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GED Math crash course
GED math test principles and formulas
184
Mathematics
12th Grade
02/18/2018

Additional Mathematics Flashcards

 


 

Cards

Term
formula for the circumference of a circle
Definition
3.14 x diameter
Term
formula for the volume of a box (rectangular prism)
Definition
length x width x height
Term
formula for the area of a triangle
Definition
1/2 base x height
Term
formula for the area of a square or rectangle
Definition
length x width    often called  base x height or bh
Term
number of degrees inside a parallelogram (square, rectangle)
Definition
360
Term
number of degrees inside a triangle
Definition
180
Term
surface area of a box
Definition

2(surface area of front)

2(surface area of left side)

2(surface area of the top)   added together

Term
volume of a cylinder
Definition
3.14 x r x r x height
Term
volume of a  cone
Definition
a cone is 1/3 a cylinder  =   3.14 x r x r  x h/ 3
Term
volume of a pyramid
Definition
l x w x h/3
Term
surface area of a sphere (ball)
Definition
Find the surface area of the interior circle x 4
Term
surface area of a cone
Definition

3.14 x r x s +  area of the base

 

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

Term
solve   2x =6
Definition

divorce and divide

 

x =  3        which is 6/2

Term
Solve  x + 3 = 0
Definition

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

 

x =  -3

Term
solve  x/4 = 2
Definition

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

Term
Write 1,000 in scientific notation
Definition

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)

Term
Write .0001 in scientific notation
Definition

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

Term
RULE FOR MULTIPLYING SCIENTIFIC NOTATION
Definition

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

 

1 x 102  x  2 x 104  =  2 x 106

Term
RULE FOR DIVIDING SCIENTIFIC NOTATION
Definition

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

 

2 x 104

                  ________     =  2 x 102

1 x 102    

Term
rule for adding and subtracting scientific notation
Definition

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

Term
Pythagorean theorum finding the hypotenuse(longest side)
Definition

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

Term
Pythagorean theorum for a side other than the longest2
Definition

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

Term
how does the radius relate to the diameter
Definition
the radius is 1/2 the diameter
Term
.1  as a fraction
Definition
1/10
Term
.2 as a fraction
Definition
1/5
Term
.3 as a fraction
Definition
1/3
Term
.4 as a fraction
Definition
2/5
Term
.5 as a fraction
Definition
1/2
Term
.25 as a fraction
Definition
1/4
Term
.67 as a fraction
Definition
2/3
Term
.75 as a fraction
Definition
3/4
Term
.60 as a fraction
Definition
3/5
Term
.80 as a fraction
Definition
4/5
Term
100 cm =
Definition
1 m
Term
10 mm =
Definition
1 cm
Term
10 cm =
Definition
1 decimeter    1 dm
Term
How to convert metric units
Definition

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

 

 

Term

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?

Definition

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

Term
value of pi
Definition
3.14
Term
volume of a sphere
Definition
4/3 pi x r3
Term

Which math property is this?

 

a(b +C) =  ab  +ac 

Definition
We call this the distributive property where the value outside the parenthesis is multiplied by everyone inside or "distributed"
Term

What math property is this?

 

a + b = b + a

Definition

commutative property

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

Term

What math property is this?

A (B + C) =  (A + B) C

Definition
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. 
Term
Name the first 10 prime numbers
Definition

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

Term
What is the formula for calculating interest on a loan?
Definition

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

Term
Formula for distance, time, and speed problems
Definition

"dst"    dust formula with d on top

 

speed =  d/t

distance = st

time = d/s

Term
Cost formula????
Definition

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

Term

Percent increase or decrease

What formula

Definition

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

Term
How do you change a fraction to a decimal?
Definition
divide
Term

How do you change a decimal to a fraction?

 

 

Definition

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

Term
How do you change a decimal to a percentage?
Definition

move the decimal two places to the right

 

.30  =  30%

Term
How do you interpret a ratio problem?
Definition

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

 

Four out of five boys prefer football

 

4:5

Term
If given three numbers in a word problem, what do they probably want you to do especially in recipies?
Definition

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

 

 

 

Term
How do you know if two proportions are equal?
Definition

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

Term
How would you calculate the area between a shape inside another?
Definition

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

Term

Find the product of these two binomials

(x + 2)(x - 4)

Definition

Use FOIL

multiply first x first

multiply outside x outside

multiply inside x inside

multiply the last number in each parenthesis

 

x2 -2x-8

 

 

Term

Simplify this formula

6x2y  - 3x +2x2y  -2+7x + 15

Definition

Combine only terms that look alike

 

8x2y  +4x +13

Term

Factor this quadratic equation

 

x2 -4x -12

Definition

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)

Term

Find the slope of a line using two ordered pairs.

(2,4)  (-1,8)

Definition

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

Term

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

(0,4) with a slope of 2

Definition

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"

Term

How do you add and subtract decimals?

 

Definition
line up the decimal point
Term
How do you multiply decimals?
Definition

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

Term

How do you divide fractions?

 

Definition

flip the second one upside down and multiply

 

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

Term
How do you multiply fractions?
Definition

multiply straight across

 

1/2 x 1/3  =  1/6

Term
How do you add fractions with different denominators?
Definition

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

Term
How do you add or subtract mixed fractions?
Definition

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

Term
How do you find the surface area of a pyramid?
Definition

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

 

perimeter = distance all around the bottom

slant height will be marked "s"

Term

Find the next number in the sequence

 

2,4,16,____

Definition

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

Term
How do you answer a probability problem?
Definition

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

Term
How do you do probability with multiple activities at the same time?
Definition

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

Term
How do you do combinations with different items?
Definition

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

Term
How do you do permutations?
Definition

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.

Term

Know your slope formulas

x = 3

y = 3

y = 2x

y = 2x + 1

y = -2x +4

y = 1/2x + 2

Definition

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

Term
How do you solve a pair of linear equations?
Definition

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)

Term
How do you work with integers?
Definition

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

Term
What is absolute value?
Definition

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

Term
What do you do when there is a - sign in front of a parenthesis
Definition
change the sign of everything inside.......
Term

What are the first 15 perfect squares?

 

know these

Definition
1,4,9,16,25,36,49,64,81,100,121,144,169,196,225
Term
What are the rules for exponents?
Definition

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

 

Term
How would you solve √150√
Definition

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

Term

How would you write?

 

42/3

Definition

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

Term
How do you find the slope of a line graph?
Definition
If the x axis has a one mark go to it and go up and find the line.  This is the slope of the line.
Term
What is the formula for the slope of two dots?
Definition

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

Term

How do you simplify polynomial division problems?

 

60x3  + 30x

___________

5x

Definition

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

 

 

Term
Vertical angles
Definition

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

Term

supplementary angles

 

____ is supplementary to a 120*

Definition

two angles that add up to 180 or a straight line

 

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

Term

complimentary angles

 

___ is complimentary to a 62*

Definition

two angles that add up to equal 90 degrees

 

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

Term
What are the basic four angles of geometry?
Definition

straight ________  = 180

acute= less than 90

obtuse = more than 90

reflex = greater than 180

Term
How do you figure out all the angles when a line cuts across parallel lines?
Definition

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"

Term

How do you find the surface area of a cylinder?

 

12 cm tall with a radius of 4 cm

Definition

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

Term
formula for pythagorean theorum with hypotenuse wanted
Definition
square root of   A2  +  B2
Term
formula for pythagorean theorum with the hypotenuse given
Definition
square root of   C2  - A2
Term
What is the probability of getting all heads on four quarters at the same time?
Definition

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

Term

Find the missing number in the sequence

 

12, 8, 6, _____

Definition

5

 

Pattern is  -4   -2   -1

Term

Simplify the polynomial

 

4 x2y  + 3x - 7x2y  + 6x - 21 + x + 4

Definition
-3x2y + 10x -17
Term

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

 

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

Definition

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

Median =  two middle numbers averaged  =  12

Mode =  12

Term

Solve these word problems.

 

What percent is 18 of 20?

18 is 20 % of what number?

What is 17 % of 50?

Definition

Use the percent circle to solve all word problems.

 

first =  18/20  =90%

second answer =  18/.20 = 90

third answer =  50 x .17 =  85

Term

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

Angle 1 = 57

Angle 2 = 36

Angle 3 =  ?????

Definition

All interior angles of a triangle add up to 180.

Add the two known angles and subtract from 180.

180 -  57 + 36 =  87

Term

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

Angle 1 =  47

Angle 2 = 93

Angle 3 = 97

Angle 4 =  ??????

Definition

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

Term

What is the relationship between the two equations below?

(parallel or perpendicular)

 

y = 2x + 1     y = 2x -4

Definition
Linear equations that have the same slope are parallel lines.
Term

What is the relationship between the two linear equations below?

parallel or perpendicular

 

y = 2x + 4    y = -1/2x +4

Definition
Linear equations that show the negative reciprocal of the other lines slope are perpendicular.
Term
Susan is cooking a pie that requires 2 cups of sugar and 1/2 cup of flour.  If she sues 3 cups of flour, how many cups of sugar will she need to make 6 pies?
Definition

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

Term
If I am driving at 50 mi/hr, how miles could I drive in 6 hours?
Definition

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

 

50 mi/1 hour  =  x/6 hours

 

1 x = 50 x 6   =  300 miles

Term

Solve these integer problems

 

7-8=

7 --8

7-(2+4) =

4/-2 =

-2/-4 =

-8 x -8 =

Definition

-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

Term
What is the I -107 I ?
Definition
Absolute value is the distance a number is from zero , so the absolute value is 107..........it is always positive if the number is inside the brackets
Term
What is the value of -I 6 I ?
Definition
The absolute value is 6 but the negative on the outside makes the answer -6
Term
a number that can be expressed as a fraction
Definition
rational number

whole numbers can be rational because they can be shown as a fraction 2 = 2/1
Term
numbers that include both positive and negative forms including zero on a number line
Definition
integer
Term
numbers like square root of 2 or square root of 11 or pi that do not have repeating decimals
Definition
irrational number
Term
numbers that we use in everyday calculations that include rational and irrational numbers
Definition
real numbers
Term
How do you determine the total amount of all interior angles of any polygon?
Definition
N -2(180)

a square would have 4 angles
so 4 -2(180) = 360

a heptagon would have 7 -2(180) = 900
Term
How do you determine the individual amount of one interior angle of any polygon?
Definition
N -2(180)/N

N = number of angles

for a hexagon = 6-2(180)/6

720/6 = 120 degrees
Term
What is 600% of 20?
Definition
120 6.00 x 20 = 120
Term
Tim is 24 years less that 2x my age. I am 54. How old is Tim?
Definition
84
Term
7 more that 3 times something
Definition
3x + 7
Term
7 - - 8
Definition
15
Term
-2 + 12
Definition
10
Term
Which is bigger P or 1/P if P is a negative number?
Definition
1/P think about it -3 or -1/3

-1/3 is closer to zero
Term
Solve for A F = MA
Definition
A = F/M
Term
Solve for V D = m/v
Definition
V = m/D
Term
Solve for g D = 1/2gt
Definition
g =2D/t
Term
Evaluate the following: x =2 y=6
2x + 3y =
Definition
22
Term
Evaluate the following: x =2 y = 4

3x + 1/4y- 2 =
Definition
1/2
Term
2/3 x 3/2 =
Definition
1
Term
2/3 divided by 3/2 =
Definition
4/9
Term
vertical angles are always ________
Definition
equal
Term
angles on the same side of a bisecting line but inside parallel lines are called
Definition
co-interior angles
Term
co-interior angles always add up to ______
Definition
180
Term
co-exterior angles always add up to ____
Definition
180
Term
angles on the same side of a bisecting line but outside the two parallel lines are called
Definition
co-exterior
Term
angles on opposite sides of the bisecting line but within the parallel lines are called
Definition
alternate interior
Term
alternate interior angles are
Definition
the same
Term
what is the angle value of a straight line
Definition
180
Term
What is the angle value of a perpendicular line intersect?
Definition
90 degrees
Term
What is the name for an angle that is less than 90 degrees?
Definition
acute
Term
What is the name for an angle that is greater than 90 but less than 180?
Definition
obtuse
Term
What is the name for an angle that is greater than 180?
Definition
reflex angle
Term
What is the name of a triangle with three sides exactly equal?
Definition
equalateral
Term
What is the name for a triangle with two sides exactly equal?
Definition
isosceles
Term
What is the name of a triangle with no sides equal at all?
Definition
scalene
Term
What is the sum of the interior angles of a triangle?
Definition
180
Term
What is one of the best known ratios for a right triangle?
Definition
a 3...4...5 or variations of it

6...8...10
Term
What are the two most common angle patterns for right triangles?
Definition
90 .....45...45 Which means two sides were equal

or 90.... 30....... 60 which means the two sides were not equal
Term
I have a car with a speed of 70 mi/hr and it is traveling for 30 minutes?
What is its distance?
Definition
You must compare apples with apples
minutes must be converted to hours

.5 hr x 70 mi/hr = 35 mi.
Term
I am baking beans for a barbque dinner.
The original recipe calls for 2/3 cup of sugar for every 4 people. I am going to feed 80 people. How many supplies must I buy?
Definition
2/3 cup sugar/4 people = x/80 people
SET UP A PROPORTION AND CROSS MULTIPLY

4x = 2/3 x 80 NOW SOLVE FOR X

TO FIND THE NUMBER OF CUPS OF SUGAR NEEDED TO FEED 80
Term

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 _________

Definition

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

Term
A half circle sits on top of a rectangle with a width of 5 cm and a length of 10 cm.  What is the area of the whole composite shape?
Definition

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

Term
Rewrite   3-2
Definition
1/(3)2  or   1/9
Term
Rewrite   32/3
Definition
√(3)3
Term
Is a circular shape on a graph a function?
Definition
No , because it does not follow the vertical line test that says a vertical line only crosses a function once.
Term
Can a function have more than one output for an input?
Definition

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

Term

W4y10

_________

W8y6

Definition

y4

_____

W4

Term

9x2y4

_____________

6x-1y7

Definition

3x3

_______

2y3

Term
1/4 +  1/8 =
Definition

3/8

 

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

Term
1/4  x  1/8 =
Definition

1 x 1

___________=   1/32

4 x 8 

Term
1/4 divided by  1/8 =
Definition

flip the second fraction upside down and multiply =

1/4 x 8/1  =  8/4  =   2

Term
complimentary angles add up to ____
Definition
90
Term
supplementary angles add up to _____
Definition
180
Term
one angle of a vertical angle is 62, what is the other angle?
Definition
62
Term
The inside angles of a triangle are  x + 67, 90, and x + 37.  What is the value of x?
Definition

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.

Term
square root of  144
Definition
12
Term
square root of 196
Definition
14
Term
square root of 150
Definition

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

Term
x  *  x =
Definition
x2
Term
x * x * x =
Definition
x3
Term
What is the cube root of 8?
Definition

2

 

8 =  2 x 2 x 2

Term
What is the cube root of 27?
Definition

3

 

27 =  3 x 3 x 3

Term
What is the cube root of 64?
Definition

4

 

64 = 4 x 4 x 4

Term
What is the cube root of 125?
Definition

5

125 = 5 x 5 x 5

Term
What is the cube root of 216?
Definition

6

 

216 = 6 x 6 x 6

Term
What is 70?
Definition

1

 

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

Term
What is 121?
Definition

12

 

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

Term
What is 112?
Definition

121

 

11 x 11 =  121

Term
10 people are in a race.  We are giving 1st , 2nd, and 3rd ribbons.  How many permutations will this make?
Definition

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

Term
There are 11 people in a room, 4 are selected to be watchmen.  How many combinations are there?
Definition

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

Term
(3x3  + 2x2)  - (2x3 - 4x2)  =
Definition

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

Term
Which decimal means  1/3?
Definition
.33
Term
Which decimal means 2/3?
Definition
.66
Term
Which decimal means 4/5?
Definition
.80
Term
Which decimal means  1/4?
Definition
.25
Term
What is the volume of a  box with dimensions  3 x 5 x 10?
Definition

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

Term
What is the area of a triangle with a base of 10 in and a height of 5 in?
Definition

1/2 b h

 

5 x 5 =  25 in sq

Term
What is the area of a trapezoid with base 1 = 10 in,  base 2 = 20 in,  and a height of 5 in?
Definition

1/2(b1 + b2) h

 

1/2 (10 + 20)5

 

=  75 in sq

Term
What is the volume of a cylinder with a radius of  6cm and a height of 10 cm?
Definition

3.14 x r x r x h

 

3.14 x 6 x 6 x 10 =  113.04 cm2

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