Ch 10 - Mathematics

Question 1

What is scientific notation?

Answer 1

• a method of writing numbers in a way that improve the ease of calculations and the comparability of significant digits - takes the format [significand] x 10^[exponent]

Question 2

What are the requirements for the significand and the exponent in scientific notation?

Answer 2

• significand must be greater than or equal to 1 and less than 10
• exponent must be an integer

Question 3

What are significant figures?

Answer 3

include all nonzero digits and any trailing zeroes in a number with a decimal point

• measures are an exception, in that the last digit provided is not significant
• zeroes in front are not significant, zeroes at the end are if decimal present

Question 4

How are sig figs determined in addition/subtraction and multiplication/division?

Answer 4

• +/-: reduce the answer to have the same number of decimal places as the number with the fewest number of decimal places
• x./: reduce the answer to have the same number of sig figs as the number with the fewest number of sig figs
• the entire number should be maintained throughout calculations to minimize rounding error

Question 5

How are numbers rounded in multiplication and division?

Answer 5

x: if one number is rounded up, the other should be rounded down in proportion
/: if one number s rounded up, the other should also be rounded up in proportion

Question 6

What are exponents?

Answer 6

a notation of repeated multiplication (may be manipulated mathematically, especially when bases are the same)
X^a x X^b = X^a+b
X^a/X^b = X^a-b
(X^a)^b = X^axb
(X/Y)^a = X^a/Y^a
X^a/b = b x square root (X^a)

Question 7

What are logarithms?

Answer 7

the inverse of exponents and are subject to similar mathematical manipulations
loga 1 = 0
loga A = 1
log A x B = log A + log B
log (A/B) = log A - log B
log A^B = BlogA
log (1/A) = -logA

Question 8

What is the natural logarithm?

Answer 8

which use base e can be converted into common base 10

log x = ln x/2.303

Question 9

How are sine, cosine, and tangent calculated?

Answer 9

• sin: opposite/hypotenuse
• cos: adjacent/hypotenuse
• tan: opposite/adjacent

Question 10

What are inverse trigonometric functions?

Answer 10

use the calculated value from a ration of side lengths to calculate the angle of interest

Question 11

What is the difference between direct and indirect repaltionships?

Answer 11

• direct: as one variable increases, the other increases in proportion
• indirect: as one variable increases, the other decreases in proportion

Question 12

What are the sin values of angles 0, 30, 45, 60, 90, 180?

Answer 12

0 = 0
30 = 1/2
45 = root 2/2
60 = root 3/2
90 = 1
180 = 0

Question 13

What are the cos values of angles 0, 30, 45, 60, 90, 180?

Answer 13

0 = 1
30 = root 3/2
45 = root 2/2
60 = 1/2
90 = 0
180 = -1

Question 14

What are the tan values of angles 0, 30, 45, 60, 90, 180?

Answer 14

0 = 0
30 = root 3/3
45 = 1
60 = root 3
90 = undefined 
180 = 0

Question 15

How to convert between Fahrenheit, Celsius, and Kelvin?

Answer 15

F = 9/5C + 32
K = C + 273