Algebra Notes: Wednesday 2/16/00

I. Vocabulary: evaluate    expression

like terms    combine like terms   

II. Simplify the expression.

1.) 3x + 5 - 2x - 4   Answers x + 1

2.) 3x² + 5x² - 8x² + 9x²   Answers 9x²

3.) x - 2 + x - 6   Answers 2x - 8

IV. Complete the computation.

4.) Add: - 5xy + 3yx   Answers - 2xy or - 2yx

5.) Multiply: (- 5xy)(3yx)   Answers - 15x²y² or - 15y²x²

6.) Subtract: - 5xy - 3yx   Answers - 8yx or - 8xy

7.) Divide:

- 5xy
-------
  3yx

  Answers -5/3

8.) Square: (- 5xy)²   Answers 25x²y² or 25y²x²

9.) Square: (3yx)²   Answers 9x²y² or 9y²x²

V. Evaluate the expression when x = - 3 and y = 2.

10.)     x² - y

Answer x² - y (x)² - (y) (-3)² - (2) 9 - 2 7

 

11.)     4x - y

Answer 4x - y 4(x) - (y) 4(-3) - (2) -12 - 2 -14

 

12.)     4x - 3y

Answer 4x - 3y 4(x) - 3(y) 4(-3) - 3(2) -12 - 6 -18

 

13.)     xy - (x + y)

Answer xy - (x + y) (x)(y) - ((x) + (y)) (-3)(2) - ((-3) + (2)) -6 - (-1) -6 + 1 -5

 

VI. Write an expression.

14.) one more than a number   Answers x + 1 or 1 + x

15.) one less than a number   Answers x - 1

VII. Homework: Complete questionbook assignments.

VIII. Placement of a Negative Sign in a Fraction

- 5        5	       5
-----  = ----- = - ----
  3       - 3       3

The first and the last are prefered.

Algebra Notes: Thursday 2/17/00

I. Write an algebraic expression

1.) one more than twice a number   Answers 2x + 1

2.) one less than a number   Answers x - 1

3.) twice the sum of a number and 1   Answers 2(x + 1)

II. Evaluate when x is -1 and y = 4

4.) 2x² + xy   Answers 2x² + xy 2(x)² + (x)(y) 2(-1)² + (-1)(4) 2 - 4 -2

5.) , read as "x to the y"   Answer

III. Combine Like Terms

6.) 3x - 6y + 5x - 5y   Answers 8x - 11y

7.) 9x² + 8x - 6x + 4x²   Answers 13x² + 2x

8.) xy² + x²y - 3x²y - xy   Answers xy² - 2x²y - xy

III. Vocabulary: distribute

IV. Calculator Techniques

Using STO to evaluate an expression.

    STO permits the user to store a constant value in the calculator so that its value may be used.

Ex. Evaluate 2x when x is 6

1st: Type 6 on the display.

2nd: Press the STO key.

3rd: Press the X key or ALPHA then X.

    The color of the ALPHA key is the same as the color of the printing of the letters above the keys.

4th: Press ENTER and the 6 appears on the display.

5th: Type 2x on the display.

6th: Press ENTER and 12 appears on the display

because 2(6) is 12.

Algebra Notes: Tuesday 2/22/00

I. Page 122, #49, #55, #53

II. Simplify.

1. a³ · a²

2. a⁴ · a¹

3. a^-4 · a⁵

4. a^-6 · a^-4

5. a² · a · a⁵ · a^-2 · a³

6. a⁵ ÷ a³

7. a⁵ ÷ a⁴

8. a⁵ ÷ a⁵

9. a⁵ ÷ a⁶

10. a⁵ ÷ a⁷

III. The Laws of Exponents

Algebra Notes: Wednesday 2/23/00

I. Vocabulary: term    coefficient

base    binomial    pi    exponent    literal exponent

II. page 129, #29, #35

Algebra Notes: Thursday 2/24/00

I. Without referring to your notes, state The Laws of Exponents

Ia. Vocabulary     exponent    radical sign    radicand    index    square root   

II. Simplify.

1. a⁴ ÷ a²   Answers a^2

2. a⁴ ÷ a³   Answers a

3. a⁴ ÷ a⁴   Answers a^0 = 1

4. a⁴ ÷ a⁵   Answers a^(-1) or 1/a

6. a⁴ ÷ a⁶   Answers a^(-2) or 1/(a^2)

7. a⁴ · a⁴ · a⁴   Answers (a^4)^3 = a^12

8. a² · a² · a² · a² · a²   Answers (a^2)^5 = a^10

 

9-.   Answers

10. 7^1/2 · 7^1/2 · 7^1/2 · 7^1/2   Answers (7^(1/2))^4 = 7^(4/2) = 7^2 = 49

IV. Vocabulary: distribute   

Simplify by order of operations and the distributive property

2(4 + 5) = 2 · 4 + 2 · 5
2(4)+2(5)= 8 + 10
8 + 10 = 18
  18 = 18

14.) Distribute     3( 4 + 5 - 6 - 3)

Answer 3( 4 + 5 - 6 - 3) 3(4) + 3(5) - 3(6) - 3(3) 12 + 15 - 18 - 9 0

 

15.) Distribute     3(x + 4)

Answer 3(x + 4) 3(x) + 3(4) 3x + 12

 

16.) Distribute by factoring     3x + 12

Answer 3x + 12 3(x) + 3(4) 3(x + 4)

 

VII. Homework:

pg 132 ex 1, 2 and side problems

pg 139 # 13 on