Algebra 2 (& Honors) Prerequisite Packet

Algebra 2 (& Honors) Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
The problems in this packet are designed to help you review topics from previous math
courses that are important to your success in Algebra 2 or Honors Algebra 2.
It is important that you take time during summer break to review the math concepts you learned this past school
year. In order to ensure that you are appropriately placed in, and prepared for Algebra 2 or Honors Algebra 2
you may be required to take a course pre-assessment when you return to school next year.
It is YOUR responsibility to prepare for the course pre-assessment!
The specific math concepts that will be assessed are listed on the front page of this summer packet. To prepare
for the course pre-assessment, you are encouraged to complete this summer math packet. Please note, this
summer math packet will not be collected or graded. Instead, the course pre-assessment will be used to measure
your knowledge of the prerequisite skills.
If you have any questions, please feel free to email the resource teacher, [email protected]
Concepts To Be Assessed
on the Algebra 2 and Honors Algebra 2 Course Pre-assessment.
Students should be able to:
 Simplify, add, subtract, multiply and divide fractions.
 Simplify, add, subtract, multiply and factor polynomial expressions.
 Solve multistep linear equations in one variable.
 Write the equation of a linear function in slope-intercept and point-slope form.
 Graph a linear equation in two variables.
 Solve a system of linear equations in two variables.
 Add, subtract, and scalar multiply matrices.
 Solve quadratic equations.
 Graph and identify properties of a quadratic function.
Algebra 2 (& Honors) Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Standard Form:
Slope-Intercept Form:
Ax + By = C
y =mx+b
where A and B are not both
zero
where m = slope and b = yintercept
Name _____________________________________
Let x1 , y1  and x2 , y 2  be two
points in the plane.
slope =
y 2  y1
x 2  x1
Date ___________________ Pd _______
Factor each of the following polynomials:
1) x 2  x  72
2) 10m3 n 2  15m 2 n
3) x 2  12 x  36
4) x 2  64
5) a 2  10a  24
6) 3x 2  18x  27
Solve the following quadratic equations:
7) ( x  1)( x  3)  0
8) p 2  6 p  0
Algebra 2 (& Honors) Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Simplify each of the following:
9) (3x 2  4 x  7)  (2 x 2  7 x  8)
10) (4a 3  2a 2  a  7)  (3a 3  2a 2  a  8)
11) ( x  7)( x  5)
12)  3xy 3 ( x  2 y)
13) (15a 4 b 2 c) 0
14) (8a 3b 2 )(2a 4 b 5 )
(3x 2 y ) 3
15)
6 x 2 y 5
16) ( x  6) 2
Solve for x:
17)  4(3  x)  8
18) 3x  2( x  1)  0
Algebra 2 (& Honors) Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Solve the system of equations:
19)  2 x  y  8
y  3x  2
Graph each of the following without using a calculator.
3
20) y   x  4
4
21) y  3x
y
y
x
x
Complete these problems WITHOUT using a calculator.
6  3
5 6 
B
Given the following matrices, A  

 C  0
2 1 
2  1
22) A + B
23) A - B
5 , determine:
24) -2C
Algebra 2 (& Honors) Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Perform the given operations with fractions WITHOUT using a calculator. Show all work and simplify your
final answer.
1 1
3 5
3
25) 
27) 
26) 2 
2 4
4 7
4
28)
17 2

5 10
29)
31)
2
8
3
32)
1 5

x x
9
5
16
30)
5 1

2 4
5 2  1
33)     2 
 6 10   4 
Answer the following questions concerning linear equations.
34) Determine the slope of the line
1
35) Determine an equation for a line with slope
containing the points (6,-2) and (-1,5).
2
and y-intercept at (0, -3).
Algebra 2 (& Honors) Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
36) Solve the system of equations:
 x  3y  0
2 x  6 y  12
37) Find the area of a square whose diagonal is equal to 4x.
38) Is (0,-5) a solution to the following system of inequalities? 6 3y 4(3 x)
Algebra 2 (& Honors) Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
39) A car salesman’s weekly salary is a base amount plus an additional amount for each car sold. The
table below shows a person’s weekly salary earned for the last three weeks.
Cars sold (c)
4
9
12
Weekly Salary (S)
$500
$1000
$1300
What is the person’s weekly salary when 13 cars are sold? Justify your answer.
40) Sketch a graph of f ( x)  x 2  x  2 . Then complete the characteristics below.
Domain:
Range:
y
Axis of Symmetry:
Increases:
Decreases
x-intercepts:
y-intercept:
Minimum Value:
Maximum Value:
Continuous:
x