1/25/15 Final Review Day 1

Algebra II

To remember everything in 1st Semetser!

Learning Objective

1. x = -10 y = 2Evaluate

Real #s – not imaginaryRational #s – can be written as a fraction , Irrational #s – cannot be written as a fraction Integer = ….-2, -1, 0, 1, 2, …Whole # = 0, 1, 2, 3…Natural # = 1, 2, 3…

2. Number Sets

3. -1 + 3(3x + 7) = 32 + 7x-1 + 9x + 21 = 32 + 7x9x + 20 = 32 + 7x2x = 12x = 6

Solve

4.

-2x + 9 = 21 or -2x + 9 = -21-2x = 12 -2x = -30

x = -6 x = 15

Solve

5.

or

Solve

6. Or or

or

7. Less thAND-10x – 8 < 38 And -10x – 8 > -38-10x < 46 And -10x > -30x > And x < 3x > And x < 3 Or

Solve

8. GreatOR

Or Or

Or Or

Solve

9. -88 < 6x + 4(x – 7) -88 < 6x + 4x – 28 -88 < 10x – 28 -60 < 10x -6 < xx > -6

Solve & Graph

10. {(-3, 4), (2, 4), (0, 1)}Domain: -3, 0, 2Is a function

Find Domain & Is it a Function?

{(-1, 2), (3, -2), (-1, 0)}Domain: -1, 3Is NOT a function, x = -1 repeats

11. Evaluate

-2𝑥2 𝑥¿30 −7

3−6−6125

𝑥¿ 𝑅

12. Standard Form Ax + By = CA = positiveNo Fractions!

4y – x = 3Multiply everything by -1!!x – 4y = -3

Write in Standard Form

13. Multiply everything by 3!2x – 15 = 12y2x = 12y + 152x – 12y = 15

Write in Standard Form

14. Slope Slope =

Find slope & x & y - intercepts

x-intercept (y = 0)-3x + 4(0) = 48-3x = 48x = -16(-16, 0) y-intercept (x = 0)

-3(0) + 4y = 484y = 48

y = 12(0, 12)

15. (-4, -11) & (-4, 14)

Find slope

= undefined(-14, 7) & (6, -18)

(10, -17) & (13, -17) = 0

16. Passes through (0, -2) and is perpendicular to y = 3x – 5Perpendicular slope = Point Slope Form Slope-Intercept Form

Write an equation of a line

17. Passes through (4, -3) and is parallel to Parallel slope = Point Slope Form Slope-Intercept Form

Write an equation of a line

18. Solve

(5)( ) (5)

0 = 6No Solutions!Parallel Lines!

19. Solve

(-2)( ) (-2)

0 = 0Infinite Solutions!Same Line!

20. Solve

3x + 8(3) = 93x + 24 = 93x = -15x = -5

15y = 45y = 3

(-5, 3)One Solution!

(2)( ) (2)

21. Solve by Substitution

5(7y + 11) + 4y = - 23 35y + 55 + 4y = - 2339y = - 78y = -2

Now plug y = -2 into either equation to solve for x.

x – 7(-2) = 11x + 14 = 11x = -3

(-3, -2)

Assignment:

Final Review Packet