What are you expected to know before beginning Geometry ?

1.  Know how to simplify an algebraic variable expression.

simplify    2x - 3x(2x - 5) + 7x

simplify    (3x - 4)^2

Show all work Distribute -3x Combine Like Terms

FOIL    (3x - 4)(3x - 4) Combine Like Terms

Did you get      24x - 6x^2

Did you get     9x^2 - 24x + 16

For examples, lessons, and practice, go to Purple Math.

2.  Solve linear equations with one variable.

Solve     (1/3)(27x + 18) = 12 + 6(x - 4)

For examples of solving multi-step linear equations like this one,                  click here.

Simplify first. Use opposite operations of + and - to get x-terms on one side and constant terms on opposite side of = sign.

Show all of your work. Did you get     x =  -6

3.  Graph a linear equation with 2 variables.

Graph the line described by the equation       2x - 3y = 6

method 1. Find the x-intercept and the y-intercept

method 2. Solve for "y" and use the slope and y-intercept

method 3.  Solve for "y" and make a table of values.

Try this link for help with graphing lines.

Purple Math

4.  Write the equation for a given line in the coordinate plane.

Write the Equation of this line.   Find 2 points on the line.   ( -3 , 1) and ( 2 , -3)             Find the slope     m = (-3 - 1) / (2 - -3)

m = -4 / 5

Use the slope and points in slope-intercept form y = mx + b        or in  point-slope form (y2 - y1) = m(x2 - x1)

to finish writing the equation of the line.

Did you get       y = (-4/5)x - (7/5)    or          (y - 1) = (-4/5)(x + 3)

For help on this now, go to Dr. Math

5.  Solve a system of linear equations to find the intersection of 2 lines.

y = 3x - 4      and     2x + 3y = 10                represent 2 different lines.

Find the point of intersecton of these two lines without graphing.

You could use substitution or linear combination to solve this system.

Substitution might be better for this system since the first equation is already solved for y.

Using Substitution would result in 2x + 3(3x - 4) = 10 Now solve for  x  then plug it back in to find y.

Did you get   ( 2 , 2)

If you need help with Systems of Equations, try one or both of these.

Substitution

Elimination or Linear Combination

6.  Solve a quadratic equation by 3 different methods.

by Factoring

by Quadratic Formula

Solve

by factoring

factor into 2 binomials  (x + 2)(x + 3) = 0

Set each factor = 0  then solve                { -2 , -3 }

Identify a, b, and c ,  plug in then simplify.

Factoring help

Good Luck, Work Hard

For help click here.

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