Algebra 2H
2016 Summer Algebra 1 Review
MHRD
Dear prospective Algebra 2 Honors student,
This assignment is intended to help you to review Algebra 1 before starting school in
September. You are expected to be proficient in all of these skills prior to entering
Algebra 2. Bring your work with you to class on the first day of school. Answers will be
provided when you return to school after which you will be tested on this material.
DISCLAIMER: Algebra 2 at the Honors level is more rigorous than this review. Topics
listed in this assignment will not be re-taught. If you find any of the problems difficult
you can use resources below for assistance. While the videos are an excellent resource
for review of specific skills, they may not be of sufficient rigor for an honors course and
do not constitute an Algebra course in and of themselves.
Enjoy your summer! We look forward to meeting you in September!
SOME HELPFUL RESOURCES
PatrickJMT
http://patrickjmt.com/
Math TV
http://www.mathtv.com/
Brightstorm homework help
http://www.brightstorm.com/math/algebra/
Kahn Academy
https://www.khanacademy.org/math/algebra
Kahn Academy on iTunes and Google Play
https://itunes.apple.com/us/app/khan-academy/id469863705?mt=8
https://play.google.com/store/apps/details?id=org.khanacademy.android&hl=en
1. Simplify Numerical Expressions without a calculator
52  (3  5)  28
2(5  4) 2
2. Simplify Algebraic Expressions
(9 x2  13xy)  (6 x2  7 xy  5 y 2 )
3. Evaluate Algebraic Expressions
Evaluate: 2 a 2  b  (2c)3 for a = -2, b = 5, c = -3
4. Graph lines
2y  x  4
3x  2 y  6
5. Graph inequalities in the coordinate plane
2 y  3x  4
5x  2 y  10
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6.
Solve Equations
b) 9m  6( 4m  5 )  15  5m  7( 2m  9 )
a) y  ( 8  y )   20
c)
e)
c c  12

10
6
d)
3n  5 10 n


6
n 2
f)
g) 3 6 x  1  21
7.
h)
4h 5h

 2
3
6
3 x  2  4
| 7  x | 4
Solve Literal Equations
a) Solve for x 4
c) Solve for y
a
x1  x2  x3  x4
4
ax  by  c
b) Solve for b1
d) Solve for t
2a  ( b1  b2 )h
i  prt
8. Graph the solution set to inequalities on the number line
3r  9  2r  ( 12  2r )
3
9. Solve equations involving more than one variable
a) Find w given that:
3w  2 x  6 and x  2w  3
b) Find x given that:
x  2 y  3z  100 , y  x  2 , and z  2 x  5
10. Solve Quadratic Equations using factoring, the zero product property, and the quadratic formula
a) x( x  10 )  0
b) 2 x 2  9 x  18  0
c) x 2  144
d) x 2  10 x  20
11. Analyze equations of lines
a) Find the slope and write an equation of the line in point-slope form:
b) Write an equation in slopeintercept form and graph the
line that goes through (2,-5)
3
with slope  then graph:
4
Slope-intercept form: y = mx + b
Point-slope form: y2  y1  m( x2  x1 )
Standard form: Ax + By = C
c) Find the slope, yintercept, and graph:
4 x  5 y  15
4
12. Use diagrams to solve problems
a) In the diagram, AB = CD
Find x and the length of AB
b) The two rectangles have
equal perimeters.
x
Find the length and the
width of each rectangle.
x
x+5
3x - 5
c) The perimeter of the rectangle is 36.
Find the length and width of the recrectangle.
d) For what values of x will the
rectangle be a square?
13. Simplify Polynomials: distribute, expand, collect like terms, and simplify
c)  4a 2 b( 5ab )
d) 2ab(3a 2  4ab  5b2 )
42m 6 n 5
8 x5 y  2 xy
a)
b)
2x
7m 3 n 2
e) ( 2a  3 )( 3a  1 )
h)
7 x 3x

4a 5a
f) ( 3x  7 )2
i)
4a 3cd

3c 4b
g) ( x  2 )( x 2  3x  4 )
j)
a 2a

5 3
h)
4a 4 y 9 5b 5 d 8

9b 8 d 4 7a 2 y 11
5
14. Factor Quadratic Polynomials: express each quadratic expression in completely factored form
a) y 2  6 y  7
b) c 2  17c  30
c) 3a 2  75
d) 81  t 2
e) 20  x  x 2
f) 3d 2  17d  10
15. Solve Systems of Equations
a)
5 x  y  14
b)
3x  y  2
3x  5 y  13
4x  3y  2
16. Simplify Radicals
a)
18
d)
1
20
2
40
c)
e) 8 5  2 5
f)
b)
1
50
5
48  12  27
17. Solve Word Problems
a) Mike has $1.55 in nickels and dimes. He has 7 more nickels than dimes. Find the number of each
kind of coin. Let n = number of nickels and d = number of dimes.
b) Zap Electric Company charges $40 for a service call plus $16.57 for each electrical outlet installed.

Write an expression for the total bill if Zap Electric Company install x outlets.

Wally Walrus had 11 outlets installed. What was his bill?

Mrs. Lite Ning’s bill was $172.56. How many outlets did she have installed?
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