ATI TEAS V Math Study Guide

Order of Operations - Rules - What to do first?
'PEMDAS'
Parentheses, Exponents, Multiplication and Division (Left to Right) and Addition and Subtraction (Left to Right)

Square Feet Review - Finding Total Square Feet
Add up all four sides to find total square feet
A fence that is 25 feet by 30 feet means Total SqFt = 25+25+30+30 = 110 square feet

Addition and Subtraction of Fractions with Unlike Denominators - Summary of Steps
1. Convert mixed numbers to improper fractions
2. Simplify if possible
3. Find Least Common Denominator (LCD) - will be new denominator for both fractions
4. Make fractions equivalent - multiply numerator and denominator by same number to get LCD
5. Add or subtract numerators, leave Den. unchanged
6. Always Simplify! Never leave improper fractions

Division and Multiplication of Fractions or Mixed Numbers - Summary of Steps
Multiplication:
1. Convert Mixed Number to Improper Fraction
2. Simplify
3.Multiple numerators and denominators together
4. Simplify and convert any improper fractions
Division: Simplify, flip second fraction and multiply as above

Simplify Fractions while Multiplying - Saving time!
You can Cross Simplify fractions by dividing opposite numerators and denominators with a common factor before multiplying.

Multiplying Decimals
1. Multiple numbers as if whole numbers.
2. Then count total number of decimal places in the factors and add them (Ex: 2.2 and 2.33 has three total decimal places)
3. Add the total number of Decimal places to product, counting left to right (Ex: 22*233 = 5126 --> 5.126 final answer)

Real Number - Define
either rational or irrational

Irrational Number - Define
Cannot be written as fractions. Common ones are some square roots, cube roots, and pie

Rational Number
Real number that can be a fraction, terminating decimal or repeating decimal

Approximating Decimals of Irrational Numbers - What is the cube root of 10?
You know cube root of 8 and the cube root of 27 is 3 so it must be between 2 and 3 and closer to 2 - estimation: 2.15

What irrational number can be approximated by the number 3.3166?
If the square root of 9 is 3 and the square root of 16 is 4 then it must be between those two square roots. Square Root of 11 is a good estimate be 3.3166 is closer to 3 than 16

Calculation of Percents
The word 'of' = multiply.
15 of 500 = % --- > 15*500 =25%
What percent of 250 is 10? ---> set up equation and solve 250X = 10 -->X = 4%

Calculate Percent Decrease
(Original Value - New Value) / Original Value  100

Calculate Percent Increase
(New Value - Original Value) / Original Value  100

Dividend and Divisor - which is which
Numerator = Dividend
Denominator = Divisor (divisor goes on outside of fraction bar)

Convert from Decimals to Fractions
1. Write the digits of the decimal in numerator
2. Denominator should be the power of ten equal to number of decimal places right of decimal (.025 = 25/1000)
3. Simplify fraction

Convert Percent to Fraction Ex: 35%
1. 35
2. 35/100
3. simplify - > 7/20

How do you find which fraction is greater?
Find least common denominator and compare numerators

Convert Roman Numeral To arabic
1. Write from left to right as a sum
2. Start with largest, M = 1000, D = 500, C = 100, L = 50, X = 10, I = 1
3. When I, X, or C is used to left of larger, it is subtracted
MCCXXXIV = 1234

Convert Arabic to Roman Numeral
1. Write left to write
2. Convert each place value
3. I, X, C may be written two or three times in a row as long as they NOT followed by a larger value
4. Use I, X, C to left of larger values to indicate subtraction from larger values
5. V, L, D never used to left of larger values
6. V, L, and D never used more than on time

Convert 825 to roman number
800= 500 +100+100+100
DCCC
20 = 10 + 10 = XX
5 = 5 = V
DCCXXV

Metric: Length
Meter

Metric: Volume
Liter

Metric: Weight
Gram

10^3
Kilo (k) = 1,000

10^2
Hcto (h) = 100

10^1
deka (da) = 10

10^0
1 no prefix

10^-1
deci (d) = 1/10

10^-2
centi (c) = 1/100

10^-3
milli (m) = 1/1000

1 inch = ___cm
1 inch = 2.54 cm

1 km = ___miles
1 km = .62 miles

1 m = ___inches
1 m = 39.37 inches

1 cm = ___inches
1 cm = .394 inches

1 miles = ___km
1 miles = 1.6 km

1 yard = ___m
1 yard = .914 m

1 kg = __lb
1 kg = 2.2 lb

1 ounce = ___grams
1 ounce = 28 grams

1 pound = ___kg
1 pound = .45 kg

1 L = ___ quarts
1 L = 1.06 quart

1 ounce = ___ml
1 ounce = 30 mL

1 teaspoon = ___ml
1 teaspoon = 5 ml

1 quart = ___ L
1 quart = 0.95 L

1 gallon = ___liters
1 gallon = 3.785 L

how many inches are in 12.75 cm?
1 inch = .394 inches so 1.75 cm *.394 cm =5.02

how many centiliters are in 10 liters?
set up as proportion, 1 Liter / 100 centiliters = 10 liters / X centiliters , so x = 1,000 centiliters

Rulers
used to measure no longer than 12 inches

caliper
used t measure very small lengths

yard stick
measures no longer than 1 yard, 3 feet, or 36 inches

meter stick
measures no longer than 1 meter

tape measures
used to measure something no longer than 50 feet long

what measures columes
beakers, graduated cylinders, cups, pipettes, measuring spoons

Dependent versus independent
independent = input, unaffected by other
dependent - output, dependent on the other

'the amount of studying she did for the TEAS impacted her score'
The score is dependent on the studying

Line graph shows
changes over a period of time or compares relationship between two quantities

Way to remember x,y
always alphabetical, x,y

Circle or pie graph
shows percentage or frequency - whole pie = 100%

Histogram
shows/compares frequency of continuous data,
bars have to touch

Bar graph
shows/compares frequency of non-continuous data
bars don't always touch

When should you use a chart over table?
use chart when visual presentation is important

Variable
unknown quantity, x,y, or z

coefficient
number being multiplied by variable

[x-n] = a
[x-n] = a OR [x-n]= -a

[x-n] < a
- a < [x-n] < a

[x-n] is less than or equal to a
-a is less than or equal to [x-n] which is less than or equal to a

[x-n]> a
[x-n] > a OR [x-n]< - a

[x-n] is greater or equal to a
[x-n] is great than or equal to a OR [x-n] is less than or equal to -a

then is there no solution to absolute prob
If [x-n] = negative number
if [x-n] < 0
if [x-n]< negative number
If [x-n] is less than or equal to negative number

When will the solution be all real numbers
If [x-n] > 0
If [x-n] > negative number

When doing absolute value problems, always remember to ____before doing problem
always remember to isolate absolute value if possible