Algebra 1 Review

Conceptual

100

What is a solution to an equation?

A solution is the number or set of numbers that makes the equation true.

200

What does the line of an equation represent?

All possible solutions to a particular equation.

300

What is a solution to a system of equations?

The point in which both equations share.

400

What are intercepts on a graph?

Where the line crosses one of the axes (x-axis, y-axis)

500

What does the slope of an equation represent and how do you find it?

The slope is the rate a change of the equation.

You find the slope using the slope formula,        (y₂-y₁)/(x₂-x₁)

Functions

100

What is a function?

For an equation to be a function, every input must have exactly one output. (Passes the vertical line test)

200

What is the domain AND range or a function?

The domain is all the possible x-values that a function has.

The range is all the possible y-values that a function has.

300

Create a table for the following function: f(x)=x²+6. Let your x values be {-2, -1, 0, 1, 2}

(-2, 10) (-1, 7) (0,6) (1,7) (2,10)

400

Create a table for the function: f(x)=-2^x+26. Let your x values be {0, 1, 2, 3, 4, 5}

(0,25) (1,24) (2,22) (3,18) (4,10) (5,-6)

500

What is the vertex for the following function: f(x)=67(x-8)²-9.

Vertex (8,-9)

Solving Equations

100

Solve for x. 4(x-10)=120

x=40

200

Solve for x. 3x-2(6x+14)-10=34

x=-8

300

Solve for x. -2(3x-6)+5x=6(x+7)+5

x=-5

400

Solve the system using substitution. 

2x-4y=-4

y=7x-25

(4,3)

500

Solve the system using Elimination. 

8x-2y=10

2x+2y=20

(3,7)

Polynomials

100

Simplify the following Expression. 

(2x³y⁴)⁶

64x¹⁸y²⁴

200

Simplify the following Expression.

4x⁷/8x²

x⁵/2

300

Simplify the following Expression.

(2x+1)(6x²+5x-7)

12x³+16x²-9x-7

400

Simplify the following Expression.

(x²-x-1)(2x²+2x+2)

2x⁴-2x²-4x-2

500

Simplify the following Expression.

(16x¹⁰y³/3z⁷)

(16x¹⁰y³/3z⁷)

Slope

100

Find the slope of the two points: (-2,3) (6,-9)

-3/2

200

Find the slope of the following two points. (5,6) (-4,-12)

2

300

Write an equation in slope-intercept form using the given points. (8,-5) (-4,4)

y=(-3/4)x+1

400

Write an equation in slope-intercept form using the given points. (-6,8) (2,0)

y=-x+2

500

Write an equation in slope-intercept form using the given points. (6,4) (-4,-46)

y=5x-26