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64 terms

Teas math study guide

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rational #'s
any # that can be written as a fraction, terminating (ending) decimal (0.25), or repeating decimal (0.212121....)
irrational #'s
#'s that cannot be written as fractions (square roots, cube roots)
calculation of percents
step 1. change the written statement into a mathematical equation. Keep in mind:
- the word of translates into multiply
- the word is translates into equals
- the decimal form of the percent should be used in the equation
step 2. solve for the unknown quantity
step 3. rewrite the statement & make sure that the answer is reasonable (example: 15% of 500 is what #?= 0.15 x 500= 75 )
solving for percent decrease
percent decrease = original value minus new value
divided by original value
then multiply by 100
solving for percent increase
percent increase = new value minus original value
divided by original value
then multiply by 100
converting from fractions to decimals
divide the numerator by the denominator
converting from decimals to fractions
the decimal # expressed becomes the numerator of the fraction & the # of decimal places to the right of the decimal determines the value of the denominator
converting from fractions to percents
1st, convert the fraction to a decimal - convert the decimal to a percent by multiplying by 100 & adding the % symbol
5/8= 0.625 = 62.5%
converting from percents to fractions
step 1. remove the % sign
step 2. write the number from step 1 in the numerator of the fraction & write 100 in the denominator
step 3. simplify the fraction
converting from percents to decimals
remove the % symbol & move the decimal point left 2 places
(example: 0.045= 4.5 %)
determining which fraction is greatest
find a common denominator for the fractions- the fraction with the greater numerator is the greater fraction
estimation
the approximate value= the 1st digit in the # will not be zero but all the other digits will be zeros
to balance a checking or savings
1st group the deposits & add them together -then group the checks & add them together- next add the deposits to the previous balance & subtract the checks from the result- then subtract the service charge & add interest
proportion
this states that 2 ratios are equal- when setting up this, the numerators must be in the same units & the denominators of both ratios must be in the same units- use this formula to solve for this:

units of an item = units of an item
divided by units of a different # Divided by units of a different #
ratio
this is used to express a relationship between 2 quantities
rate of change problems
use proportions to determine the difference in completion times for a given task
example: 10 pages / 1 hour = 288 pages / A hours
use the method of cross products to solve:
10 x A= 288 x 1 - 10A / 10 = 288 / 10 A= 28.8 hrs
roman numerals
M, D, C, L, X, V & I
1000
roman numeral M=
500
roman numeral D=
100
roman numeral C=
50
roman numeral L=
10
roman numeral X=
5
roman numeral V=
1
roman numeral I=
subtraction from the larger values
the use of I, X, & C to the left of larger values indicates what
2.54 cm
1 inch is how many cm?
2.2 pounds
1 kilogram is how many pounds?
3 feet
1 yard is how many feet?
4 quarts
1 gallon is how many quarts?
calipers
this is used to measure very small lengths, usually 6 inches or fewer with greater precision than a ruler
rulers
this is used for measurements no longer than 12 inches
yard sticks
this is used for measurements no longer than 1 yard, 3 feet, or 36 inches
scales
these are used to measure weight
beakers
these are used for measurements in teaspoons
graduated cylinders
these are used for measurements in tablespoons
measuring cups
these are used for measurements in pints
pipettes
instrument used for measuring small volumes of fluid
independent variable
the variable that is put into the set of data, or the input, (statistics) a variable whose values are independent of changes in the values of other variables
dependent variable
is the output based on the input, (statistics) a variable in a logical or mathematical expression whose value depends in the independent variable
line graphs
these graphs show changes over a period of time or compares the relationship between 2 quantities (compare time of day to temperature)
pie (circle) graphs
a circular graph divided into sectors representing the frequency of an event- percentage of a whole, where the whole circle or pie equals 100%- shows how much of the whole each part represents
bar graphs
this graph is used to compare the frequencies of an event
(the number of inches of rain that fell in a certain city in the each month)
tables
these are helpful for organizing raw data
constant
a quantity that does not change
adding integers
positive + positive = positive
negative + negative = negative
when signs are different = subtract the smaller # from larger & give the sign of the larger #
subtracting integers
- subtracting a positive is the same as adding a negative
- subtracting a negative is the same as adding a positive
multiplying integers
positive x positive = positive
negative x negative = positive
positive x negative = negative
percentage discount & tax increase
to find the amount of discount or increase when the % is known
1. change the percentage to a decimal (or fraction)
2. multiply by the original cost
3. add or subtract accordingly
percentage increase & decrease
often the problem asks you to determine the percentage of increase or decrease. This type of problem is easily solved by making a fraction out of the information provided
1. write the amount of increase or decrease as the numerator
2. write the original amount as the denominator
3. change fraction to percent
ratio
a comparison of 2 #'s, usually by division
(ex: in a class of 15 people, there are 7 boys & 8 girls. The ratio pf boys to girls is 7 to 8 or 7:8 or 7/8)
rate
a ratio made up of 2 different units of measurement or amounts
(ex: I can drive my car 250 mi on 10 gal of gas. This relationship can be expressed as a ratio of miles to gallons: 250 to 10, 250:10, or 250 mi/ 10 gal = 25/ 1 or 25 miles per gal)
proportion
an equation of 2 equal ratios. All proportions equations have have a special property: cross products are equal. When you multiply the numerator on the left side of the equation by the denominator on the other side & then multiply the left-side denominator by the right-side numerator, the are products equal to each other
(ex: if a car gets 25 miles to the gallon, then how many gallons do I need to drive 125 miles?
set up a proportion to solve this problem. Make sure you align your units correctly on both sides of the equation: in this case, miles across from miles & gallons across from gallons
25 mi / 1 gal = 125 mi / x gal
now cross multiply: 25x = 125
now divide both sides by 25 to solve for x. x = 5
this is your answer- you need 5 gal to go 125 mi
evaluate
means to find the value of something
addition
"increased by", "more than" & "total"
subtraction
"decreased by", "less than," or "less"
"is"
means "="
the formula for area
A = 1/2 bh A = area, b = base, h = height
exponent rules
1. when multiplying similar bases, add the exponents
2. when dividing similar bases, subtract the exponents
3. when raising a power to another power, multiply the exponents
(ex:(s^2)^3 = s^ 6
4. when the exponent is negative, move its base to the denominator & make the exponent positive
5. any base (except zero) to the 0 power equals 1
area of a rectangle
A= lw A = area, l = length, w = width
area of a square
A = s^2 A = area, s = side
area of a triangle
A = 1/2 bh A = area, b = base, h = height
perimeter of a rectangle
P = 2l + 2w
perimeter of square
P = 4s
perimeter of a triangle
P = s + s + s