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Triangle
- area= 1/2 of the base x the height
- A= 1/2 bh
perimeter= a+b+c
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square
- area= length x width
- A= lw
- perimeter= side + side + side + sidep= 4s
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rectangle
- area= length x width
- a= lw
- perimeter= 2 x length + 2 x width
- p= 2l + 2w
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parallelogram and rhombus
- area= base x height
- A= bh
- perimeter= 2 x length + 2 x width
- p= 2l + 2w
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Trapezoid
- Area= the sum of the two bases divided by 2 x height
- A= (b1+ b2/2) h
- p= a+ b1 + b2 + c
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cube
- volume= side x side x side
- v= s3
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rectangular
- volume = length x width x height
- v= lwh
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cylinder
- volume= ?r2 x height
- v = ?r2h
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simple interest
- interest = principal x rate x time
- i= prt
- rate= 3% per year x 5 years x principal= 300
- I= (300)(0.03)(5)
- I= $45
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1 square foot
144 square inches
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9 square feet
1 square yard
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1000 kilograms
1 metric ton
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multiply 3 times 6
(3)(6)
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P.E.M.D.A.S
3+5(6-3)=
3+5(3)
3+15
18
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P.E.M.D.A.S
4+(19-42)2
4+(19-16)2
4+(3)2
4+9
13
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P.E.M.D.A.S
23-(2*3)+(-4)
23-(6)+(-4)
23-10
8-10
-2
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P.E.M.D.A.S
3(10-6)(3-7)
3(4)(-4)
3(-16)
-48
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- round to nearest thousand 34,578
- 35,000
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- round to nearest tenth 12.8892
- 12.9
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4+(-8)+2+(-6)
-4+2+(-6)
-2+(-6)
-8
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subtracting a negative is the same as adding
6-(-3)
6+3=9
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subtracting a positive
6-(+3)=
6-3=3
- adding a negative is subtraction
- 5+(-7)=
- 5-7=-2
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two like signs become a positive sign +(+) -(-)
3+(+2)=3+2=5
6-(-3)=6+3=9
- two unlike signs become a negative sign +(-)
- 7+(-2)=7-2=5
- 8-(+2)=8-2=6
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(-5)(-3)(-2)=
(-15)(-2)
-30
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reduce to lowest terms
18*1
18*2
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fraction to decimal
0.75
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decimal to fraction
0.008=
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percent to decimal
9%
0.09
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what is 75% of 1,250
937.50
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25 is what % of 200
outside
0.125*100=12.5
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scientific notation
0.0002392=
2.392x10-4
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two unlike signs become a negative sign +(-)
(2.3x105)x(7.1x10-3)
(2.3)(7.1)=16.33
(105)(10-3)=2
16.33x102
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what is the square root of 100?
10
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what is the mean(average) of the following set of numbers?
12 14 18 22 45 78
(12+14+18+22+45+78)/6
31.5
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Last month, the librarian @ a library kept track of all books checked out. What % of all the books checked out last month were travel
7.5
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how many feet are in 2 miles
5280 feet = 1 mile
5280*2=
10,560
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how many square inches are in 3 square feet
432 square inch = 3 square feet
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how many quarts are in 3 gallons?
4 quarts = 1 gallon
4 quarts x 3 gallons
12 quarts
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how many meters are in 4 kilometers?
1 meter = 0.001 kilometers
4,000 meters
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how many grams are in 2.5 kilograms
1 gram = 0.001 kilograms
2500 grams
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4 kilograms is about how many pounds
1 kilograms = 2.2 pounds
4*2.2
8.8
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solve for x
25x = 200
x=8
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45x=15
0.33
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50x=3500
x=70
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interest = principal x rate x time
Martina has $300 in a savings account that pays simple interest at a rate of 3% per year. how much interest will she earn on that $300 if she keeps it in the account for 5 years?
I=(300)(0.03)(5)
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i=prt
5 years ago, Robin deposited $500 in a savings account that pays simple interest. She made no further deposits, and today the account is worth $750. What is the rate of interest?
750-500=250
250=500x5
250=2,500x
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i=prt
Ricardo bought a $1000 savings bond that earns 5% interest compounded annually. How much will he earn in 2 years.
principal = 1000;rate=5%; time= 2 years
yr 1 i=(1000)(0.05)(1) i = 50
new principal=1050
yr 2 i =(1050)0.05)(1) i= 52.50
total interest 50+52.50=102.50
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kim reads an average of 150 pages per week. at that rate, how many weeks will it take him to read 1800 pages.
150x=1800
x=12 weeks
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It takes 8 hours to fill a swimming pool that holds 3500 gallons of water. at that rate how many hours will it take to fill a pool that holds 8750 gallons?
3500x=(8)(8750)
x=20 hours
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an airplane travels the 1700 miles from Phoenix to Nashville in 2.5 hours. Flying at the same speed, the plane could travel the 2550 miles from Phoenix to Boston in how many hours?
1700x=(2.5)(2550)
1700x=6375
x=3.75 hours
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If a racing boat travels at a steady rate of 80 miles per hour, how many miles could it travel in 3.5 hours?
distance=rate x time
d=(80)(3.5)
d=280 miles
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Lilly's bill at a restaurant is $22 and she wants to leave a 15% tip. How much money should her tip be?
Tip=15% x $22
t= (0.15)(22)
t=$3.30
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Frederick ears 1500 per month at his job, but 28% of that money is deducted for taxes. What is his monthly take-home pay?
T=1500-(1500x0.25)
T=1500-(420)
T=1080
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40 is 80% of what #?
40=0.8x
0.8x=40
x=50
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Samantha earns $300 per month, but starting next month her salary will be $375. Her new salary will be what % increase over her current salary?
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On his 16th birthday, Brad was 60 inches tall. On his 17th birthday, he was 65 inches tall. What was the % increase in Brad's height during the year?
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At a certain store, every item is discounted by 15% off the original price. If Kevin buys a CD originally priced at 15 and a baseball cap originally priced at 11.50, how much will he save?
- 15+11.50=26.50
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one number is twice the size of another, and the two numbers together total(=) 150. What are the two numbers?
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Jessica is 26 years old. Two years ago she twice as old as her brother Ned. How old is Ned now?
Ned's age two years later=12+2=14years
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How many cups of milk are in 5 pints of milk?
Let x= the number of cups in 5 pint.
5 pints=x cups
1 pint= 2 cups
5x1pint=5x2cups
5pints=10 cups=x cups
x=10
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The u.s. treasury department spends 3.5 cents to manufacture every quarter 3.5 cents is what % of the value of the coin?
.14 or 14%
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If stuart is 5 feet 10 inches tall, what is his recommended weight?
1 feet= 12inch
12 feet*5=60+10=70
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It takes 200 lb of sugar cane to produce 5 lb of refined sugar. How many pounds of sugar cane does it take to produce 200 lb of refined sugar?
5/200=40
40*200=8000
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If 45 is 120% of a #, what is 80% of the same #?
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John=1 house in 2 days
Bob=1 house in 3 days
5x=6
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Tommy has 360 marbles in his collection. The ratio of black marbles to red is 2:7. How many marbles are red?
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rudy is training for a race. On monday he ran 2km. on tuesday he ran 15% farther than on monday. if he increases his running distance by the same % each day, on which day will he 1st run more than 4km.
15/100=0.15
- M-2km
- T-2km*0.15=0.3+2=2.3
- w-2.3*0.15=0.345+2.3=2.645
- th-2.6*0.15=0.39+2.6=2.99 or 3.0
- fr-3.0*0.15=0.45+3=3.45
- sat-3.45*0.15=0.51+3.45=3.96 or 4.0
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your salary is $600 per month, but after taxes & insurance are deducted, your monthly pay check is $444. What % of your monthly salary goes for taxes & insurance.
% is out of 100
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You worked 75 hours during July @ a pay rate of $12.50/hr. What were your total earning for the month before taxes & insurance
12.50*75=937.50
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Your walking to raise $ for your favorite charity. Your being sponsored by Sally @10 cents per mile, by Lucie @12 cents per mile & Kelsey @14cents. If you walk 8 miles, how much $ will you raise?
- 8*10=80
- 8*12=96
- 8*14=112
- 80+96+112=288
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You have save 150 quarters in a jar. Of that total, 25 were minted before 1970, 35 were minted between 1970 and 1980, and the remaining quarters were minted after 1980. If you pick a quarter out of the jar without looking, what is the probability the you will pick a quarter minted after 1980?
- 25+35=60
- 150-60=90
- 90/150=9/15=3/5
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What % of all the workers surveyed said that they take the bus to work?
bike-10
car-28
bus-16
sub-20
walking-6
10+28+16+20+6=70
16/70=0.22 or 20%
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In the town of RodPowersville, all the license plates have four characters. The 1st character is always an R or a P(2). The 2nd and 3rd(2) characters are digits between 0 and 9(10). The 4th character is a single letter of the alphabet from A to Z (26alphabet). How many possible license plates are there.
2*10*10*26=5200
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Patty is 45 years old. She is 15 years older than twice her daughter's age. How old is Patty's daughter?
d=daughter
45=2d+15
- 45-15=2d
- 30=2d
- d=15
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John wants to buy a new computer that costs $3280. He decides to use his own car and hire out as a taxi during the four months of summer. It costs him $693 to insure his car for those 4months. He spends $452 per month on gas. Assuming no other expenses, how many fares will he have to get before he earns enough money for the computer, if he charges an average of $7 per fare.
- $3280+693+(452*4)=
- 3280+693+1808=5781
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Jeanie has twice as many quarters(25) as nickels(5). She has a total of $8.25. How many quarters does she have?
- 5(x)+25(2x)=825
- 5x+50x=825
- 55x=825
- x=15
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Patrick was going to buy a car for $5800. The car dealer offered him two options for buying the car. He could pay the full amount in cash, plus 10% for tax and license, or he could pay $1000 down and $230 a month for 24 months, and the dealer would pick up the tax and license costs. Which is the better deal?
- cash 5800*0.1=580+5800=6380
- payment plan 230*24=5520+1000=6520
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Pop's House of Nuts offers a mixture of walnuts and almonds that sells for $6 per pound. If walnuts sell for 4.50 per pound and almonds sell for $7 per pound, what should be the weight of the walnuts in a 1-pound mix?
- 4.5x+7(1-x)=6
- 4.5+7-7x=6
- -2.5x+7=6
- -2.5x=6-7
- -2.5x=-1
- x=0.4
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A rectangle with an area of 60 square inches is 4 inches longer than it is wide. What is the width of the rectangle?
formula
a=wl
- 60=(w+4)w
- 60=w2+4w
- 0=w2+4w-60
- 0=(w-6)(w+10)
- w=6,-10
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