1Murrieta Valley Unified School District
Algebra 1 Proficiency Test Study Guide
Simplifying Expressions
1. Evaluate by substituting numbers in for
variables then perform any operations
according to the Order of Operations
5. Multiply binomials and polynomials using
the FOIL method or rectangles
6. Divide any polynomials using cancelling
with each term or long division.
2. Distribute
3. Combine/Collect like terms
7. Simplify rational expressions by factoring
and cancelling.
4. Simplify exponential notation by raising
powers to powers or
dividing/cancelling/multiplying monomials
Simplify.
1.
3a(2a  4)  5(6a  3)
7. If x = 4 and y = –3 then
6a2 -42a - 15
2.
6x  4 y

3x  2 y
6
(3x  2)(6 x  5)

8. 3x 2 y 3
18x2 -3x -10

4
81x8y12
3. (3 x  5)(3 x  5)
9.
x12 y 4
=
x5 y 6
x7
y2
9x2 -25
4. (b  4)
2
10.
3b 4 c 2  15b 3 c  9bc
= b3c + 5b2 - 3
3bc
11.
q 2  5q  6
q +3
q2
12.
p6
p 2  36
=
2
p4
p  10 p  24
b2 -8b + 16

5. 8 x3 y 2  3x 2 y 5

-24x5y7
6. (2a  4a  5)  (5a  6a  3)
2
-3a2 -10a + 8
2
Murrieta Valley Unified School District
Solving Equations and Inequalities
1. Solve multi-step equations and
inequalities in one variable by distributing,
collecting like terms, isolating the variable,
and solving by multiplying or dividing at the
end. Don’t forget to flip the inequality
symbol if you multiply or divide by a
negative number!
2. Solve quadratic equations by factoring
and using the zero product property or by
using the quadratic formula. Remember that
solutions to quadratic equations are the points
where the graph would cross the x-axis!
Solve:
13. 6 y  12  4 y  16
y = 14
Algebra 1 Proficiency Test Study Guide - 2
3. Solve rational equations by finding a
common denominator then multiplying both
sides of the equation by the common
denominator then add or subtract to solve.
Some rational equations can be solved as
proportions. Always check for extraneous
solutions!
4. Solve systems of equations using
substitution or elimination. Be sure to
express your solution as an ordered pair!
5. Be sure to consider the positive and
negative cases when solving absolute value
equations and inequalities. Remember to flip
the inequality symbol with the negative case!
20. Solve the following system of equations:
2 x  4 y  8
( 2, - 1 )

3x  y  5
x2 x4

6
4
14. 4( x  3)  5 x  3x  12
x=4
a 2 3
15.  
5 3 10
5
a = -1
6
16. r  4  16
r = 20, -12
21.
17. 2x  6  4x  2
24. x 2  2 x  15  0
x > -4
a  b  4
18. If 
, then b = -1
a  b  6
19. Solve the following system of equations:
 y  4x  2
( 2, 6 )

4 x  2 y  20
x = 16
22. x2 + 7x – 18 = 0 x = -9, 2
23. Use the quadratic formula to solve the
equation: x 2  7 x  4  0
 7  33
x=
2
x = 5, -3
25. Where will the parabola cross the x-axis
for the given equation?
x 2  8 x  20  0
(-10, 0 ) and ( 2, 0 )
26. There were 216 students at the dance.
There were 8 more boys than girls. How
many girls were at the dance? 104 girls
Murrieta Valley Unified School District
Algebra 1 Proficiency Test Study Guide - 2
Graphing Linear Equations and
Inequalities
1. We can graph lines using t-charts,
intercepts, or slope-intercept form
y = mx + b. m represents the slope and b
the y-intercept. Begin the graph at the
y-intercept then count off the slope as rise
over run.
5. To write an equation for a line when you
know one point and the slope, use the
point-slope formula. m is the slope and
x1 and y1 are the coordinates of the given
point.
y – y1 = m ( x – x1 )
2. Use the slope formula to find the slope of
a line when you know two points:
m =
y2  y1
x2  x1
6. To graph linear inequalities, graph the
boundary line. Use a solid line for > or
<. Use a dashed line for > or < . Choose
a checkpoint to determine which side of
the boundary line to shade.
3. To find the x-intercept of the graph, let
y = 0. To find the y-intercept, let x = 0.
4. Parallel lines have the same slope.
Perpendicular lines have slopes that are
opposite signed reciprocals of each other.
27. Solve for y: 3 x  4 y  12
3
y=
x-3
4
28. Find the slope of the line that passes
through the points (6, 10) and (-3, 2).
8
m=
9
29. Find the slope and y-intercept for the line:
 5 x  3 y  15
5
Slope =
y-int = 5
3
30. Find the x and y intercepts for the line:
3 x  6 y  18
x-int = (6, 0) y-int = (0, -3)
32. What is the slope of the line
3
4
perpendicular to y   x  5 ? m =
4
3
2
33. Graph y  x  3
3
y
f(x)=2x/3 - 3
31. Write the equation of a line that has a
slope of 3 and passes through the point
(3, 5).
y = 3x - 4
x
34. Graph the inequality 2 x  5 y  10 ?
y
f(x)=-2x/5 + 2
Shading 1
x
Murrieta Valley Unified School District
Algebra 1 Proficiency Test Study Guide - 2
Quadratic Polynomials
1. To factor a quadratic polynomial, first
factor out the GCF if there is one. Then use
the appropriate method:
Difference of Squares (binomials)
Diamonds (leading coefficient is 1)
Diamonds and Rectangles (leading
coefficient is not 1)
2. To complete the square, first “clear the
space” by adding or subtracting “c” on both
sides. Then divide “b” by 2 and square the
answer. Add this number to both sides to
complete the square. Factor the trinomial
square then take the square root of both sides.
Don’t forget the plus/minus! Finish solving
the equation.
Factor each of the following:
35. a2 – 36
(a+6)(a-6)
38. x 2  x  12
(x+4)(x–3)
36. 3x2 + 5x + 2
( 3x + 2 ) ( x + 1 )
39. What number completes the square:
x2 + 22x + ____
121
37. 3b3 + 15b2 + 18b
40. What number completes the square:
2x2 + 3x + ____
3b ( b + 3 ) ( b + 2 )
9
16
Murrieta Valley Unified School District
Algebra 1 Proficiency Test Study Guide - 2