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Principles of Mathematics
The Story of 1
The world is a vast and complicated machine, made up of infinite numbers that provide
structure and stability. As is evidenced by the film, The Story of 1, the number one is the basis
for all of this.
MAT 160: College Algebra
Group 1: Domain
Domain is all the possible x values that will give you a y value
Ex. (1, 2) The domain in the ordered pair is 1.
Group 2: Range
The resulting y-values we get after substituting all possible xvalues.
MAT 160-01: College Algebra Course Calendar
Tuesdays: 12pm 2:50pm
Textbook: Functions and Change: A Modeling Approach to College Algebra (6 th Edition)
Week 1 Topics
A. Definition of a Funct
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FS-107-230 - Develop Conf & Skills in Math
Select a course.
1. If a person is dealt 5 cards from a standard deck of 52 cards, what is the probability (to four decimal places)
of being dealt 4 of a kind?
2. The hypergeometric distribution is a distribution of a variable that has two ou
Table 1: DCP aspect 1 = partial
a. Titration of standard NaOH against vinegar
Initial volume i I:m3
Volume of base required i om3 mm
Colour of solution at end point light pink dark pink
Table 2: DCP aspect 1 = partial
b. Titration of stand
5.1 5.4 VERIFYING TRIGONOMETRIC IDENTITIES
Hints for Verifying Identities
1.) Learn the fundamental identities given in section 5.1. Whenever you see either side of a fundamental
identity, the other side should come to mind. Also, be aware of equivalent f
5.5 TRIGONOMETRIC EQUATIONS
Solving a Trigonometric Equations
1.) Decide whether the equation is linear or quadratic in form, so you can determine the solution method.
2.) If only one trig function is present, first solve the equation for that function.
3.5 EXPONENTIAL GROWTH & DECAY; MONDELING DATA
Exponential Growth & Decay Models
The mathematical model for EXPONENTIAL GROWTH or DECAY is given by
f (t ) A0 e kt or A A0 e kt
where A0 is the original amount, or size at time t = 0, A is the amount at time
3.2 LOGARITHMIC FUNCTIONS
Recall that an exponential function is a one to one function and therefore has an inverse. The
inverse functions of the exponential functions are called logarithmic functions.
DEF: A LOGARITHMIC FUNCTION WITH BASE b is a function
5.4 PRODUCT TO SUM AND SUM TO PRODUCT FORMULAS
Product to Sum Formulas
Express as a sum of difference.
EX: sin8x sin4 x
cos8x 4x cos8x 4x
3.4 EXPONENTIAL AND LOGARITHMIC EQUATIONS
One to One Properties
bx b y
log b ( x) log b ( y)
b log ( x) x , x 0
if and only if x = y
if and only if x = y
log b (b x ) x
1.) If both sides can be w
3.1 EXPONENTIAL FUNCTIONS
DEF: An EXPONENTIAL FUNCTION f WITH BASE b is a function of the form f ( x) b x or
y b x , b > 0 and b 1, and x is any real number.
EX: Let f ( x) 15.41.4x 2 . Find f(6). Round to the nearest hundredth if necessary.
3.3 PROPERTIES OF LOGARITHMS
Properties of Logarithms
Let b, M and N be positive real numbers, b 1, and p and x be real numbers, then
1.) log b (1) 0
2.) log b (b) 1
3.) log b (b x ) x
4.) b log ( x) x , x 0
5.) log b (MN ) log b (M ) log b ( N ) .
Unit 6: Redox Reactions and Electrochemistry
Practice Set 1: Oxidation Numbers and Redox Reactions
1. Determine the oxidation number of each element in the following compounds.
1. Pure elements have an oxidation number of 0
2. If the c
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Chemistry 30 Revrew Handout DHH' nalists E, Page 11
Review of Chemistry 20 Stoiclu'ometry h t @ C53" -
1. If 15.4 niL of 0.236 moL/L hydrochloric acid is used to titrate 23.1 mL of sodium
Chemistry 30 Review Handout
Review at Science 10 Chemical Equations
For each of the followin
s - . .
equation. g tatements determme the reaction type and write a balanced chemical
l. I ' -
n 1774 Joseph PTICStly discovered oxygen by decomposing an