HESI A2 math section
Common factor
A number that is a factor of two or more numbers
Prime Number
A whole number that has exactly two factors, 1 and itself.
GCF (Greatest Common Factor)
The largest number that is factor of two or more numbers. Ex. The G.C.F. of 15 & 35 is 5
Integers
The set of whole numbers and their opposites {. . .-2, -1, 0, 1, 2. . .}.
Multiplying and dividing fractions
When multiplying two or more fractions, just multiply their numerators and then their denominators. Then, simplify. To divide fractions, flip the second fraction and multiply in the regular way. Then, simplify.
Adding and Subtracting Fractions
The denomination has to be the same. If it is different find the lowest common multiple of the denominators. 5/6 - 3/4 = 5/6 x 2/2 - 3/4 x 3/3 = 10/12 - 9/12 = *1/12.*
Absolute Value
The distance a number is from zero on a number line. ALWAYS POSITIVE Denoted from a pair of vertical lines surrounding the value! ex) |3| = *3* |-3| = *3* |3-8| = |-5| = *5* |8-3| = |5| = *5*
formula for the volume of a cube
V= S³
How many feet in a meter?
1 meter = 3.3 feet
multiples
Counting by that number. Numbers you say when you skip count. Multiples of 2 are: 2,4,6,8,...
Decimals
use place values to the right of the decimal point, to represent an amount.
Solving for X with Absolute Value
you have to solve the equation two times: 1 equation: assuming the absolute value is positive. 2 equation: assuming the absolute value is negative. This, results in (2) solutions.
Adding and subtracting Decimals
Line up the decimal points and proceed as usual
Roman Numerals
# RN.. ..# RN .........# RN 1 I ..........11 XI ...........21 XXI 2 II .......12 XII .........22 XXII 3 III..... 13 XIII ........23 XXIII 4 IV .....14 XIV........ 24 XXIV 5 V .......15 XV .........25 XXV 6 VI .....16 XVI ........26 XXVI 7 VII ....17 XVII .......27 XXVII 8 VIII ..18 XVIII .....28 XXVIII 9 IX .....19 XIX .........29 XXIX 10 X ....20 XX.......... 30 XXX I - 1 V - 5 X - 10 L - 50 C - 100 D - 500 M - 1000
Dividing Fractions
**KEEP-SWITCH-FLIP** Ex). 2/3 / 1/3 = 2/3 X 3/1 = 6/3 = 2 6/3 is an Improper Fraction because the numerator is greater than the denominator Ex) 1/2 / 2/5 = 1/2 X 5/2 = 5/4 = 1 1/4 5/4 is also improper fraction. 4 goes into 5 only 1 time which becomes the whole number. After 4 goes into 5, only 1 is left over and thats the numerator. The denominator stays the same.
Difference between Ratio and Percentage
-*Ratio* : A way to describe the relationship between two different quantities. -*Percentages* : Compare part of something to a whole. Ratio ex) 20 Red 25 Blue. 20:25 (20:25) / 5 = *4:5* -Always check if the ratio can be divided by same #. Percentage Ex) 20 red 25 blue 5 white what is the percentage if red marbles in the bag? 20/50total X 2/2 = 40/100 ~~*40%* -Divide top and bottom by 2 to get the denominator = 100
Finding the percent increase
-Formula will be the same for decimals, fractions, and currency; but process will be different depending on the problem. - formula: (2nd# -1st#) / 1st# ex) (1.8, 3.0) 3.0-1.8 / 1.8 = 1.2 / 1.8 = *66.7%* ex)(1/4, 2/5) (2/5 - 1/4) / 1/4 [2/5(4/4) - 1/4(5/5)] / 1/4 (8/20 - 5/20) / 1/4 3/20 / 1/4 ~~ 3/20 / 4/1 -cross cancel by diving by 4- =3/5 = *60%*
Computation with percentages
-in problems involving percentages, it is usually easiest too convert to a fraction or a decimal -"of" in math, means to multiply. ex) Calculate 40% of 62 40% x 62 .4 x 62 = *24.8* ex) Calculate a 20% tip on a $28.75 meal. 20% of(x) $28.75 .2 x $28.75 = *5.75* Total bill : *34.50*
Finding the percentage decrease
-similar to finding the increase, but the formula is a little different. -when using fractions in numerator make sure they have a common denominators -formula: 1st# - 2nd# / 1st# ex) (3.6, 2.0) 3.6-2.0 / 3.6 =1.6 / 3.6 =*44.4%* ex) (5/6, 2/3) (5/6 - 2/3) / 5/6 [5/6 - 2/3 (2/2)] / 5/6 (5/6 - 4/6) / 5/6 1/6 / 5/6 ~~ 1/6 / 6/5 = 1/5 = *20%* ex) ($200, $30) (200-30)/ 200 = 170/200 divided by 2 = 85/100 =*85%*
Calculation of a percentage
-were being asked to find the percentage -when finding the percentage, think of the percent as a part divided by a whole. (part/whole) ex) what percent of 40 is 35? part/whole = 35/40 = .875 =*87.5%* ex)what percent of 25 is 12? part/whole= 12/25 x 4 = 48/100 =*48%*
What is the freezing point of water?
0 degrees Celsius or 32 degrees Fahrenheit
How many miles are in a kilometer?
1 kilometer (km) = 0.621 mile (mi)
How many inches in 1 meter (m)?
1 meter (m) = 39.37 inches
How many kilograms are in a pound?
1 pound (lb) = 0.45 kg
How many ounces are in a pound?
1 pound = 16 ounces (oz)
PEMDAS "Order of Operations"
1) perform any calculations inside parentheses 2) perform all multiplication and divisions from LEFT to RIGHT 3) perform all Addition and Subtraction from LEFT to RIGHT
How many kilometers are in a mile?
1.61 km = 1 mile
what is the boiling point of water?
100 degrees Celsius and 212 degrees Fahrenheit
How many Inches(in) in a foot(ft)?
12 inches(in) = 1 foot (ft)
How many pounds are in a ton?
2,000 pounds
How many pounds are in a kilogram?
2.2 pounds
How many centimeters are in an inch?
2.54 centimeters (cm) = 1 inch
How many feet in 1 yard?
3 feet = 1 yard (yd)
Solving Inequalities using all 4 basic operations
4 Operations: Addition, Subtraction, Multiplication, Division -same as solving an equation, expect if multiplying or dividing by negative #, you have to flip inequality sign. ex) 5-3x- (3x+2)/4 <12 x4[5-3x- (3x+2)/4 <12] 20-12x-(3x+2) <48 20-12x-3x-2<48 -15x+18<48 -18 ------------- -15x/-15 < 30/-15 = *x > -2*
How many feet in a mile?
5,280 feet = 1 mile
converting percentages to decimals & fractions
68% = .68 = *0.68* = 68/100= 17/25 (68/100) / 4 = *17/25*
How many ounces in a cup?
8 ounces (oz)
Decimals
A decimal representation divides the space between 0 and 1 into ten different segments.
Arithmetic Sequence Formula
A formula used to find the nth term of an arithmetic sequence: *Xsubn= a+d(n-1)* a=first term d=constant difference n= number sequence order ex) 9, 17, 25, 33, 41, 49, 57, 65, 73, 81... Xsub4= 9 + 8(4-1) = 33 ex) Xsub1,698= 9 + 8(1,698-1)= 13,585
Fractions
A fraction is a way to divide a section between integers into equally-spaced segments.
Root
A radical symbol that indicates the power of "two". any two real numbers multiplied shall sum the root number. it can be 3rd root, 4th root,..
formula for area of a rectangle
A= length x width (A=lw)
Area of a circle
A= πr²
Formula for area of a square?
A=s²
Converting Improper Fractions to Mixed Numbers & Decimals
Both share the first step of converting improper fractions to Mixed Numbers. To convert to Decimals, bring down the whole number from the mixed number and place it left from the decimal point. the rest of the mixed number is simplified, making sure the denominator stays to the power of 10, 100, 1000. ex) 34/5 = *6 4/5* 4/5 x 2/2 = 8/10 *6.8*
Converting Improper Fractions to Mixed Numbers
Divide the numerator by the denominator to get an Mixed Number. 22/5 =4 2/5 *Remember to simplify to lowest form*
Converting decimals to improper fractions and mixed numbers
First step, convert the decimal to a mixed number: take the left part of the decimal to be a whole number and then the right part of the decimal to be the fraction. Reduce. second step: convert mixed number to improper fraction. Ex) 5.35 (5 35/100) / 5 = 5 7/20 *107/20*
Dividing Decimals
First, move the decimal point in the divisor so it's a whole number. Then, move the decimal point in the dividend, the same number of places and then move the decimal point up. Divide as you would normally, until you have no remainder. Add on zero's until your remainder is zero.
Changing # from standard form to Scientific Notation
First, re-write #, so its between 1 & 10 by moving the decimal to the left or right. Next, multiply the # times 10 raised to -and this power is found by determining how many places we had to move our decimal. ex) 32,581 = *3.2581 x 10^4* ex) 0.065 = *6.5 x 10^-2*
Solving Equations and Inequalities
For *equations* you can perform any operations the same way on both sides of the equation and the equation remains true. *Inequalities* consist of two mathematical expressions separated by a sign indicated which side is greater or lesser. For example: 1<2. **For Inequalities; we ONLY multiply or divide by Negative numbers when reversing the inequality sign.
Solving Absolute Value Inequalities
Isolate the Absolute Value expression. Write down the (2) solutions of the absolute value expression, one + and one -, for the - flip the sign. If the number on the side of the Inequality sign is negative, the equation either has no solution or all real numbers are solutions. Ex) |x| < 3 x < 3 & x > -3 = *-3<x<3* (two finite bonds) ex) |x| >3 x>3 & x<-3 = *3<x<oo / oo<x<-3* (infinity bonds) ex) |x|+3<2 -3 -3 ----------- = |x|<-1 (x has to be positive; therefore there's no absolute value of x that can satisfy this inequality)
linear inequalities
Linear inequalities are solved basically the same way as linear equations. It can only be solved for one variable in terms of the other. One quantity is larger than the other. Ex. Y>X-2 Ex: 8y-4x< 8 8/(8y-4x)< 8/8 y-1/2x< 1 +1/2x *y< 1/2x+1* & graph
Converting mixed numbers to improper fractions and decimals
Methods for converting a mixed number to a fraction and a decimal are very different from one another. First, convert mixed number to improper fraction. When converting to decimal, denominator has to be of 100. ex) 4 2/5= *22/5* 2/5 x 20/20 = 40/100 *4.40*
Converting mixed numbers to improper fractions
Multiply the denominator of the mixed number by the whole number and add the numerator to this product. Then place the sum over the denominator of the mixed number.
Solving Equations using 4 basic operations
Start by removing the fractions by multiplying both sides of equation by the product of the two denominators. ex) 3x+17-11.... 10 -------- = ---- x .................3 ......3x+17-11... 10 3x -------- = --- 3x ...........x ............3 3 (3x+17-11) = 10x 9x+51-33 =10x -9x -9x ================ 51-33=x = *18*
Exponents
The number that tells you how many times to multiply the base number by itself. Any real number raised to the power of 0 =1. Any real number raised to the power of 1 = the real number.
Associative Property
The way in which numbers are grouped does not change their sum or product. Applies only for addition and multiplication.
Graphing Solutions for Linear Inequalities
To graph the Linear Inequality, you graph the line as if the ">", "<" were an equal sign. Graph the " greater than" or "less than" with a dash line. Graph the "greater than or equal to" etc.. with a solid line. After drawing the line, you shade. Pick a point on either side of the line, and see if it satisfies the inequality. If it does, you shade that side if it doesn't you shade the other side. A good point to plug in is: (0,0)
Formula for Volume of rectangular prism
V = lwh
scientific notation
a method of expressing a quantity as a number multiplied by 10 to the appropriate power
factors
are numbers that are multiplied together to obtain a product. ex) 2x3=6
Distributive Property
each term inside a set of parentheses can be multiplied by the term outside the parentheses, such as: a(b + c) = a(b) + a(c)
Converting decimals numbers to fractions and percentages
ex) 0.215 = *21.5%* (215/1000) / 5 = *43/200* ex) 0.842 = *84.2%* (842/1000) / 2 = *421/500*
Solving for X by Multiplying and dividing
isolate x on one side of the equation and move everything else to the other side.The first thing you want to do in solving this problem is to rewrite it in a simplified form, and then get X all by it'self. ex) (3x)(12)/ (5) = (2x)(15x)/ (20) 36/5 = 30/20x^2 36/5 = 3/2x (2/3)36/5 = 3/2x (2/3) *24/5=x or 4 4/5 = 4.8*
Formula for the slope of a line
m = (y2 - y1) / (x2 - x1)
LCM (Least Common Multiple)
of two numbers is the smallest value divisible by both the numbers. Or it's the smallest number that both of your numbers divide into evenly. 18: 2x3x3 30: 2x3x5 GCF= 2x3=6 LCM= 6x3x5=90
