Term
How to find the
SUM OF CONSECUTIVE NUMBERS
(Ex: What is the sum of the integers from 10 through 50, inclusive?) |
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Definition
(Average) * (# of terms) = (Sum)
Ex:
Average = (10+50)/2 = 30
# of terms = 50 - 10 + 1 = 41
Sum = 30 * 41 = 1,230 |
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Term
How to solve a
COMPOUND INTEREST PROBLEM
(Ex: If $10,000 is invested at 8% annual interest, compounded semiannually, what is the balance after 1 year?) |
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Definition
(Principal) * (1 + r/C)T*C = (Final Balance)
where C is # of time compounded annually
and T is time.
($10,000) * [1 + (.08)/(2)](1)*(2) = $10,816 |
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Term
How to solve a
COMBINED WORK PROBLEM
(What is the limitation of this formula and
how can I solve it otherwise?) |
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Definition
The inverse of the time it would take everyone working together equals the sum of the inverses of the times it would take each working individually.
If the problem refers to different tasks (painting 1 house versus painting 4 houses, etc.) you should just compute man-hours or union-years, etc. |
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Term
How to solve a
GROUP PROBLEM INVOLVING BOTH/NEITHER
or a
GROUP PROB INVOLVING EITHER/OR CATEGORIES |
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Definition
Both/neither:
VENN DIAGRAM or
Group1 + Group2 + Neither - Both = Total
Either/or:
2x2-cross grid |
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Term
How to solve a PERMUTATION problem
(What is the formula?
&
Does order matter?) |
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Definition
nPk = n! / (n-k)!
where n = (# in the larger group) &
k = (# you're arranging)
Order matters (how many possible arrangements are there?) |
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Term
How to solve a COMBINATION problem
(Does order matter?
&
What's the formula?) |
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Definition
nCk = n! / k!(n-k)!
where n = (# in the larger group) &
k = (# you're choosing)
Order DOESN'T matter (How many different ways to choose k?)
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