Beginning of the Year Math Problems (30 points) Answers
Answer the questions. Use a separate sheet of paper if necessary. Show all work
1) What is ten thousand times one hundred million? Show your work in scientific notation. Give the
answer in scientific notation and in words. 1 x 1012 or 100 x 1010; One trillion; terra; one times 10 to
the 12th power.
10,000
x
100,000,000
(1 x 104)
x
(1 X 108)_
4
10
x
108____
12
_________ 10 _____________
2) A population of deer had 325 individuals. If the population grows by 16% in one year, how many deer
will there be the next year? 0.16 x 325 = 52; 325 + 52 = 377
3) One year I had 124 AP Environmental Science students and the next year I had 87 Environmental
Science students. What percentage did the population of APES students decrease by (round to the
nearest tenth)? 124 – 87 = 37; 124/37 = 0.298 or 30% when rounded
4) Electricity costs 7 cents per kilowatt hour. In one month one home uses 1.8 megawatt hours of
electricity. How much will the electric bill be? (be sure to look at the prefixes chart on the previous
page for the conversion of kilo to mega) 1.8x 1,000 = 18,000; 18,000 x 0.07 = 126; $126
5) Your car gets 21 miles to the gallon and your friend’s car gets 28 miles to the gallon. You decide to go
on a road trip to the University of Virginia, which is 175 miles away. If gas costs $4 per gallon and you
decide to split the gas money, how much money will each of you save in gas by driving your friend’s
car? 175/28 = 6.25; 175/21 = 8.333; 6.25 x $4 = $25; 8.333 x $4 = $33.33: $33.33 - $25.00 =
$8.32; $8.32/2 = $4.16
6) Virginia Beach is about 20 miles wide and 28 miles long. If one inch of rain falls on Virginia Beach, how
many cubic feet of rain fell on Virginia Beach. (Hint: convert all units to feet first). 1 mile = 5280 feet;
20 x 5280 = 105,600; 28 x 5280 = 147,840; 1 inch = 0.0833333333; 105,600 x 147,840 x
0.0833333333 = 130,991,999
7) The concentration of mercury in a water supply changes from 10ppm (parts per million) to 56ppm over
a ten-year period. What is the percentage change of the mercury concentration? 56 – 10 = 46; 46/56
= 0.821428571; 82% or 46/100 x 56/100 = 46/100 x 100/56 = 46/56
8) Consider a wind turbine that is rated at 1.5 MW (megawatts). This means that with sufficiently high
winds, it will produce 1.5 MW or 1,500 kW (kilowatts) of power. If this wind turbine runs at its rated
power of 100% of the time for a full year, how much energy would it produce in a year? Give your
answer in kWh/year (kilowatt hours per year). 24 x 365 = 8760; 8760 x 1500 = 13,140,000 kw of
power
9) Show your work for the following multiplication and division problems. You can use a calculator to
check your work, but I want to see that you understand how to solve these problems by hand. Just like
on the AP exam, no credit is given if you don’t show your work.
a. 75.3 x 16.9 = 1272.57
b. 1964 x .0718 = 141.0152
75.3
16.9
6777
4518
+753__
1,272.57
1964
.0718
15712
1964
42748
0000___
141.0152
c. 5.80 x 10-3 x 2.17 = 5.8 x 0.01 x 2.17 = 0.12586
d. 2362 / 71.9 = 32.8511822
5.80
2.17
4060
580
1160_
12.5860
__32.8511822______
71.9) 2362000
215.7____
205.0
143 8___
6120
5752___
368 0
359.5_
85
7 1.9
13.1
71.9
59.10
575.2
158.0
143.8
14 2
12.5860
0.01
0.125860
e. .08 / .0094 = 8.510638298
f.
8.510638298____
.0094) 0.0800
0.0752_________
0.0048
0.0047_________
0.000100
0.000094
0.000006
4.60x104 / .0530 = 4.60 x 10,000/0.0530 = 46,000/0.0530 = 867,924.5283