Q: Convert from degrees to radians: 330°
Answer:
Explanation:
My TI-84 Plus program ‘DEG2RAD’ will convert this for you.
Q: How many ways are there to go from point A to point B on the rectangular prism below, by traveling only along exactly 3 edges of the prism?
Answer: 6
Explanation: There are 3 ways to travel away from A, shown below in green. There are 2 ways to continue along each of these paths to B, shown in blue. That’s 3 x 2 = 6 paths to B along three edges of the prism. This is easier than making a mess of the diagram trying to draw all 6 paths (and making it hard to count them).
Q: When 5 people met for dinner, each person shook hands with each other person once. How many handshakes happened?
Answer: 10
Explanation 1: Two people = a handshake. This question is really ‘How many ways are there to choose 2 people from a total of 5, if the order is not important?’ It’s a combination question. Find the nCr function on your calculator. Type in 5 nCr 2. It’s 10. (There is a longer way to do it by hand, using the formula for nCr.)
Explanation 2: Person A shook hands with 4 people. That’s 4 handshakes so far. Person B shook hands with 3 other people (his shake with A has already been counted). Person C shook hands with 2 other people. Person D shook hands with 1 other person (E). Add: 4 + 3 + 2 + 1 = 10.
Q: Find the equation of the line that has the following intercepts:
x-intercept: 5, y-intercept: -3
Answer: y = 3/5 x – 3
Explanation: The x-intercept is the point (5, 0). The y-intercept is the point (0, -3). Calculate the slope of the line passing through these points:
m= (0- -3)/(5 – 0) = 3/5
Using slope intercept form (y = mx + b), the equation is y = 3/5 x + b. We just need to find b. Or do we? We could plug in an ordered pair and solve for b, but it’s not necessary. We already have b, because in slope-intercept form, b always stands for the y-intercept. So, b = -3.
The equation is: y = 3/5 x – 3
My TI-84 Plus program ‘LINES’ will find this equation for you, given the two intercepts.
Q: When the positive integer b is divided by 5, the remainder is 1. When b is divided by 7, the remainder is also 1. If b is less than 100, what is the largest possible value for b?
Answer: 71
Explanation: b is an integer that is one more than a multiple of both 5 and 7. The smallest such value is 35 +1 = 36. But, we need the largest one less than 100. The next common multiple of 5 and 7 is 70 (do 35 x 2), and the next one is 105 (35 x 3). Use 70, and add 1. 71.