Download VisualMath by Jessika Sobanski PDF

TitleVisualMath by Jessika Sobanski
TagsTypes School Work
File Size3.7 MB
Total Pages270
Table of Contents
                            Table of Contents
Chapter 1 Number Concepts and Properties
Chapter 2 Fractions and Decimals
Chapter 3 Rations and Proportions
Chapter 4 Percents
Chapter 5 Algebra
Chapter 6 Geometry and Measurement
Chapter 7 Probability and Statistics
Chapter 8 Tables and Charts
Chapter 9 Test Your Math Skills
Document Text Contents
Page 1

visual math

Page 135

What we put into the A = P(1 + �n
�)nt formula:

� A is the total amount
� P is the original principal
� r is the rate
� n is the number of yearly compounds
� t is time (in years)

To find your “n” look out for these terms:
� compounded annually means interest is paid each year
� compounded semiannually means interest is paid two times per year
� compounded quarterly means interest is paid four times per year
� compounded monthly means interest is paid every month
� compounded daily means interest is paid every day

So, let’s look at an example. You open a savings account that pays 3% in-
terest semiannually. If you put in $1,000 initially, how much do you have af-
ter 2 years?

We use A = P(1 + �n
�)nt, and you substitute in the following values:

P = 1,000

r = 3%, or .03

n = 2 (compounded semiannually means twice a year)

t = 2

A = P(1 + �n
�)nt = 1000(1 + �.02


= 1,000(1 + .015)4

= 1,000(1.015)4

= 1,000(1.06)

= 1,061.36

= 1,061.37

Always round money to the nearest cent. Thus, you’d have $1,061.37.


Page 136

You ask: “What if I don’t want to memorize that scary formula?” Well, you have a
few options:

� You can do the calculation “the long way.” For example you would
know that after �12� a year, the $1,000 principal above would earn I =
PRT, or I = 1,000 × .03 × �12� = $15. Now the account has $1015. In
another �12� year you earn I = PRT = 1,015 × .03 × �

2� = 15.23, and you

would have $1,030.23. You would continue calculating in this manner
until you completed two years worth of money making.

� You can find out if there is a reference sheet that may contain this for-
mula (if you are taking a standardized test).

� You can use process of elimination on tests. Cross off any preposterous
answers and try to pick one that would make sense.

� TIP: In doing a compound interest test question, you know that a lot
of people would tend to accidentally solve it as if it were a simple inter-
est question. And you can bet the test designers know this! So, you can
cross off the answer that represents I = PRT (the simple interest for-
mula) and pick an answer that is greater.

Exercise 8: Evan opens a savings account that pays 5% interest quarterly. If
he put in $2,000 initially, how much does he have after six months?

algebraic percents

Let’s say that Jaclyn buys a printer for D dollars and gets a 20% discount. How
do you represent this mathematically?

Well, if Jaclyn is getting a 20% discount, she must be paying 80% of the orig-
inal price. What is the original price? D. So she is paying 80% of D. This is
just .8 • D, or .8D.

What if she was buying three items that cost D, E, and F dollars each, and
she was getting the same 20% discount on her entire order?

Well, without the discount, her cost would be (D + E + F ).

non-discounted = (D + E + F )

visual math128

Page 269

29. b. To figure out the probability for the given outcome, you need to cal-
culate the total possible outcomes. You know that the record com-
pany brought 300 hip-hop CDs, 500 alternative rock CDs, 200 easy
listening CDs, and 400 country CDs. The total possible outcomes
equal 300 + 500 + 200 + 400 = 1,400. The outcomes that fit the
criteria in the question = 200. This is because 200 easy listening CDs
will be given out. This means that the chance of getting an easy lis-
tening CD will be �1

0�. This reduces to �


30. c. Given log10 10
5, you spiral through and say:

The power would be 5, so log10 10
5 = 5.

31. b. The area of the square is s2 = 72 = 49. If you double the side, the
new area equals s2 = 142 = 196. 49 times 4 equals 196, so you
quadrupled the area. Notice that you can “see” this effect below:

Algebraically, any square that has its side doubled will also have its
area quadrupled because when you compare s2 to (2s)2 you get:

s2 versus (2s)2


s2 versus 4s2

4s2 is obviously 4 times the s2.

261test your math skills

Page 270

visual math262

32. b. You set up the proportion as follows:

�7 day
s p

week� = �1


Thus, choice b is correct.

33. d. You need to take V and add 25% of V. 25% = .25 or �1
0� = �

4�. Thus,

choice a, V + �14� V is true. This is the same as V + .25 V, which is
choice c. If you actually add choice c, you get choice b.

34. c. Note the dimensions of the label (when peeled from the can):

The area of the label will be L × W = circumference × 4 in. C =
2πr = 2 • �27

� • 3.5 = 7 • �27

� = 22 in. Thus, the area = 22 in × 4 in =

88 in2.

35. d. You need to find the area of the big (outer) circle and subtract the
area of the small (inner) circle. You draw in the radius of the “big”

You can also draw in the radius of the small circle:

The big circle has an area equal to A = πr2 = π(12)2 = 144π. The
small circle has an area of A = πr2 = π(8)2 = 144π. Thus, the area of
the shaded region is 144π − 64π = 80π ft2.

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