Download Algebra Review Toolkit part 1- 2 2013

Geometry
Name ____________________________________ Period _____
These are expected Algebra 1 skills needed for success in Geometry. Show all work.
ALGEBRA 1 REVIEW TOOLKIT
1. Expressions. Simplify.
a. 4  6( x  2)  x 2
part 1
b. when x  3
c. when x  3
3x  2 x  8
3x 2  2 x  8
2
2. Equations. Solve for the variable. Check your solution.
6 z  3  8z  7
a.
b.
3(m  2)  2m  14
3. Proportions. Solve for the variable.
a.
5
x

8 100
b.
4 r

r 9
c.
3
6

y y2
4. Simplifying radicals (square roots). Leave in exact form means you should have no decimals.
9
a.
b.
18
d. 5 32
c. 2 49
5. Rationalizing the denominator. Leave in exact form.
a.
10
2
b.
2
3
e. 4 20
6. Write the equation of the line below.
7. Identify the slope and y-intercept.
y
a.
5
4 x  2 y  10
b.  3 y  2 x  12
4
3
2
1
x
-7 -6 -5 -4 -3 -2 -1
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
8. Parallel lines have the same slope (m1 = m2) and a
different y-intercept. They never intersect.
y1 
1
x4
3
y2 
1
x  2
3
9. Perpendicular lines have opposite reciprocal slopes.
Multiplying the slopes equals -1.
y1 
3
x4
2
2
y2   x  2
3
m1 =
m2 =
m1 =
m2 =
b1 =
b2 =
b1 =
b2 =
y rise

x run
Geometry
Name ____________________________________ Period _____
Algebra 1 skills that will be seen in review/preview practice. Show all work.
ALGEBRA 1 REVIEW TOOLKIT
PART 2
SYSTEMS: a graph that may or may not have a point of intersection of two equations (x,y).
Sometimes two lines have no points (parallel lines) or an infinite number of points (lines lie on top of each.)
Equal Values Method (Substitution Method)
y  3x  5
y  4x  8
Substitution Method
x  3 y  1
4 x  3 y  11
Elimination Method
a.
x  y  4
 x  2 y  13
b.
x  5y  1
x  4y  2
c.
4x  3y  7
2 x  9 y  35
QUADRATICS: A graphed parabola that may have one or two solutions, called roots. If the
discriminant is negative like  49 then it has no real roots (imaginary number).
Multiplying polynomials. Simplify each expression.
a.
 y  7 y  2
b. 2 x  5

c. 2 x x 2  3x  2
2

Factor the trinomials completely. Do not solve.
a. x 2  13x  42
b. x 2  18 x  81
Graph the following quadratic without a table.
y  x 2  4x  3
c. 2 x 2  9 x  9
Review of how to graph a quadratic equation:
1. First factor and find the roots by using the Zero Product Property.
2. Find the line of symmetry by using the vertex formula x 
b
.
2a
3. Substitute the x into the equation to find the y coordinate of the
vertex.
3. Plot the y-intercept.
Quadratic Formula.
x 2  8x  6  0
Solve and leave in exact form.
 b  b 2  4ac
x
2a