Algebra 2 – exponential functions

Q: In 2010, River City had a population of 500. If the population has increased by 6% each year since then, what is the population this year, in 2014?

Answer: 631

Explanation:

Alternatively,

Calcululate 6% of 500 by doing .06 * 500 = 30.

Increase 500 by 30, and you find that the population is 530 in 2011.

Now, increase 530 by 6% (530*.06, added to 530, or shortcut is to do 530*1.06).

The population is 561.8 in 2012. Don’t round this number yet – not until you get to the end of the problem.

Doing this calculation 2 more times gives you 595.508 for 2013 and 631.23… for 2014.

Now, round to the nearest whole number: 631. It’s not the most efficient way, but you get the right answer.

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Precalculus – Probability

Q: In a group of 10 randomly chosen people, what is the probability that at least two people share the same birthday? (same month and day)

Answer: 12% 

Explanation: (For simplicity, this explanation doesn’t take into account people with leap-day birthdays, but it wouldn’t change the answer by much!)

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Trig / Precalculus – convert degrees to radians

Q: Convert from degrees to radians:  330°

Answer:

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Explanation:

 

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My TI-84 Plus program ‘DEG2RAD’ will convert this for you.

 

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Geometry – Triangles

Q: In triangle ABC below, what is sin C ?
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Answer: 4/5
Explanation:  Use the Pythagorean Theorem or the 3-4-5 Pythagorean triple to find out that the hypotenuse is 10.
Then, sin C = (opposite)/(hypotenuse) = 8/10 = 4/5.
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