Math Concepts to Memorize Flashcards
Multiply Units - 10” long * 4” w * 7” h = ?
280 in3 (cubed)
Distance/Work Rate Formula
Rate * Time = Distance/Work or Rate = Work/Time
If an object moves the same distance twice at different speeds, the average will be…
closer to the slower speed. Pick a smart number for the distance and create a R*T=D chart for both trips. Trip 1: 4*3 = 12 Trip 2: 6*2 = 12 Aveg: ?*(3+2) = 24 ?*5=24 ?=4.8MPH
When two machines work together ____ the rates
ADD the rates. Rate A + Rate B = Rate A+B
2 Average Formals
Average = Sum/# of Terms OR Average * # of items = sum
Small Standard Deviation =
Closely clustered data
3 Properties of Evenly Spaced Sets
Arithmetic Mean = Median
Mean & Median = Avg of 1st & Last Terms
Sum of Elements = Mean * # of items
Formula for Counting Integers in a Set
Last-First + 1 OR (Last-First) / Increment + 1
5 Properties of Consecutive Integer Sets
Average First & Last Term to Find Middle
Count * of Terms (First-Last) + 1
Multiple middle term by # of terms
The average of an odd # of integers is an integer
The average of an even # of consecutive integers will never be an integer
To Examine Overlapping Sets
Create a Double Set Matrix. Use algebra.
To Examine 3 Overlapping Sets
Create A Venn Diagram. Work from Inside to Out.
Solving Inequalities (mult/div & add/sub)
When you multiply or divide by a NEGATIVE, flip the sign. You can ADD inequalities when symbols face the same way. You can NOT SUBTRACT inequalities.
If someone is younger ____ the difference to keep the parties equal.
ADD
Formula for distance when traveling towards each other
Sum of Rates * Time to Meet = Initial Separation
Formula for two parties working at different speeds, working together.
Add rates. 1/5 + 1/7 = 7/35 + 5/35 = 12/35
Formula for speed as two people walk towards each other at different speeds.
Person 1 Rate + Person 2 Rate = Rate of Travel. i.e. 5MPH + 6MPH = 11MPH
Setup for two different people walk towards each other but one starts 2 hours later.
R * T = D chart. One party will be T+2 (if time is in hours already).
If one party is undoing the work of the other party _____ the rates of work.
SUBTRACT
When comparing rates of work for different machines, first
express the rates in equivalent units. How much can it finish per second/minute/hour.
x*x
x2
square root 2 * square root 2
2
pull out the common factor: x2y-xy2 =
xy(x-y)
14-3(4-6) =
20
-(52)=
-25
3 x 99 - 2 x 99 - 1 x 99 =
0
(2xy)2=
4x2y2
3y + xy - 2y =
3y-2y+xy
(3-2)y + xy
1y + xy
(1+x)y
(x+1)y
12xy - (6x + 2y) =
12xy - 6x - 2y
2x2 - 4x2 - 1x2 =
(2-4-1)x2
(-3)x2
-3x2
square root 3(sq root 2 + sq root 3) =
square 3 * square 2 + square 3 * square 3
square 6 + 3
an integer is divisible by 3 if…
…the sume of the integer’s digits is a multiple of 3.
an integer is divisible by 9 if..
the sum of the integer’s digits is a multiple of 9.
All the primes less than 20 are…
2, 3, 5, 7, 11, 13, 17, 19
What is the factor foundation rule?
Every number is divisible by the factors of its factors.
Also you can multiply two factors and it will still be divisble. (If 20 is divisible by 2 & 5, it is also divisible by 2 x 5).
To find all the factors of a number…
setup a factors pairs table
1 x 30
2 x 15
3 x 10
5 x 6
To find all the prime factors of a number…
use a factors tree.
28
2 * 14
2 * 7
X is divisible by 10 & 17.
Is X divisible by 5?
Is X divisible by 170?
Is X divisible by 15?
Yes (5 is a factor of 10)
Yes (170 is the LCM of 10 * 17)
Maybe (5 is a factor but we don’t know if a 3 is present)
What does LCM stand for?
What is the LCM of 6 & 9?
Least Common Multiple
18
If x is divisible by A & by B then x is divisible by…
the LCM of A and B.
When you combine two factors trees of x that contain overlapping primes…
drop the overlap.
If x is divisible by 8, 12, and 45, what is the largest number that x must be divisible by?
Create factor trees for each number. Count the number of unique prime factors.
*8 has three 2s so include *
2 x 2 x 2
45 has two 3s and one 5
3 x 3 x 5
12 has two 2s and one 3 (but those are covered by previous factors)
add nothing
2 x 2 x 2 x 3 x 3 x 5 = 360
7 x 6 =
42
7 x 7 =
49
8 x 7 =
56
8 x 8 =
64
42=
16
52=
25
62=
36
72=
49
82=
64
92=
81
112=
121
122=
144
132=
169
142=
196
152=
225
202=
400
302=
900
33=
27
34=
81
53=
125
23=
8
33=
27
43=
64
53=
125
103=
1,000
23=
8
24=
16
25=
32
26=
64
27=
128
28=
256
29=
512
210=
1024
43=
64
x2 = 16
x equals ???
4 or -4
Which is larger?
(-32) or (-3)2
(-3)2= 9
(-32) = 3 x 3 x -1 = -9
To multiply exponential terms with the same base …
y(y6) =
add the exponents.
y1 x y6 = y7
When you divide exponential terms that have the same base, …
a5 / a3 =
subtract the exponents.
a5-3=a2
For any nonezero value of a,
a0=
1
2-3=
three forms of the answer
2-3 = 1/23 = 1/8 = 0.125
When you move an exponent from the top to the bottom of a fraction (or vice versa)…
_ 1 _
z-4
Switch the sign of the exponent. If you move the entire denominator, leave 1 behind.
_ 1_ = 1*z4 = z4
z-4 = 1 = 1
When you raise something that already has an exponent to another power…
(a2)4=
multiply the exponents together.
(a2)4= a2*4 = a8
When multiplying exponents with different bases….
22 x 43 x 16=
try breaking down the bases into prime factors.
22 x 43 x 16 = 22 x (22)3 x 24
22 x 26 x 24 =22+6+4
212
When you apply an exponent to a product…
(xy)3 =
(wz3)x =
…apply the exponent to each factor.
(xy)3 = x3y3
(wz3)x = wxz3x
To add or subtract exponential terms with the same base…
38 - 37 - 36=
pull out a common factor.
(36)(32 - 31 - 30)
36(9 - 3 - 1)
(36)(5)
To add or subtract exponential terms with different bases…
23 + 63=
break down the bases and pull out the common factor.
23 + 63=
23(1+33)
The square root of 16 * the square root of 16 =
16
sqr(-5)2=
sqr25 = 5
When you square a square root vs. Square-root a square
(sqr10)2 vs. sqr102
Get the original number vs. Get the absolute value of the original number
sqr2 =
about 1.4
sqr3 =
about 1.7
sqr70 is bretween what two integers?
sqr64 = 8
sqr81 = 9
so between 8 & 9
The square root of a number bigger than 1 is _______ than the original number.
The square root of a number between 0 & 1 is __________ than the original number.
Both are closer to 1.
SMALLER
BIGGER1
On the GMAT, the square root of a number is…
always positive.
Unlike the x2 which can be negative or positive.
sqr722=
(two formulas)
sqr722 = (722)1/2 = 722/2 = 711
sqr722 = sqr711x 711 = 711
cube root -64 =
-4
cube roots can be negative (unlike square roots)
To raise a number to a fractional power…
1252/3 =
Apply the numerator as is and the denominator as a root in either order.
1252/3 = (cuberoot 125)2 = 52 = 25
To mulitply and divide square roots…
Multiply or devide the insides, then square-root.
sqr(a) x sqr(b) = sqr(ab)
sqr a / sqr b = sqr(a/b)
When you have a sqr of a large number…
sqr12 =
Pull the square factors out of the number under the radical sign.
sqr12 = sqr(4x3) = sqr4 x sqr 3 = 2sqr3
Break the number down into primes if you don’t recognize the perfect square factors.
To add or subtract inside the root…
sqr(32+42) =
Do not break apart like multiplication/division!
Factor out a squre factor from the sum
sqr[310+311] = sqr[310(1+3)] = sqr[310(4)] = sqr[310] x sqr[4] = 35 x 2
OR (if small numbers)
Follow PEMDAS under the radical and then take the square root.
sqr(32+42) = sqr(9+15) = sqr(25) = 5
56 x 54x
54
5(6+4x-4) = 54x+2
-33=
-27
43+43+43+43+32+32+32 =
Factor 43 out of the first four terms and 32 out of the last three terms.
43(1+1+1+1) + 32(1+1+1) =
43(4) + 32(3) =
44+33
sqr[24] =
sqr[2*2*2*3] =
2sqr[2*3] =
2sqr[6]
To solve sqr[352-212]
Pull out the great common factor 72
sqr[72(52-32)] =
sqr[72(25-9)] =
sqr[72(16)] =
square root eliminated by perfect squares
7*4 = 28
In factions, the denominator can never equal ______.
zero.
The larger the numerator, the _________ the fraction.
larger
Which is larger?
3/5 or 4/7?
Corss-multiply from the bottom and across…
7x3 = 21 3/5 vs. 4/7 5x4=20
3/5 is larger.
To simplify a fraction…
cancel out common fators from the numerator and demonminator.
18x2 = 6x * 3x = 3x
60x 6x * 10 10
To multiply fractions…
first cancel any factors and then multiply the tops and bottoms together.
The reciprocal of a negative fractions is ____________.
also negative.
To divide by a fraction…
multiply by the reciprocal.
If you have addition or subtraction in the numberator of a fraction…
9x - 6
3x
Pull out a factor form the entire numorator and cancel that factor with one in the denominator.
9x - 6 = 3(3x-2) = 3x-2
3x = 3x x
If you have addition or subtraction in the numerator, you can rewrite…
the fraction as the sum of two fractions.
9x - 6 = 3(3x-2) = 3x-3 = 3x - 2 = 3 - 2
3x 3x x x x x
If you have addition or subraction in the denominator ___________.
NEVER split a fraction in two.
Look for a common factor on the top and bottom to simpilfy out.
To compute “nasty” fractions…
put parentheses around the nasty numerators and denominators and then proceed normally.
If you encounter a fraction within a fraction…
work your way out from the deepest level inside.
To simplify sqr[18]…
look for the perfect squares.
sqr[2*3*3] = 3sqr[2]
Another word for ratio is _________
proporation.
To convert a percent to a fraction….
write the percent “over one hundred”.
45% = 45/100
5/8 = 0.?? = ??%
5/8 = 0.625 = 62.5%
7/8 = 0.?? = ??%
7/8 = 0.875 = 87.5%
6/5 = ??? = ??%
6/5 = 1.2 = 120%
3/8 = ??? = ???%
3/8 = 0.375 = 37.5%
To calculate 0.004 * 10-3 =
Change teh negative power to postiive and divide instead of mutliply.
- 004 * 10-3 =
- 004 / 103 =
.000004
To multiply a decimal and a big number….
4,000,000 * 0.0003 =
Move the decimal to the right in the small number and to the left in the large number.
4,000,000 * 0.0003 =
400 x 3 = 120
To divide two decimals…
300 / 0.05
move points in the SAME direction until you kill the decimals.
300 / 0.05 =
30,000 / 5 =
6,000
When the GMAT says “what percent of”, you should…
What percent of 200 is 60?
Turn “what percent” into x/100, then multiply.
x/100 * 200 = 60
To find percent change…
If the price increases from $200 to $230, what perecent does it change?
divide the change in value by the original value.
$30/$200 = 15%
To find the new value after a percent change has been applied…
The $60 purse was marked up by 25%
Find the new percent (100% + 25%), convert to a fraction (5/4) and multiply by the original value.
(5/4) * $60 = $75
To find the percent more/less than..
$200 is what percent more than $150?
Divide the change in value by the original value.
$50/$200 = 25%
When you have successive percent changes…
What is 120% of 150% of 30?
multiply the origianl value by the new percents for both percent changes.
(using fractions might allow you to cancel)
6/5 * 3/2 * 30 = 54
If you have a ratio, write it out as ________ to compute the whole.
For every 2 girls in the class there are 3 boys.
Part : Part : Whole
2 girls : 3 boys : 7 students
How are expressions and equations different?
Expressions don’t have equal signs.
4 ways to simplify expressions.
Combine like terms. 3x + 4x -> 7x
Find a common denominator and then combine. 3/5 + 4/10 ->10/10
Pull out a common factor. x + xy -> x(1+y)
Cancel common factors. 3x2 / 6x -> x/2
Simplifying the expression NEVER changes its value.
What is the order of operations?
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
What are two things you can do to one side of the equation but not the other?
Simplify the expression on one side OR
Evaluate the expression on one side.
You may NEVER change one expression without changing the other.
When changing one side of an equation by multiplying, dividing, squaring or taking the square root, you must….
x + 4 = x/2
Put parenthesis on the other side of the equation to perform the same action to the ENTIRE other side.
x + 4 = x/2
2(x+4) = (x/2)2
2x + 8 = x
When you take the square root of an equation…
x2 = 49
sqr[x2] = sqr[49]
the equation usually splits into two separate equations.
x = 7 OR x = -7
What is x in terms of y?
7x + 4 = y
Means create and equation where x = something containing only y’s.
7x + 4 = y
-4 to both sides
divide by 7 both sides
x = (y-4) / 7
To isoloate a variable deep inside an expression…
2y3 - 3 = 51
follow PEMDAS in reverse to undo the expression.
2y3 - 3 = 51
+3 to both sides
divide by 2 both sides
take the cubed root to both sides
What is the first thing you should in an equation like this?
(5x - 3) / 2x = 10
Get rid of the denominator. Always get vartiables out of the denominators.
(5x - 3) / 2x = 10
mulitply by 2x both sides first!
When you have variables in the exponents…
3x = 274
Rewrite the terms so that they have the same base, usually by breaking the bases into primes.
3x = 274
3x = (33)4
3x = 312
x = 12
When you have variables in the exponents, there are three bases you cannot set the exponents the same for to solve.
1, 0, -1
What are the two strategies to solve a system of equations?
Isolate, then Subsitute OR
Combine Equations
How to do you Isolate, then Substitute to solve a system of equations. (aka subsitution)
2x - 3y = 16
y - x = -7
First isolate the variable you don’t ultimately want. If the problem asks for x, isolate y. Isolate the variable in the equaition that’s easier to deal with.
y - x = -7, add x to both sides y = x -7
No replace y in the second equation with (x-7).
2x - 3(x-7) = 16 and solve for x.
If you need to solve for y two, use the new value of x in the equation you created to isolate y.
How do you kill an equation and an unknown (aka combination)?
If adding or subtracting the equations together will kill off a variable, it may be faster than subsitution.
You may also multiply or divide the ONE ENTIRE equation to setup an expression that can be combined to eliminate a variable.
If the system of equations have three or more unknowns…
a + b - c = 12 and c - b = 8
What is the value of c in terms of a & b?
Isolate whatever the question asks for, and use subsitution to eliminate unwanted variables.
What is a quadratic expression?
A quadratic express contains a squared variable and no higher power, such as…
z2
y2 + y - 6
x2 + 8x +16
When dealing with quadratic equations, what is the factored form and what is the distributed form?
The factored form is
(x+2)(x+3) =
The distrubted form is
x2 + 5x + 6 =
When factoring a quadratic expression, the two factors must _____ to the x coefficient and they must ____ to the constant.
Factors must ADD to the x coefficient and they must MULTIPLY to the constant.
in a quadratic expression, if the constant is positive, the two numbers in the factored form must be…
z2 + 7z + 12 =
x2 - 9x +18 =
both positive or both negative, depending on the sign of the x term.
z2 + 7z + 12 = (z+3)(z+4)
x2 - 9x +18 = (x-3)(x-6)
In a quadratic expression if the constant is negative, the factored numbers must be..
w2 + 3w - 10 =
One number is positive and the other one is negative.
In a quadratic expression if the constant is negative, how do you find the factor pair?
w2 + 3w - 10 =
First find the factor pairs of your constant that differ by the coefficent. (5 & 2).
Then make one of the factors negative so they add to the correct coefficent. (5 + -2, NOT -5 + 2)
Now keep the signs when you place the pair.
w2 + 3w - 10 = (w + 5)(w - 2)
How do you factor this?
3x2 + 21x + 36 =
The express is multiplied through by a common numerical factor. Pull out the common factor FIRST and then calculate normally.
3x2 + 21x + 36 = 3(x2 + 7x + 12) = 3(x+3)(x+4)
How do you deal with a negative x2 term?
-x2 + 9x + 18 =
Pull out the -1, which becomes a minus side outside the parentheses.
- x2 + 9x + 18 =
- (x2 - 9x + 18) =
- (x-3)(x-6)
How do you solve a quadratic expression?
Rearrange the equpation to make one side euqal to 0.
x2 + x = 6 —-> x2 + x + 6 = 0
Factor the quadratic expression.
(x+3)(x-2) = 0
Set each factor equal to 0.
x + 3 = 0 -> x = -3
x - 2 = 0 -> x = 2
Th esolution is called its roots. Only one is true at the same time.
How do you solve a quadratic equation with squared parentheses?
(y + 1)2 = 16
Either treat (y+1) as a new variable like z. OR
Take the postiive and negative square roots of 16 right away. OR
FOIL (y+1)(y+1) to create a normal quadratic equation.
How to solve a higher power quadratic formula.
x3 = x
Solve like a normal quadratic: set the equation to zero, factor, and set factors equal to zero. Never divide by x unless you know x does not equal 0. X to the third power usually means three solutions.
x3 = x
x3 - x = 0
x(x2-1) = 0
x(x+1)(x-1) = 0
x = 0, -1, or 1
If you see a quadratic expression in the numerator or denominator, try…
(x2 - 2x - 3) / x +1 =
Try factoring the quadratic expression to see if one of the factor pairs can be canceled out.
(x2 - 2x - 3) = (x + 1)(x -3)
cancels out with x+1 on the bottom.
If x does not equal y, then (y-x) / (x-y) =
The two expressions are identical except for the sign change.
(y-x) = -(x-y)
Expressions that only differ by a sign change are only different by a factor of -1.
If you cancel -(x-y) / (x-y) you are left with -1.
What does the factored version of squar of a sum look like?
(x+y)2 =
x2 + 2xy + y2
Only one solution will be valid.
What is the factored form of square of a difference?
(x - y)2
x2 - 2xy + y2
There is only one valid soution.
What is the factored form of difference of squares?
(x + y )(x - y) =
x2 - y2
The inner and outer temes cancel the coefficent term.
Square each term and subtract the difference.
Unlike equations, inequalities have how many solutions?
A whole range.
The only thing you can do to one side of an inequality and not the other is…
simplify. Do NOT change the value.
What operations can you perform on a system of inequalities? What should you avoid?
Add or subtract from both sides.
Multiply or divide both sides. If you multiply or divide by a negaive number flip the sign.
You shouldn’t divide by a variable unless you know the variables sign.
Treat absolute numbers in inequalities as ________.
|4-7| =
as parentheses. Solve the equation inside first and then find the absolute value of the result.
How do you solve an equation with a variable inside the absolute value signs?
6 x |2x + 4| = 30
First isolate the absolute value on one side of the inequality or equation.
6 x |2x + 4| = 30 –> |2x + 4| = 5
Set-up two equations, one negative and the other positive.
2x + 4 = 5 & -(2x + 4) = 5 –> -2x - 4 = 5
Solve both.
Get two possible values.
How do you solve an absolute value in an inequality?
|y + 3| < 5
Isolate the absolute value on one side.
Setup two inequalities (positive & negative).
|y + 3| < 5 –> -y - 3 < 5 &
+ y + 3 < 5
Isolate the variable and solve both. Remember to flip the sign if you mult/divide by a negative number.
If you know the radius of a circle, you can also find…
Diameter (2r)
Circumference (πd)
Area (π r2)
You can find the radius from any of these pieces of imformation too.
What is the formula for circumference of a circle?
πd
~3.14 * diameter
What is the forumal for the area of circle?
π(r)2
~3.14 * radius2
What is a fractional portion of a circle know as?
What is its portion of circumference called?
A sector (like a slice of pizza).
Arc length.
How do you calculate the sector area?
Central angle = 45
Radius = 5
Figure out the faction of the circle that the sector represents.
45/360 = 1/8
1/8π52 = (25/8)π
What are the four steps to solve a word problem?
- What do they want? (write down variable = ?) 2. What do they give me? (note any relationships or specific numbers.) 3. How do I turn this information into equations? (write down the information as an equation). 4. How do I solve the quations for the desired value (use algebra).
If you multiply two quantities that each have units…
Area = 6 feet x 9 feet
multiply the units too.
= 54 feet2
When a problem has multiple units in it…
How many hours are in two days?
you can cancel units in the same way numbers and variables do.
2 days * 24/hours / 1 day = 48 hours
the day units cancel each other
How do you convert from one unit to another?
How many seconds in 20 minutes?
Mulitiply by a conversion factor (fancy form of 1/1 with units on top and whole on the bottom) and cancel.
20 min * (60 sec / 1 min) = 1,200 sec
the minutes cancel each other
When express rates as time and distance…
It took Joe 4 hours to go 60 miles.
always put the time in the denominator.
60 miles / 4 hours = 15 miles per hour
The sum of any two sides of a tringle ______ than the third side.
Any side is _______ than the difference of the other two side lengths.
The sum of any two sides is greater than the third side.
Any side is greater than the difference of the other two side lengths.
The sum of all three interior angles of a triangle is _______.
180 degrees
On a triangle, the largest angle will be across from the ________ side.
largest angle will be across from the longest side.
like an alligator opening its mouth
What is an isoceles triangle?
A triangle that has 2 equal angles and 2 equal sides.
What is an equilateral triangle?
A triangle with 3 equal angles (60) and 3 equal sides.
What is the forumula for the area of a triangle?
1/2 base * height
any side of the triangle can act as the base, as long as the height is perpendicular to it.
What is a right triangle?
Any triangle in which one of the angles is a right angle (90 degrees).
What is the Pythagorean Theorem?
a2 + b2 = c2
For any right triangle where a & b are the legs and c is they hypotenuse.
What are the three most common right triangles on the GMAT?
3-4-5 (and 6-8-10)
5-12-13 (and 10-24-26)
8-15-17
What is a parallelogram?
Any 4 sided fiture in which the oppostie sides are parallel and equal. Opposite angles are also equal and the adjacent angles add up to 180 degrees. They can be divided into 2 equal triangles on the diagonal.
How do you calculate the perimeter of a parallelogram?
Add the lengths of all sides. Since the opposite sides are equal you just need one of the top and side lengths to calculate this.
How do you calculate the area of a parallelogram?
Base x Height
What makes a rectangle?
All 4 internal angles are right angles. (It’s a parallelogram with right angles.)
Rectangles may be cut into two right triangles with a diagonal.
What are the four steps to solving geometry problem?
- Redraw the figures, fill in all the given information, indentify the target (make note of any equal sides/angles).
- Identify relationships and create equations (the GMAT rarely provides extraneous info).
- Solve the equations for the missing value.
- Make inferences from the figures.
What is the formula for a line in a coordinate plane?
y = mx + b
b is the y-intercept (where the line crosses the y-axis)
m = slope of the line
How do you calculate the slope of a line?
rise / run = change in y / change in x
What is the formulate for weighted average?
WA = (weight * data point) + (weight * data point) + (weight * data point) …. / Sum of Weights
How many arithmetic operations will the right answer require on the GMAT?
at least two
When answers are spread out (and/or use the word “approximately) you can…
Round one number and the other one down to estimate an anwer.
How do you figure out the ratio of a weighted average problem?
Solution X at 40% strength and Y at 25% strength are mixed to create a 30% mixture. What is the ratio of the X & Y used?
Place 30% in the middle.
X is 10 away from the middle and Y is 5 away from the middle.
Swap the two.
5 X : 10 Y = 1: 2 Ratio
How do you find the first number in a string of 5 consecutive integers with a sum of 560?
x + (x+1) + (x+2) + (x+3) + (x+4) = 560
5x + 10 = 560
5x = 550
x = 110
Is 5! divisible by 5?
Yes!
5 * 4 * 3 * 2 *1
What is the forumla for the sum of interior angles for any polygon?
(n-2) * 180
Pentagon = 540
Hexagon = 720
What is the formula for the area of a trapezoid?
[(Base1 + Base2) * Height] / 2
What is the formula for the area of a Rhombus?
(Diagonal 1 + Diagonal 2) / 2
What is the formula for the length of the legs on an isoceles triangle?
45 - 45 - 90 Triangle
45 = x leg
45 = x leg
90 = x * sqr[2]
What is the formula for the lengths of legs on an equilateral triangle?
30 - 60 - 90 Triangle
30 (short) = x
60 (long) = x*sqr[3]
90 (hyponteneuse) = 2x
What is the formula for the diagonal of a square?
d = s*sqr[2]
s = side of square
What is the formula for the diagonal of a cube?
d = s * sqr[3]
s = side of cube
What is the formula for the diagonal of a rectangle?
h2 + w2 + l2 = d2
How do you calculate a central angle from the inscribed angle?
inscribed angle = 45 degrees
Double it.
45 x 2 = 90 degree central angle
What is the formula for surface area of a cylinder?
SA = 2(π * r2) + 2π*rh
What is the formula for the volume of a cylinder?
V = π*r2h
On a coordinate plane, how do you find the distance between two points?
Draw a right triangle with the points on the hyponteneuse.
Find the length of the legs by calculating rise over run.
Use the pythagorean theorem.
When a triangle is inscribed in a circle and one side of the triangle is the diameter it must be…
a right triangle.
How do you know if a number is divisible by 4?
If it’s divisible by 2 twice OR the last two digits are divisible by 4.
How do you know if a number is divisible by 6?
If it is divisible by 2 and 3.
How do you know if a number is divisible by 8?
If it is divisible by 2 three times or the last 3 digits are divisible by 8.
How do you know if a number is divisible by 9?
If the sume of the integer’s digits are divisible by 9.
What is GCF?
The greatest common factor. The largest divsor of 2+ integers.
If no primes in common, the GCF = 1.
Even +/- Odd =
Odd
Odd +/- Odd =
Even
In multiplication, how do you know if the result will be even or odd?
If any integer is even = even.
If all integers are odd = odd.
If you multiply 3 even integers, the product is divisible by ?
2, 4, 8
Even / Even will be …
Even (12/6)
Odd (12/4)
Non-integer (12/8)
Odd / Even will be…
Even (12/3)
Non Integer (12/5)
Odd / Even will be…
Non integer (9/6)
Odd / Odd will be..
Odd (15/5)
Non Integer (15/25)
The algebraic representation for odds and evens is…
Evens = 2n
Odds = 2n + 1 or 2n - 1
An exterior angle of a triange is equal to:
the sum of the two non-adjacent (opposite) interior angles of the triangle.
To divide 12.42 by 0.3
Move the decimal in the same direction until the divsor is a whole number.
124.2 / 3
To raise a decimal to a power of 4 or higher:
(0.5)4 =
Rewrite the decimal as the product of an integer and a power of 10: 0.5 = 5 x 10-1
Apply the exponent to each part: (5 x 10-1)4 = 54 x 10-4
Compute the first part and combine: 54 = 252 = 625
625 x 10-4 = 0.0625
Use the same method for roots of decimals (raise them a fractional power).
How many decimal points?
(0.04)3 =
Multiply the existing number of declimal points by the exponent.
2 places x 3 = 6 places
0.000064
How many decimal points?
cube root (0.000000008)
DIVIDE the number of existing decimals points by root.
9 places / 3 = 3 places
0.002
When dealing with a ration equation. How do you simplify and solve?
4 girls / 7 boys = x girls / 35 boys
You can simplify vertically or horizontall but never diagonally across the equal sign.
4 girls / 1 boy = x girls / 5 boys
cross multiply
4 girls * 5 boys = x
20 girls = x
