Weekly Notes for Algebra and Trigonometry
Algebra Notes

Chapter 10

10.1 Factors and Greatest Common Factors

I. Prime Numbers - a whole number greater than 1 whose only factors are one and itself. examples: 1, 2, 3, 19, 123 etc.
II. Composite Numbers - a whole number greater than 1 that is not prime. examples: 4, 6, 8, 222, 438 etc.
III.Prime factorization - the expression of a whole number in terms of prime factors. Example: the prime factorization of 12 is 2 x 2 x 3

Ex 1: Factor - 150 completely
-150 = -1 x 150
= -1 x 2 x 75
= -1 x 2 x 3 x 25
= -1 x 2 x 3 x 5 x 5

Ex 2: Factor 45y^3z^2 completley
45y^3z^2 = 3 x 15 x y x y x y x z x z
= 3 x 3 x 5 x y x y x y x z x z

IV. Greatest Common Factor (GCF) - the greatest common factor of two or more integers is the largest number that divides evenly into both numbers.
Ex 3: Find the GCF of 54, 63, and 180
54 = 2 x 3 x 3 x 3
63 = 3 x 3 x 7
180 = 2 x 2 x 3 x 3 x 5
They all have two 3's there fore 3 x 3 = 9 so 9 is the GCF
10.1 Homework: page 561-562 18-35 all, 36-52 even

Trigonometry Notes

Chapter 11

11.1 Arithmetic Sequence
I. An arithmetic sequences is a sequence where each term after the first is found by adding a constant called the common difference.
II. A sequence is a set of numbers called terms.

Ex 1: Find the next four terms in this arithmetic sequence
91, 83, 75, __, __, __, __
ANS: 67, 59, 51, 43 (decreasing by 8)

III. Formula for the nth term of an arithmetic sequence
an = a1 + ( n - 1 ) d
where an is the nth term, a1 is the first term, n is the number of the term, and d is the common difference.

Ex 2: Find the 12th term if a1 = 3 and d = 7
an = 3 + (12 - 1)7
an = 3 + 77
an = 80
11.1 Homework page 656 28-41 all

11.2 Arithmetic Series
I. An arithmetic series is the sum of and arithmetic sequence.
If a sequence is 1, 5, 9, 14 then the corresponding series is 1+5+9+14.
II. Sn is the sum of the first n terms.

Ex 1: What does S3 mean?
ANS: The sum of the first three terms.

III. Formula for finding the sum of the first n terms.
Sn= n/2(a1 + an) where n is positive.

Ex 2: Find the sum of the first 50 positive even integers.
therefore: n = 50, the first term = 2, the last term = 100
S50 = 50/2(2 + 100)
25(102) = 2550

11.2 Homework page 660 16 - 34 all Click Here to return to the Home Page.