 = 𝜃 𝑡
, where 𝜃 is usually expressed in radians and t represents time.
Find the angular velocity in radians per second of a point on a bicycle tire if it completes two revolutions in 3 seconds.
35.) A trucker drives 55 miles per hour. His truck’s tires have a diameter of 26 inches. What is the angular velocity of the wheels in revolutions per second? (Be careful – unit conversions are required!)
36.) A tire with a 9 inch radius is rotating at 30 mph. Find the angular velocity of a point on the outside of the tire.
37.) How many rotations per minute does the tire make?