Math Final

Variables and Exponents: ab^-3 c^5 / b^2 a^2 c

ab^-3 c^5 / b^2 a^2 c ac^5 / b^5 a^2 c c^4/ b^5 a

Arithmetic Sequences: Find the 10th term of the sequence 1, 10, 19, 28

an = a + (n-1) X d a 10 = 1 + 9 X 9 a 10 = 1 + 81 a 10 = 82

Combining Like Terms: -2ab -3a +4 -4ab -2a

(-2ab + -4ab) + (-3a + -2a) + 4 = -6ab -5a + 4

Solving Two Step Equations: (1/8)a + 3/4 = 7/ 12

(1/8)a + 3/4 = 7/12 (3/24)a + 18/24 = 14/24 (3/24)a = -4/24 a = -4/24 X 24/3 a = -4/3

Complex Fractions: (1/m + 5) / (2/m - x/m)

(1/m + 5) / (2/m - x/m) (1/m + 5m/m) / (2 - x/m) 5m + 1/m X m/2 - x 5m + 1 / 2 - x

Pythagorean Theorem: Find m to the nearest tenth, height of 2, hypotenuse of 11, and a base of m

(11^2) - (2^2) = m^2 121 - 4 = m^2 117 = m^2 square root of 117 = 10.8 m = 10.8

Inputting Values: ab [-a(a - b)] a = 2 b = -1

(2)(-1) [-(2) ((2)-(-1))] = 12

Unlike Denominators: (3x^2 / x^2 - 25) + (x - 1 / 4x - 20)

(3x^2 / x^2 - 25) + (x - 1 / 4x - 20) (answer wrong will check with Mrs. Grogan)

Power Property of Exponents: (3y^4/4)^3

(3y^4/4)^3 27y^12/64

Dividing Polynomials: (6x + 5x^3 - 8) / x - 4

(6x + 5x^3 - 8) / x - 4 (5x^3 + 0x^2) - (5x^3 - 20x^2) (-20x^2 + 6x) - (-20x^2 - 80x) (86x - 8) - (86x - 344) 5x^2 + 20x + 86 + (336/x - 4)

Distributive Property: (fs/d^4)(fhs/d + 2sk - 7/d^6)

(fs/d^4)(fhs/d + 2sk - 7/d^6) (f^2 hs^2/d^5) + (2fs^2 k/d^4) - (7fs/d^10)

Multiplying Polynomials: (x - 5)(x -2)

(x - 5)(x -2) x^2 - 7x + 10

Adding and Subtracting Rational Expressions: (x/x+3) - (3/x^2 + 5x +6)

(x/x+3) - (3/x^2 + 5x +6) (x/x+3) - (3/(x+3)(x+2) (x(x+2)/(x+3)(x+2)) - (3/(x+3)(x+2) x^2 + 2x - 3/(x+3)(x+2) (x+3)(x-1) / (x+3)(x+2) x-1 / x+2

Dividing Polynomials: (x^2 - 10x + 25) / 7x^2

(x^2 - 10x + 25) / x - 5 (x-5)(x-5) / x - 5 x - 5

Slope Formula: Find the slope with points (-2, 7) and (2, -9)

(y1-y2) / (x1-x2) (7- -9) / (-2 -2) (7 + 9) / (-2 + -2) 16/ -4 -4

Solving Decimal Equations: -0.5a + 1.4 = 8.9

-0.5a + 1.4 = 8.9 -0.5a = 7.5 a = 7.5/-0.5 a = -15

Linear Equations: Solve by elimination 11x + 6y = 21 and 11x +4y = 25

-1 (11x + 6y = 21) = (-11x + -6y = -21) (-11x + -6y = -21) + (11x +4y = 25) -2y = 4 y = -2 11x + 6(-2) = 21 11x + -12 = 21 11x = 33 x = 3 (3, -2)

Adding and Subtracting Radical Expressions: -11 times the square root of 10a added to 3 times the square root of 250a added to the square root of 160a

-11 times the square root of 10a added to 3 times the square root of 250a added to the square root of 160a Reduce to -11 times the square root of 10a added to 15 times the square root of 10a added to 4 times the square root of 10a Add them together to get 8 times the square root of 10a

Locating and Using Intercepts: Find the x and y intercepts for -6x + 9y = 36

-6x + 9y = 36 -6(0) + 9y = 36 9y = 36 Y-intercept = 4 -6x + 9(0) = 36 -6x = 36 X-intercept = -6

Rational Equations: 12/2x + 16/4x = 5

12/2x + 16/4x = 5 6/x + 4/x = 5 6 + 4 = 5x 10 = 5x 2 = x

GCF: 18a + 45a^3 / 9a

18a + 45a^3 / 9a 9a (2 + 5a^2) / 9a 2 + 5a^2

GCF-ing Trinomials: 18fh - 240h + 6f^2h

18fh - 240h + 6f^2h 6h(f^2 + 3f - 40) 6h(f + 8)(f - 5)

Variables on Both Sides: 2 + 3(3a-6) = 5(a-3) + 15

2 + 3(3a-6) = 5(a-3) + 15 2 + 9a -18 = 5a -15 + 15 9a -16 = 5a -16 = 5a -9a -16 = -4a 4 = a

Compound Inequalities: 24 less than or equal to 2x + 8 less than 36

24 less than or equal to 2x + 8 less than 36 16 less than or equal to 2x less than 28 8 less than or equal to x less than 14 with a solid circle with a line segment ending with a clear circle

Simplifying Radical Expressions: Find the square root of 25x^3y^7

25x^3y^7 5xy^3 square root xy

Factoring: 2x^2 + 13x + 15 = 0

2x^2 + 13x + 15 = 0 (2x + 3)(x + 5) = 0 x = -3/2 x = -5

Completing the Square: 2x^2 + 6x = -6

2x^2 + 6x = -6

Percent of Change: What is the percent of decrease if the original price was $4.95 and now it is $3.87?

3.87/4.95 = x/100 3.87(100) = 387 387/4.95 = 78 100 - 78 = 22 22% decrease

Equation of Line With 2 Point: Write an equation with the points (2, -3) and (7, 4) in slope-intercept form

4 + 3/7-2 = 7/5 y - 4 = 7/5(x - 7) y - 4 = 7/5x - 49/5 y = 7/5x - 29/5 or y = 7/5x - 5 4/5

Independent and Dependent Events: A bag contains 4 red blocks and 3 blue blocks; what is the prob of drawing a red block, keeping it, and drawing another red block?

4/7 X 3/6 2/7 X 3/3 2/7 X 1 2/7 probability

Inequalities with Variables: 4x - 8 greater than -2x + 4

4x - 8 greater than -2x + 4 6x - 8 greater than 4 6x greater than 12 x greater than 2 with an open circle and a line going to the right

LCM: Find LCM of 6c^2 d^7 and 15c^5d

6c^2 d^7 = 2 X 3 X c^2 X d^7 15c^5d = 3 X 5 X c^5 X d 2 X 3 X 5 X c^5 X d^7 30c^5d^7

5 + [6 (2^3 + 4)]

77

Inequalities: 8( 6 times the square of 4 added to 5 times the square of 4)

8( 6 times the square of 40 added to 8(5 times the square of 4) 8(12) + 8(10) 96 + 80 176 X 2 352 ft

Grouping: 99x^3y - 33x^3 + 33x^2y - 11x^2

99x^3y - 33x^3 + 33x^2y - 11x^2 (99x^3y - 33x^3) + (33x^2y - 11x^2) 33x^3(3y -1) + 11x^2(3y - 1) (33x^3 + 11x^2)(3y - 1) 11x^2[(3x + 1)(3y - 1)]

Graphing Inequalities: Graph y is less than or equal to 3 1/3

Filled in circle on 3 1/3 with a line going to the left

Graphing Functions

Find the vertex and set the range less than or equal to / greater than or equal to then set the domain

Absolute Value Equations: I x-5 I + 3 = 3

I x-5 I + 3 = 3 I x-5 I = 0 {5}

Absolute-Value Inequality: IxI + 21 less than or equal to 14

IxI + 21 less than or equal to 14 IxI less than or equal to -7 {} or slashed 0

Characteristics of Quadratic Functions: Give the parabola's vertex, minimum/ maximum, domain, and range. y = x^2 - 10x + 22 (see graph on pg. 589 in your math book)

Vertex = 5 Minimum = -5 Domain = {all real numbers} Range = {y greater than or equal to -5}

Unit Multipliers: X in cubed over hr to X ft cubed over min

X in/hr times X in/hr times X in/hr times ft/ 12 in times ft/ 12 in times ft/ 12 in times hr/ 60 min

Relations and Functions: Write a function rule that tells how many pages the author has left to write before reaching page 400 if her rate is 30 pages/day

f(x) = 400 - 30d

Rates of Change and Slope: Find the slope

rise/run If it goes down the slope is negative If it is horizontal then it's 0/run If its vertical then it's rise/0 = undefined

Midpoint and Length of a Line Segment: Find the distance between (-3, -2) and (4, 2)

square root of (2- -2)^2 + (4- -3)^2 square root of 16 + 49 square root of 65 or about 8

Multiplying Radical Expressions: square root of 5 times (square root of 4 - the square root of 3)

square root of 5 times (square root of 4 - the square root of 3) square root of 5 ( 2 subtract the square root of 3) 2 times the square root of 5 subtracted by the square root of 15

Midpoint and Length of a Line Segment: Find the midpoint of the line segment ending with (-2, 3) and (4, 7)

x1 + x2 / 2 , y1 + y2 / 2 4 + -2 / 2 , 3 + 7 / 2 2/2 , 10/2 (1, 5)

Quadratic Formula: Use the quadratic formula to solve x^2 + 3x - 18 = 0

x^2 + 3x - 18 = 0 [-3 + or - the square root of 3^2 - 4(1)(-18)] / 2 -3 + or - the square root of 9 + 72 / 2 -3 + or - the square root of 81 / 2 -3 + or - 9 / 2 x = 3, -6

Graphing Linear Equations: Write an inequality for the region graphed (see page 651 of your math)

y less than or equal to 4

Inverse Variation: Is this an inverse variation? 3xy = 9

y= k/x 3xy = 9 y = 9/3x y = 3/x yes