What is the reciprocal of

3π/ r²?

3π/ r²?

r²/3π

What is the reciprocal of zx

y/zx

√25 + 3√27 =?

5+ 3 = 8

What expression is equivalent to

x⁵x⁴ ?

x⁵x⁴ ?

x⁵⁺⁴

x⁹

x⁹

The perimeter, P, of a square may be found using the formula P=4√A, where A is the area of the square. What is the perimeter of a square with an area of 81 square inches?

4 x 9=

36 inches

36 inches

If x= -10,

then -x= ?

then -x= ?

-(-10)

10

10

What is the Transitive Property of Equality?

If one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity

(if a=b, and b=c, then a=c)

(if a=b, and b=c, then a=c)

What is the Reflexive Property of Equality?

Any quantity is equal to itself.

(For any number a, a=a)

(For any number a, a=a)

What is the multiplicative inverse property?

For every number a/b, where a, b ≠zero, there is exactly one number b/a such that the product of a/b and b/a is 1.

(⅔ •³⁄₂ = 6/6= 1)

(⅔ •³⁄₂ = 6/6= 1)

Which number disproves the statement below:

n² + 1 is a prime number for all numbers n.

n² + 1 is a prime number for all numbers n.

When n= 3,

n² + 1

3² + 1

9 + 1

10

n² + 1

3² + 1

9 + 1

10

If x is an integer, what is the solution set to 4ΙxΙ = 16?

x = { -4, 4}

Use the distributive property to simplify the following equation

3(3-2x) = 5-4(2-3x)

3(3-2x) = 5-4(2-3x)

9-6x= 5- 8+12x

9- 6x= -3 + 12x

+3 +3

12 - 6x = 12x

+6x +6x

12 = 18x

9- 6x= -3 + 12x

+3 +3

12 - 6x = 12x

+6x +6x

12 = 18x

Simplify

8- 2x > 5(x-4)

8- 2x > 5(x-4)

8- 2x > 5x-20

+20 +20

28 -2x > 5x

+2x +2x

28 > 7x

⎯ ⎯

7 7

4 > x (or x<4)

+20 +20

28 -2x > 5x

+2x +2x

28 > 7x

⎯ ⎯

7 7

4 > x (or x<4)

Solve the following

4 = 2

⎯ ⎯

x x-1

4 = 2

⎯ ⎯

x x-1

Cross multiply

4(x-1) = 2x

4x - 4 = 2x

-4x -4x

-4= -2x

2 = x

4(x-1) = 2x

4x - 4 = 2x

-4x -4x

-4= -2x

2 = x

Simplify the following

2-x > 2(x-3)

2-x > 2(x-3)

2-x > 2(x-3)

2-x > 2x -6

+6 +6

8 - x > 2x

+x +x

8 > 3x

8/3 >x (or x< 8/3)

2-x > 2x -6

+6 +6

8 - x > 2x

+x +x

8 > 3x

8/3 >x (or x< 8/3)

The cost, c, in dollars of renting the pool for a pool party for h hours is

c= 50 + 10h.

IF the total cost was $100, for how many hours was the pool rented?

c= 50 + 10h.

IF the total cost was $100, for how many hours was the pool rented?

c= 50 + 10h

100= 50 + 10h

-50 -50

50 = 10h

⎯ ⎯

10 10

5 = hours

100= 50 + 10h

-50 -50

50 = 10h

⎯ ⎯

10 10

5 = hours

A 10-foot-long board is cut into two pieces. The first piece is 2 feet longer than the second piece. What is the length of the longer piece of board?

x + x + 2 = 10

2x + 2= 10

2x = 8

x= 4

x+2= 6

2x + 2= 10

2x = 8

x= 4

x+2= 6

What is the

y-intercept of the graph of

3x + 2y = 6?

y-intercept of the graph of

3x + 2y = 6?

Make x= 0

2y = 6

y= 3

(o,3) is the answer

2y = 6

y= 3

(o,3) is the answer

What is the x-intercept of the graph of x + 4y = -8?

Make y = 0

x = -8

(-8, 0) is the answer

x = -8

(-8, 0) is the answer

What is the

y-intercept?

y-intercept?

The y-intercept is where the graph of the equation crosses the y-axis. (Where x= 0)

What is the

x-intercept?

x-intercept?

The x-intercept is where the graph of the equation crosses the x-axis. (Where y = 0)

What is the equation of the line that has a slope of 3 and passes through the point

(2, -4) ?

(2, -4) ?

y - (-4) = 3(x-2)

y+4= 3x-6

y= 3x-10

y+4= 3x-6

y= 3x-10

What is the point-slope form?

y - y1 = m(x- x1)

where (x1 , y1) is a point on the line &

m= slope

where (x1 , y1) is a point on the line &

m= slope

What is the slope-intercept form?

y = mx + b

Where m = slope &

b= y-intercept

Where m = slope &

b= y-intercept

What is the slope of a line?

The slope of a line is the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run) as you move in the positive direction

Slope = rise= y2-y1

⎯⎯ ⎯⎯⎯

run = x2-x1

Slope = rise= y2-y1

⎯⎯ ⎯⎯⎯

run = x2-x1

What is the standard form of a line?

The standard form of a linear equation is

Ax + By = C

Where A ≥0, A & B are not both zero, & A, B, C are integers with a GCF of 1.

Ax + By = C

Where A ≥0, A & B are not both zero, & A, B, C are integers with a GCF of 1.

Which point lies on the line defined by

2x + 5y = 15?

(2,0) (2, 5)

(5,0) (5, 1)

2x + 5y = 15?

(2,0) (2, 5)

(5,0) (5, 1)

(5, 1)

What is the slope of a line parallel to the line y= -2/3 x + 5?

-2/3

(parallel lines have the same slope).

(parallel lines have the same slope).

Parallel lines have the _______ slope.

SAME

The slopes of perpendicular lines are ____ ___.

Opposite reciprocals

(or negative inverse)

ex. ⅖ and -5/2

(or negative inverse)

ex. ⅖ and -5/2

When you have a system of two linear equations with two variables, what are the three ways you can solve them?

By elimination, substitution, or by graphing (which requires you to create a table).

Solve the following:

2x⁴

⎯⎯ =

6x⁸

2x⁴

⎯⎯ =

6x⁸

2x⁴ 1 1

⎯⎯ = ⎯⎯⎯ = ⎯⎯

6x⁸ 3x⁸ˉ⁴ 3x⁴

⎯⎯ = ⎯⎯⎯ = ⎯⎯

6x⁸ 3x⁸ˉ⁴ 3x⁴

(6x²+3x+2)-(2x²-4x+1)=

6x²+3x+2

-2x²+4x-1

⎯⎯⎯⎯⎯⎯⎯

4x2 +7x +1

-2x²+4x-1

⎯⎯⎯⎯⎯⎯⎯

4x2 +7x +1

The length of a rectangle is 4 units longer than the width. Which expression could be used to represent the area of the rectangle?

Area= length x width

A= w(w+4)= w² +4w

A= w(w+4)= w² +4w

What is the factored form of

2x²- 2xy-12y²?

2x²- 2xy-12y²?

Pull out the common factor first...

2x²- 2xy-12y²=

2(x²- xy-6y²)=

2(x +2y)(x- 3y)

2x²- 2xy-12y²=

2(x²- xy-6y²)=

2(x +2y)(x- 3y)

What does it mean to "complete the square"?

Complete the square means to rewrite the equation so that the left side is a perfect square.

What is a quadratic equation?

A quadratic equation is an equation of the form ax² + bx + c = 0, where a 0.

AND

_________

x = -b ±√b²-4ac

⎯⎯⎯⎯⎯⎯⎯⎯⎯

2a

AND

_________

x = -b ±√b²-4ac

⎯⎯⎯⎯⎯⎯⎯⎯⎯

2a

Justin can mow a lawn in 2 hours. David can mow a lawn in 3 hours. How long will it take them to mow one lawn together?

Since they are working together, it will take less time than either of them alone.

½t + ⅓t= 1

3/6t + 2/6t =1

⅚t= 1

t= 6/5 hours

½t + ⅓t= 1

3/6t + 2/6t =1

⅚t= 1

t= 6/5 hours

What is the formula for rate problems?

d= rt,

"d" is distance, "r" is rate, and "t" is time.

"d" is distance, "r" is rate, and "t" is time.

What defines a function?

In a function, each x-value must be mapped to only one y-value.

What is a variable?

Any letter used to represent a number or set of numbers

What is the domain?

The first numbers of the ordered pairs in a set; all the x-values in a line

What is the range?

The second numbers of the ordered pair in a set; all the y-values in a line.

In a graph, what is the vertical axis called?

The y-axis

In a graph, what is the horizontal axis called?

The x-axis

What is the independent variable?

The variable in a function with a value that is subject to choice; usually graphed on x-axis.

What is the dependent variable?

The variable in a relation with a value that depends on the value of the independent variable; usually graphed on the y-axis.

What is the range of the function shown below?

{(2,3), (-1,5), (3,1), (1,0)}

{(2,3), (-1,5), (3,1), (1,0)}

The range is the set of y-values:

{0,1,3, 5}

{0,1,3, 5}

What is the domain of the function shown below?

{(2,3), (-1,5), (3,1), (1,0)}

{(2,3), (-1,5), (3,1), (1,0)}

The domain is the set of x-values:

{-1, 1, 2, 3}

{-1, 1, 2, 3}

When looking at a graph, how do you determine whether a relation is a function?

Use the vertical line test.

If a vertical line can be drawn so that it crosses the graph in more than one point, then the graph is NOT a function.

If a vertical line can be drawn so that it crosses the graph in more than one point, then the graph is NOT a function.

What are the steps to "completing the square"?

Step 1: find ½ of "b", the coefficient of "x."

Step 2: Square the result of Step 1.

Step 3: Add the result of Step 2 to x²+bx, the original expression.

Step 2: Square the result of Step 1.

Step 3: Add the result of Step 2 to x²+bx, the original expression.

In the Quadratic Formula, what is the "discriminant"?

The discriminant is the expression under the radical sign,

b2 - 4ac

b2 - 4ac

What is the hypothesis of the following statement?

If it is raining, then the pool is closed.

If it is raining, then the pool is closed.

The hypothesis follows the word "if":

It is raining.

It is raining.

What is the conclusion of the following statement?

If it is raining, then the pool is closed.

If it is raining, then the pool is closed.

The conclusion follows the word "then":

The pool is closed.

The pool is closed.