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Math Tips
| Question | Answer |
|---|---|
| One foot to miles | Divide by 5280 |
| How many kilometers are in one mile? | 1.6 km |
| Celsius to farenheit formula | F = 9/5C + 32 |
| How many ounces are in a pound? | 16 ounces |
| How many pounds are in one kilogram? | 2.2 pounds |
| How to convert inches to yards? | Divide by 36 |
| How to convert feet to yards? | Divide by 3 |
| How many meters in a kilometer? | 1000 |
| How many centimeters in an inch? | 2.54 |
| How many cups in one pint? | 2 |
| How many pints in a quart? | 2 |
| How many quarts in a gallon? | 4 |
| 1 cm^3 = | 1 mL |
| 0! = | 1 |
| How many unique ways can the word DENTIST be arranged? | There are 7 total letters and the T repeats twice. So you would do 7!/2! |
| How many different ways can 5 people stand in a line? | 5! (5 * 4 * 3 * 2 * 1) |
| How many 5-digit even numbers can you make from arranging the following set of numbers without repeating any digits? {1, 3, 4, 5, 7} | First, we know that an even number will end with an even digit, so this means that 4 must be the fifth digit of the number. As a result, there are only 4 possible digits for the first digit, 3 for the second, etc. 4 * 3 * 2 * 1 |
| To perform a dog trick, three dogs must jump through a hoop, one after another. If there are five dogs, how many unique ways are there to perform this trick, assuming each dog can only jump once? | As can be seen, to select the first dog to jump through the hoop, there are 5 possible dogs to choose from. To select the second dog to jump through the hoop, there are 4 possible dogs to choose from. 5 * 4 * 3 = 60 |
| To perform a dog trick, a hoop needs to be jumped through three times. If there are five dogs, how many unique ways are there to perform this trick, assuming that each dog can jump through the hoop multiple times? | 5 * 5 * 5 = 125 |
| In how many unique ways can the letters in the word LETTERS be arranged? | 7! / (2! * 2!) |
| In how many unique ways can the letters in the word INSTITUTE be arranged? | 9! / (2! * 3!) |
| There are 3 dental assistants and 2 dentists at a local clinic. In how many ways can the employees stand in a line, if the dental assistants always stand in front of the line? | The first thing we need to do is to find the ways in which 3 dental assistants stand in front of the line. For the first person, 3 individuals can be chosen. For the second person, only 2 can be chosen, For the last, only 1 can be chosen. 3! * 2 |
| A family of 6, with 2 parents and 4 children, is lining up to enter a movie theater. In how many ways can the family stand in a line if the 4 children always stand together, and the 2 parents always stand together? | 4! * 2 * 2, parents can stand together at either the start or the front of the line |
| How many 4-digit odd numbers can you make from arranging the following set of numbers without repeating any digits? {2, 4, 5, 7} | Pretend our 4-digit odd number ends in a 5 (so it is odd). This means that there are 3 possible numbers for the first number, 2 for the second, etc. Let's pretend that our 4-digit odd number ends in a 7 (so it is odd). 3! + 3! |
| If Betty has 3 hats, 3 shirts, 2 pairs of trousers, and 2 pairs of shoes to choose from, how many complete outfits consisting of a hat, a shirt, a pair of trousers, and a pair of shoes can she put together? | 3 (hats) × 3 (shirts) × 2 (trousers) × 2 (shoes) = 36 complete outfits |
| Each license plate in Abu Dhabi consists of five characters made of either letters or digits. Letters always come before digits on the license plates. Which is more licenses with three letters + two digits or three digits + two letters? | There are more options with letters (26), so the one with more letters |
| fundamental counting principle | this principle tells us that if there are n ways to do one thing, and m ways to do another, the number of ways to do both things is calculated by n × m. |
| In a mini-softball league, the coach is arranging the batting order for the team. If the team has 5 players, but the coach does not want the team captain to be any of the first three to bat, how many batting orders are possible? | 4 × 3 × 2 × 2 × 1 = 48 ways the players can bat |
| To solve this permutations/combinations problem, we use the combination formula: | n! / (n-r)!r! Permutations are used for lists, 1st/2nd place, 4-digit PINs, or arranging people in a line). Combinations are used for groups or subsets (e.g., choosing 3 toppings on a pizza, picking 5 lottery numbers, or selecting a team of 4 people). |
| Five friends are sitting next to each other at the movie theater. Two of them split popcorn and must sit next to each other. How many possible seating arrangements are there? | 3 ˣ 2 ˣ 1 = 6 outcomes 2 ˣ 1 = 2 outcomes 6 ˣ 2 = 12 outcomes |
| When they're asking for how many ways and the order matters, use: | n! / (n-r)! |
| What to do when you have 4 coins flipped and they're asking for the probability of getting 3 heads and 1 tail? | List out the possible outcomes, like HHHT, HHTH, HTHH, THHH. 4 coins gives you 2 * 2 * 2 * 2 = 16 posibilities. 4/16 = 1/4. |
| How many of each color is in a deck of cards? | The deck is split evenly into two colors: 26 red cards and 26 black cards. |
| How many suits are there in a deck of cards? | There are 4 suits in total with 13 cards per suit 13 hearts, 13 diamonds, 13 spades, and 13 clubs |
| What are the ranks in a deck of cards? | 4 aces, 4 of each number card (2 to 10), 4 jacks, 4 queens, 4 kings |
| How many face cards and how many number cards are there? | 12 face cards and 12 number cards |
| There are 4 white marbles, 6 red marbles, and 2 blue marbles in a bag. What is the probability that you pick a white marble and a blue marble, with replacement? | In this case, because an order is not specified, you would have to find the possibility of a white then a blue + blue then white. |
| In a bowl, there are 5 red marbles, 4 blue marbles, 3 yellow marbles, and 3 green marbles. If 2 marbles are randomly picked, with replacement, what is the probability of not picking two red marbles? | Find the possibility of picking a red marble. Multiply both possibilities, subtract them from 1. |
| Probability Formula for Probability of Event Not Happening | P(event not happening) = 1 - P(event happening) |
| Non Mutually Exclusive | P(A or B) = P(A) + P(B) P(A and B) |
| Mutually Exclusive | P(A or B) = P(A) + P(B) |
| In a village, 32% of families own a cow, 47% own a pig, and 14% own both. What percentage of the village owns only a cow or a pig, but not both? | Do cow percentage - both, then pig - both. Add up the numbers |
| Mutually Exclusive | P(A or B) = P(A) + P(B) |
| P(A|B) = | P(A ∩ B) / P(B) |
| What is the probability of rolling a die and getting a value less than 4 given that an odd number is rolled? | This is a conditional probability problem, not a multipacation one because it uses the word "given." Find how many numbers are odd less than 4 AND how many numbers are odd. Odd less than 4 / odd numbers total. Find the answer. |
| Standard Deviation | sqrt of (sum(x-xavg)^2 / N ) |
| 68% of data fall within | 1 standard deviation of the mean |
| 95% of data fall within | 2 standard deviation of the mean |
| 99.6% of data fall within | 3 standard deviation of the mean |
| How many people have a standard deviation less than one above or below? | 34% |
| How many people have a standard deviation one above or below? | 13.5% |
| How many people have a standard deviation two above or below? | 2% |
| How many people have a standard deviation three above or below? | 0.5% |
| Draw the distribution hump | -- |
| Z-score Formula | (x - u)/σ x = specific data point u = average mean of population σ = standard deviation |
| Variance Formula | σ^2 |
| Box and Whisker Chart | Each section has a 25% difference from each other, Interquartile Range containing Q1,Q2,Q3 is 50% wide |
Created by:
smurtab