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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