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46 Cards in this Set
- Front
- Back
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PEMDAS
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Parentheses
Exponents(Radicals) Multiplication Division Addition Subtraction |
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How to find the 3rd angle of a triangle given two other angles?
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A+B+C=180
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How to use the percent formula?
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Part=Percent x Whole
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How to use % increase or decrease?
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% increaase = Amount of Increase/original whole x 100%
% decrease=Amount of decrease/original whole x 100% |
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Average
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Average = Sum of terms/Number of terms
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How to use average to find sum
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Sum= Average times # of terms
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What is 1 raised to any power?
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1
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What is a Negative raised to an even power?
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Even Number
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What are factors
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The number of positive integers than can be evenly divide into a number
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What is a Prime number
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An integer greater than 1 that has no factor other than 1 and itself
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What is Prime Factorization?
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Factoring a number until you reach the expression off numbers as its product of prime factors
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What a Ratio?
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Comparison of two quantities by division
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What is the sum of interior angles?
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(n-2) X180 Degrees
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How to find the average of consecutive numbers?
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The average of the smallest and largest integer
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How to count consecutive numbers?
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The number of integers from A to B inclusive is B-A+1
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How to find the sum of consecutive numbers
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Sum=(Average) x (Number of terms)
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How to find the median?
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The middle number of numerically consecutive numbers
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How to find the mode?
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The number that appears most often
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How to find the range
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The positive difference between the greatest and least values
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How to use actual numbers to determine a ratio
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The ration of A to B = A/B
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How to use a ration to determine an Actual Number?
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Setup an proportion using the given ratio
ex: ratio of boys to girl is 3 to 4. If there are 135 boy how many girls 3/4=135/G |
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How to use actual numbers to determine a rate
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Identify the quantities and the units to be compared.
ex. Anders typed 9,450 ward in 3 1/2 hours. What was his rate of words per minute 3 1/2 hours =210 min 9450 words/210 min 45 words per min |
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How to count the number of possibilities?
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Use multiplication.
ex. how many 3 digit number can be formed with 1,3,5 with each used only once. Look at each number individually first digit-3 poss sec digit-2 poss 3rd digit- 1 poss 3x2x=6 |
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How to calculate probability
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Probability=Number of favorable outcomes/ Total number of outcomes
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How to simplify binomials
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A binomial is the sum or difference of two terms Use the FOIL method
ex. (3x+5)(x-1)= (3x2-3x+5x-5= 3x2+2x-5 |
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What is the FOIL Methods
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Multiply the First terms
Then the Outer terms Then the Inner terms Then the Last term Combine Terms |
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What is a Polynomials
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A polynomial is an expression consisting of the sum of two or more terms, where at least one of the terms is a variable
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Factor..
ab+ac |
a(b+c)
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Factor..
a^2 +2ab+b^2 |
(a+b)^2
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Factor..
a^2 -2ab+b^2 |
(a-b)^2
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Factor..
a^2-b^2 |
(a-b)(a+b)
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What is the absolute value?
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The absolute value of a number is the distance from zero. Always positive
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How to find the angle formed by intersecting lines
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Vertical Angles are equal. Angles along a line add to 180 degrees
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How to find the Slope of a Line
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Slope =rise/run=change in y/change in x
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How to determine combines percent increase/decrease
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Start with 100. Find the value of the original increase/decrease. Use that value and find the value of the second increase/decrease. find the percentage of the original value and the final value
ex. $100 $100+(10% of 100)=(100+10)=$110 $110+(20% of 110)= (110+22)=$132 From 100 + 132 = 32% increase |
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How to fine the original whole before percent increase or decrease?
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Start with 1 and add or subtract the percent increase.decrease as decimal
ex. 5% decrease of original value is final value .95X(original value)= final value |
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How to solve a simple interest problem?
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Interest=(principal) x (interest rate(decimal)) x time(fraction of year))
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How to solve compound interest?
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Final balance= (Principal) x (1+Interest rate/C)^(time x C)
c=the number of times compounded annually |
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How to solve a remainders problem?
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Find a number that leaves the remainder of x when divided by the number given by taking an multiple of the number given and add x.plug that number into the equation and find the number
ex. n/7=R5 2n/7=R? 12/5-R5 2(12)/7=R? 24/7=3R3 |
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How to find a weighted average
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Give each term the appropriate weight
ex. girls aver=30 boy aver=24 twice as many boys, find overall average (1x30)+(2x24)/3 78/3=26 |
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How to find the new average when the number is added or deleted?
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Use the um of term of the old average to help find new average
ex.. 4 test average is 80 5 test score is 100 Original sum =4X80=320 320+100=420 420/5= 84 |
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How to use the original average and new average to figure out what was added or deleted
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Use sum of term
number added=(new sum)-(original sum) number deleted=(original sum)-(new sum) |
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How to find an average rate
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Average A pr B= Total A/ Total B
ex. 500 page with 150 words/page 100 page with 450 words/page Total pages (500+100) Total words (500x150)+(100x450)=120,000 120,000/600=200 words/page |
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How to solve combined work problem?
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Thhe inverse of time it would take everyone working together equals the sum of the inverses of the times it would take each working individual.
1/Time of First Person+1/Time of Second Person=1/Total time ex. J=4hours P=8hours 1/4+1/8=1/T 2/8+1/8=1/T 3/8=1/T T=1/(3/8) or 8/3 or 2.67. 2hours (40 min) |
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How to solve combine ratio?
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Mulitply one or both ratios by whatever you need inorder to get the terms they have in common to match
ex. a:b is 7:3 b:c is 2:5 a:c is? 3 and 2 have 6 in common a:b is14:6 b:c is 6:15 a:c is 14:15 |
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How to solve a Dilution or Mixture problem
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Determine the characteristics of resulting mixture
Straightforward method 5pounds at $1 pound 2 pound at 2.40 pound 5(1)+(2.40)2= 9.80/7=1.40 Balances method (% difference between A and desired value) x ( amount of A) = (% differenece between B and desired value) x (amount of B) |
