Chapter 5: Word and Graph Interpretation Problems p. 285
Technique p. 287
1.
Identify what is being asked – and write it
down!
2.
Pull out given information – draw pictures,
write down key words
3.
Set up an equation – or a chart, a table, etc.
4.
Identify whether all given information is
necessary – ignore irrelevant information
5.
Solve the equation – check units, formulae, etc.
6.
Check that you answer the question asked – go
back to the question and make sure you answer what they asked for and aren’t
stopping too soon or answering the wrong part of the question
7.
Check your computation – plug in your answers,
check your calculations, etc.
Remember: There are no small mistakes!
Key words for addition, subtraction, multiplication, and
division p. 289-290
Formulae
Memorize these formulas for efficiency:
·
Simple Interest
o
Interest = Principle * Rate * Time, or I = prt
§
Principle: the amount invested
§
Rate: the interest rate, usually given as a
percentage or as a decimal
§
Time: usually annual (once a year), but could be
biannual (every two years), semiannual (twice a year), quarterly (four times a
year)
·
Compound Interest
o
Time consuming to calculate because at the end
of each period of time, the interest is added to the principle and then
recalculated for the next period of time
o
Compute simple interest for the first year (or
first time period if interest is compounded at a time other than annually)
o
Add the interest to the principle
o
Use the new principle to compute the next year
(or second time period)
o
Repeat until you have compounded as many times
as necessary
Formula from 3rd edition:
Future Total Value Amount = Principal * (1 + [interest rate/frequency number per year])^(frequency*number of years)
or in other words: the compounded total value equals the principal times the sum of 1 and the quotient of the interest rate divided by the frequency number per year, raised to the power of the product of frequency times the number of years
·
Ratio & Proportion
o
Usually set up as two fractions equal to each
other (e.g., x/y = a/b)
o
Solve through cross-multiplication
·
Motion
o
Distance = Rate * Time or d = rt (“dirt”)
o
Rate is velocity, speed, etc.
o
Equivalent equations:
§
Rate = Distance / Time or r = d/t
§
Time = Distance / Rate or t = d/r
o
Be careful about time! Most often, you are
looking for mph or miles per hour, but sometimes time is given in days,
minutes, etc. Remember: 24 hours to a day, 60 minutes to an hour, 60 seconds to
a minute
o
Be careful about conversions! If they give you
information in mph, but want an answer in kph, look for the suggested
conversion rate or refer to your memorized conversion: 1 km » 0.6
mi
·
Percent
o
Remember: is/of = % or in other words, x% of y
is z, so z/y = x%
o
All percentages are out of 100, and can be set
up in proportions with 100 to find the missing value
·
Percent Change
o
The formula is change/starting point = % change
o
Calculate the change from the starting point to
the new value through subtraction
o
Put the change over the starting point and
divide
o
Your answer is the percent increase or decrease
from the original value
·
Number
o
These are logic problems that require careful
attention to the wording and use of our arithmetic key words that we have
memorized
o
Note down what you are looking for so you can
double-check at the end
o
Use the problem to set up an equation
o
Solve the equation
o
Check your computation
o
Check that you solved for what you are looking
for
·
Age
o
Similar to number problems
o
Using a table to track the information can be
useful
o
Double check your computation
o
Double check that you solved for what the
question is asking
·
Geometry
o
Use memorized geometry formulas
o
Draw pictures!
o
Double check your computations
o Double check that you solved for what the question is asking
·
Work
o
The combined work formula is given as the sum of
fractions equal to a third fraction, which must be inverted to answer the
question “how long does it take them working together”
o
You are solving for T, a quantity of Time
o
A, B, C, etc. are the workers involved
o
1/A + 1/B = 1/T (for two workers) or 1/A + 1/B +
1/C = 1/T (for three workers)
§
This equation requires you to find a common
denominator to solve the equation
§
This equation assumes you have 1 unit of product
per every unit of time worked for each individual
§
Other ratios may be necessary if, e.g., one
person makes 5 pies for every 11 hours of work
§
When solving for T, you have to invert 1/T
o
For two people (or machines, or animals, etc.)
the simplified version will give you T without inversion: AB/(A+B) = T
o
For three people, the simplified version is
ABC/(AB + AC + BC) = T
·
Mixture
o
To my knowledge, the only formula is: the sum of
the total costs of each type equals the total cost of the mixture, or cost(type
1) + cost(type 2) = cost(mixture)
o
However, you can set up a table to help you
compute the missing information:
|
|
Cost per unit ($ per lb) |
Amount of units (# of lbs) |
Total cost of each ($) |
|
Type 1 |
|
|
|
|
Type 2 |
|
|
|
|
Mixture |
|
|
|
Alternatively:
|
|
Rate |
Amount of solution |
Amount of substance |
|
Solution 1 |
|
|
|
|
Solution 2 |
|
|
|
|
Mixture |
|
|
|
Another alternative:
|
Coin Type |
Number of coins |
Value of each |
Total Value |
|
Type 1 |
|
|
|
|
Type 2 |
|
|
|
|
Mixture |
|
|
|
Etc.
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