2(surface area of front)

2(surface area of left side)

2(surface area of the top)   added together

3.14 x r x s +  area of the base

Pi R S  + area of base  sounds like  "IRS"

divorce and divide

x =  3        which is 6/2

jump the deer and change the sign to get rid of a number

x =  -3

When a 4 or any number is in the bottom of a fraction, multiply it times the whole other side

x =  4 x 2 =      x = 8

find the decimal in 1,000.

move it to the left until there is only one whole number to the left of the decimal

Write it times the power of 10 ,  and the power is the number of jumps you made to get to the 1

1.0 x 10³

^{numbers bigger than one have positive powers or (exponents)}

Move the decimal until there is only one whole number to its left

count the number of jumps

numbers less than one have negative powers (exponents)

1.0 X 10^-4

"multiply the numbers......add the powers"

1 x 10²  x  2 x 10⁴  =  2 x 10⁶

"divide the numbers.......subtract the powers"

2 x 10⁴

                  ________     =  2 x 10²

1 x 10²    

YOU MUST HAVE BOTH NUMBERS IN THE SAME POWER BEFORE ADDING OR SUBTRACTING

"seesaw"   if you need a power to come up, the number must go down by one decimal place

1 x 10³  +  2 x 10²

The two power must come up to a "3".....so  2 becomes .2

1 + .2 =    1.2 x 10³

We leave them both in 10³ once both numbers have the same power

Use  A²  + B² =  C²

^{C is the hypotenuse}

^{A and B are sides of the triangle}

^{A triangle has sidea  3 cm and 4 cm.  What is the length of the third side?}

3² + 4² =  9 + 16 =25

Now we must find the square root of the added squares to solve   square root of 25 = 5        The unknown side is 5 cm

C² - B² =  A²

in other words you must subtract from the square of the hypotenuse when finding a side other than the hypotenuse

Hypotenuse = 5 cm   Side B =  4 cm  What is the length of side A?

5² -4² = A²

25 - 16 = 9= A²

To get rid of A².....you must take the square root of the other side     square root of 9 =  3 cm

King Henry died Monday drinking chocolate milk

Km  Hm  DAM  m  dm  cm  mm

Each jump to the left divides by 10.

Each jump to the right multiplies by 10.

How many m are in 1,000 mm?  jump left from mm to m...= 3 jumps ...which means divide by 1,000 =  1 m

1,000 mm/1,000  =  1

How many ft/yd?

How many ft/mile?

How many seconds/minute?

How many minutes/hour?

How many quarts/gal?

How many pints/quart?

How many cups/pint?

How many ounces/pound?

3 ft/yd

5,280 ft mile

60 sec/minute

60 minutes/hour

4 quarts/gal

4 pints/quart

2 cups/pint

16 ounces/pound

Which math property is this?

a(b +C) =  ab  +ac 

What math property is this?

a + b = b + a

commutative property

the order of the numbers does not change the answer if you use the same numbers

What math property is this?

A (B + C) =  (A + B) C

A prime number is divisible by itself and 1 only..........."1"  is not a prime number

2,3,5,7,11,13,15,17,19,23

Prt

Principal = cost of item

rate= percentage changed to a decimal

t= time   if the time is less than one year the time will be a decimal also

$1500 truck   4% interest    5 years=

1500 x .04 x 5  =  $300          interest over 5 years

"dst"    dust formula with d on top

speed =  d/t

distance = st

time = d/s

Cost =  number of items x price per item

Cost goes on top of circle

number goes on bottom left

price per item is on lower right

C = n x price per item

Number bought = cost/price

price = cost/ number bought

Percent increase or decrease

What formula

large number - small number

_______________________

original price

A jacket went from $30  to $40 over the last month.  What was the percent increase?

40 -30/30  =  10/30 =  .33

There was a 33% increase in the cost.

USE THE SAME FORMULA FOR DECREASE

How do you change a decimal to a fraction?

If  .1  (one digit) put it over 10

If .01 (two digits) put it over 100

If .001  (3 digits) put it over 1,000

move the decimal two places to the right

.30  =  30%

Write the ratio numbers in the same order they are in the sentence

Four out of five boys prefer football

4:5

Set up a proportion , this means make one fraction you know equal a fraction you don't fully know

Sarah is cooking a mean for 30 people.  The original recipe says to use 2/3 cup of milk for 10 people recipe.  How many cups will she need

We need two fractions and cups need to be in the same location in each fraction

2/3 cup/10 people  =  x cups/30 people

YOU WILL NEED TO CROSS MULTIPLY THE FRACTIONS

2/3 x 30 =10x          x = 2 full cups    for 30 people

When they are cross multiplied they will be equal

2     =   4

_______

4        8

2 x 8  =  4 x 4    They are proportional because the cross products are equal in value

Calculate the area of the larger object and subtract the area of the smaller object from it

Figures with two shapes are called composite figures

Find the product of these two binomials

(x + 2)(x - 4)

Use FOIL

multiply first x first

multiply outside x outside

multiply inside x inside

multiply the last number in each parenthesis

x² -2x-8

Simplify this formula

6x²y  - 3x +2x²y  -2+7x + 15

Combine only terms that look alike

8x²y  +4x +13

Factor this quadratic equation

x² -4x -12

Find numbers that will multiply together to make 12   but add together to make negative 4

(x +2)(x-6)

Now if you are asked to identify an ordered pair........set each part = 0 and give a pair of numbers

jump the deer

x =-2   x =6

(-2,6)

Find the slope of a line using two ordered pairs.

(2,4)  (-1,8)

Y - Y.............then   x -x  and start from the right parenthesis

8 - 2   =y difference

-1 -2 =  x difference

6/-3  =   slope of -2

Slope is rise divided by run or   difference in y divided by difference in  x

Find the formula of a line using one ordered pair and a slope.

(0,4) with a slope of 2

Slope intercept form  is   y = mx +b

m is always the slope

b is where the line crosses the y axis or the "y-intercept"

You find the y intercept by using the y from the ordered pair.   They gave you the slope so............

y = 2x +4

Remember.....slope is "married to x"

How do you add and subtract decimals?

Pretend that the numbers have no decimal and count at the end of the problem how many places are behind the decimal point and put the decimal this many spots from the right of the number

.30 x 100  = 3000    move the decimal two places left because of .xx

= 30

How do you divide fractions?

flip the second one upside down and multiply

1/2 divided by 1/4 =   1/2 x 4/1  = 4/2 = 2

multiply straight across

1/2 x 1/3  =  1/6

Find a common denominator

1/5 +  5/3    .... common denominator would be 15

1/5........15      3/15

5/3.........15    25/15

=    28/15

Step 1.....turn them into improper or regular fractions

Step 2...........find a common denominator

Solve like any other fraction problem

Example   2  1/4  change.......4 x 2 + 1  =  9/4

3 1/2  ....................2 x 3 +1                =  7/2

Then you can add them as any other fractions

1/2 perimeter x slant height +  area of the base

perimeter = distance all around the bottom

slant height will be marked "s"

Find the next number in the sequence

2,4,16,____

Find the difference between the first two numbers and look for a pattern

The pattern here is that the next number is the previous number squared  = 256

Find what is wanted / total possible

A spinner has 12 numbers on it.  What is the chance of hitting a multiple of 4?

multiples of 4  are    4, 8, 12   =  3

                             total  =      12

There is a 1/4 or 25% probability of hitting a multiple of 4

Example:   Two quarters are flipped,  what is the chance that both of them will turn up heads

Each quarter has a 1/2 change of being heads.......therefore multiply the probability of each object together.

1/2 first quarter  x  1/2  second quarter =  1/4  or  25% probability

A girl has 6 pairs of pants 4 pairs of shoes and 3 shirts.  How many different combinations of this wardrobe can she make?

multiply the items together

4 x 6 x 3 = 96 combinations

Permutations are lists where items can come in different orders.

Lets say 10 people have entered a race.  We are giving 1st, second, and third places.   How many ways can the race turn out?

Start with the total number of people

10 could win first

but only 9 could go for second

then only 8 could go for third

multiply these numbers together    10 x 9 x 8 =720 permutations or ways it could turn out.

Know your slope formulas

x = 3

y = 3

y = 2x

y = 2x + 1

y = -2x +4

y = 1/2x + 2

x = a number is  undefined

y = a number is   zero slope

y = 2x  goes through point of origin

y = 2x + 1  is positive slope up to right

y= -2x +4  is negative slope down to right

y= 1/2x + 4 is perpendicular to  y = -2x +4

formulas with like slope are parallel   Y =2x  and y = 2x +1

 negative inverse of a slope is perpendicular  2x vs  -1/2x

Make a t-grid and use the values  0,1  and plot the two dots you get for each equation

Where the two lines cross is the solution given as an ordered pair (4,2)

positive + positive = positive

negative + negative = negative

different signs multiplied = negative

like signs multiplied = positive

when a negative or positive number is larger.........."big guy gets the sign"

negative integers move you left on a number line

positive integers move you right on a number line

absolute value is always a positive value if not preceded by a negative on the outside

it is the distance a number is from zero

What are the first 15 perfect squares?

know these

2⁴ positive greater than 1   2x2x2x2  =16

3^-3 turn it into a fraction 1/3x3x3 =    1/27

x²  times x² =  x⁴   add exponents

when dividing subtract exponents

Find out which perfect square will go into it?

break it down into two square roots

√25  x  √6

=  5√6       there is no perfect square in 6 so we leave it

How would you write?

4^2/3

When you have a number to a fractional power put the first number under the square root and the other number outside

3√16 

The 3 on the outside should be the cube root of 16 which means    a number x a number x a number = 16

=  2.52  x  2.52 x 2.52 = 16

Rise divided by run

Rise = up and down

Run = across

lines with positive slope go up to the right

lines with negative slope go down to the right

How do you simplify polynomial division problems?

60x³  + 30x

___________

5x

When dividing x into x it leaves just a number

When dividing into a higher power subtract the powers

divide the bottom number into the numbers at the top

12x² +6

Vertical angles look like two angles pointing at each other like arrowheads  or they make a big "x"

vertical angles are equal at all times

supplementary angles

____ is supplementary to a 120*

two angles that add up to 180 or a straight line

if you know one angle, subtract from 180 to get the other

complimentary angles

___ is complimentary to a 62*

two angles that add up to equal 90 degrees

if you know one angle you can subtract from 90 to get the other angle

straight ________  = 180

acute= less than 90

obtuse = more than 90

reflex = greater than 180

All the small angles are the same.

All the large angles are the same as each other.

The small angles add to the large angles to equal 180 for each pair next to each other.

So lets say I show you a bisecting line crossing parallel lines and I show you one angle   36*

All the little small angles are 36

All the larger angles in the diagram are  36 + ____ = 180

= 144       "easy peasy"

How do you find the surface area of a cylinder?

12 cm tall with a radius of 4 cm

A cylinder if cut up into pieces makes a rectangle and two circles.

Find the area of the two circles first using  3.14 x r x r   x  2 circles

Next take 3.14 x diameter of the circle to get the circumference of the circle..............this is the same as the unknown side of the rectangle

area of rectangle + area of the circles = surface area of the cylinder

circles =  100.48 area   +  3.14 x 8 x 12 =301.44 area of rectangle    100.48 +301.44= 401.92 square units

Probability =  multiply the individual probabilities

Each quarter has a probability for heads of 1/2.

So..... Probability =  1/2 x 1/2 x 1/2 x 1/2  =  1/16

Find the missing number in the sequence

12, 8, 6, _____

5

Pattern is  -4   -2   -1

Simplify the polynomial

4 x²y  + 3x - 7x²y  + 6x - 21 + x + 4

Find the central tendency values for mean , median , and mode for the following set of numbers

6,8,12,12,16,25,

Mean = find the average  6+8+12+12+16+25/6  =  13.17

Median =  two middle numbers averaged  =  12

Mode =  12

Solve these word problems.

What percent is 18 of 20?

18 is 20 % of what number?

What is 17 % of 50?

Use the percent circle to solve all word problems.

first =  18/20  =90%

second answer =  18/.20 = 90

third answer =  50 x .17 =  85

Given two angles in a triangle, what is the missing angle?

Angle 1 = 57

Angle 2 = 36

Angle 3 =  ?????

All interior angles of a triangle add up to 180.

Add the two known angles and subtract from 180.

180 -  57 + 36 =  87

What is the missing angle in the quadrilateral given the angles below.

Angle 1 =  47

Angle 2 = 93

Angle 3 = 97

Angle 4 =  ??????

All interior angles of a quadrilateral add up to 360.

Add up the three angles and then subtract from 360 to find the missing angle.

angle 4 =  123

What is the relationship between the two equations below?

(parallel or perpendicular)

y = 2x + 1     y = 2x -4

What is the relationship between the two linear equations below?

parallel or perpendicular

y = 2x + 4    y = -1/2x +4

You must set up two fractions in a proportion using the fraction given in the original formula.

2 cups sugar/1/2 cup flour =  x/ 3 cups of flour

1/2X = 6

When you divide by a fraction , you must turn it upside down and multiply

x = 12 cups of sugar

Set up a proportion............or do it in your head

50 mi/1 hour  =  x/6 hours

1 x = 50 x 6   =  300 miles

Solve these integer problems

7-8=

7 --8

7-(2+4) =

4/-2 =

-2/-4 =

-8 x -8 =

-1  big guy gets the sign

15  double negative means add

1   distribute a negative to every item in a ()

-2  positive divided by negative = negative

1/2  negative divided by negative = positive

64   negative x negative = positive

A circle is located inside a square with side  10 inches.

Find the area of the circle______

Find the area of the square_______

Find the shaded area of the square that surrounds the circle _________

Area of circle  =  3.14 x 5 x 5 =  78.5 in  sq.

Area of square =  L x W  =  100 in  sq

Area of shaded section around circle =  square area - circle area  =    100 - 78.5 =  21.5  in sq

Rectangle =  L x W  =  10 x 5 =  50 in sq

Circle =  3.14 x r x r/2     since it is only half of a circle

= 3.14 x 2.5 x 2.5/2  = 9.81 in sq

Total area =  rectangle plus half circle =   50 + 9.81 =  59.81 in sq

No, there can only be one y value for  each x value.

Example:   1 cannot = 2    and later on  1 = 3

1   2

1   3

2   4

3    6

W⁴y¹⁰

^_________

W⁸y⁶

y⁴

_____

W⁴

9x²y⁴

_____________

6x^-1y⁷

3x³

_______

2y³

3/8

You must use the common denominator of 8 and then solve the addition of  2/8 + 1/8 =  3/8

1 x 1

___________=   1/32

4 x 8 

flip the second fraction upside down and multiply =

1/4 x 8/1  =  8/4  =   2

x + 67  + x + 37 + 90 = 180

2x + 194 = 180

2x = - 14

x = -7

We know they must add to 180 because the interior angles of a triangle add to 180.

find two numbers that will make 150 but one of them needs to be a perfect square

√25  x  √6

The solution will be 5 radical 6  or  5√6

2

8 =  2 x 2 x 2

3

27 =  3 x 3 x 3

4

64 = 4 x 4 x 4

5

125 = 5 x 5 x 5

6

216 = 6 x 6 x 6

1

Any number to the zero power = 1   always!!!!

12

Any number to the first power is itself.  Always!!!!

121

11 x 11 =  121

10 x 9 x 8 x7x6x5x4x3x2x1

________________________

7 x 6 x 5 x 4 x 3 x 2 x 1

cancel all numbers that look alike.....this leaves  10 x 9 x 8     =  720 permutations

11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

________________________________

7 x 6 x 5 x 4 x 3 x 2 x 1  (4 x 3 x 2 x 1)

=  11 x 10 x 9 x 8

                    ____________________     7920/24  =  330

4 x 3 x 2 x 1

Remember when subtracting polynomials to change the sign of everything in the (  ) following a - sign

rewritten it becomes

3x³  + 2x²  - 2x³  + 4x²

combine like terms  =   x³ + 6x²

you need to figure the front x 2

                    side x 2

        top  x 2 

Then add all the areas together

2( 3x 5)  = 30

2(3 x 10) = 60

2( 5 x 10) = 100             Total =  190 in sq

1/2 b h

5 x 5 =  25 in sq

1/2(b₁ + b₂) h

1/2 (10 + 20)5

=  75 in sq

3.14 x r x r x h

3.14 x 6 x 6 x 10 =  113.04 cm²