Math
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49 terms
Terms | Definitions |
|---|---|
 a number is divisible by 3 if | the sum of its digits is divisible by 3 |
| a number is divisible by 4 if | its last two digits compose a two-digit number that is itself divisible by 4 |
| a number is divisible by 9 if | the sum of its digits is divisible by 9 |
| a number is divisible by 11 if | the difference between the sum of its odd-placed digits and the sum of its even-placed digits is divisible by 11 |
| average value = | sum of values / number of values |
| sum of values = | average value X number of values |
| John travels x miles in a hours and y miles in b hours. What is is his average speed? | (x + y) miles / (a + b) hours |
| How to handle complex rate problems | make a table row labels = rate, time, and distance column labels = a to b, b to c, and entire trip CANNOT add rate rate X time = distance |
| combined work total time formula for 2 people/machines | total time = AB / A + B |
| Bob can paint a room in 3 hours, and George can paint the same room in 2 hours. How many hours does it take Bob and George to paint the room if they work together but independently? | (3 X 2) / ( 3+ 2) |
| combined total work formula for more than 2 people/machines | 1/total time = 1/A + 1/B + 1/C + ... + 1/N |
| How many minutes is 1/5 of an hour? | 12 minutes |
| formula for overlapping sets | total = group 1 + group 2 - both + neither |
| overlapping sets approach if there is no one in the neither group | venn diagram |
| overlapping sets approach for complicated problems | draw a chart row labels = in group 1, not in group 1, and total column labels = in group 2, not in group 2, and total |
| if selection is unordered, then it's a | combinations problem |
| if the selection is ordered, it is a | permutations question |
| the combinations formula is used when | solving for the number of k unordered selections one can make from a group of n items nCk = n! / k!(n-k)! |
| A company is selecting 4 members of its board of directions to sit on a committee. If the board has 9 members, any of whom may serve, how many different selection of members could be made? | 9C4 = 9! / 4!(9-4)! |
| County X holds an annual math competitions, where each county high school sends a team of 4 students. If School A has 6 boys and 7 girls whose math grades qualify them to be on their school's team, and competition rules stipulate that the team must consists of 2 boys and 2 girls, how many different teams might school A send to the competition? | 6C2 and 7C2 (6! / 2!4!) X (7! / 2!5!) |
| number of permutations of n items | n! |
| How many ways are there to rearrange the letters in the word ASCENT? | 6! |
| in combinations, permutations, and probability, AND translates to ________. OR translates to ________. | and = multiply or = add |
| How many ways are there to rearrange the letters in the word ASSETS? | 6! / 3! |
| How many ways are there to rearrange the letters in the word REASSESS? | 8! / 4!2! |
| If a fair coin is flipped 3 times, what is the probability of getting at least one tail? | subtract the probability of the undesired outcomes from the total 1 - 1/2 x 1/2 x 1/2 |
| If a fair coin is flipped 5 times, what is the probability of getting exactly 3 heads? | solve for the probability of one possible desired outcome, then multiply by all the permutations of that outcome HHHTT = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32 HHHTT = 5! / 3!2! = 10 1/32 x 10 |
| probability = | # of desired outcomes / total number of possible outcomes |
| 3:?:? | 3:4:5 |
| 5:?:? | 5:12:13 |
| 7:?:? | 7:24:25 |
| 8:?:? | 8:15:17 |
| 9:?:? | 9:40:41 |
| ?:SQRT3:? | 1:SQRT3:2 |
| bisecting an equilateral triangle creates __________. | two 30-60-90 triangles |
| how to find the longest side of a triangle | longest side is across from largest angle |
| circumference of circle | pi d or 2 pi r |
| arc length where angle opens up at center | (n/360) x circumference |
| arc length where angle opens up at edge of circle | (n/180) x circumference |
| area of circle | pi r^2 |
| area of sector | (n/360) x area of circle |
| volume of a rectangular solid | lwh |
| SA of rectangular solid | 2lw x 2lh x 2wh |
| rectangular solids diagonal | diagonal^2 = l^2 + w^2 + h^2 |
| volume of cube | e^3 |
| SA of cube | 6e^2 |
| volume of cylinder | pi r^2 h |
| lateral SA of cylinder | 2 pi r h |
| total SA of cylinder | 2 pi r^2 2 pi r h |
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