Name: _________________________________________
___th Grade TAKS score: _____________
ECHS
Summer Assignment
for
Pre-AP Geometry
Directions:
Students, please complete this packet of Algebra 1 problems.
You should have this packet complete for the first day of school.
Bring the packet to class on the first day of school.
This assignment will be checked for completeness, not accuracy. All problems should be done
or well attempted. Show work on every problem in the space provided. Write neatly and circle
final answers.
You will be assessed on the topics presented in this packet during the first week of school. You
will be given an opportunity to ask some questions in class in the days prior to the assessment,
but if you have significant trouble completing this packet you should contact your guidance
counselor to reconsider your course placement.
You should not work together with other students nor receive extensive help from a tutor.
If you have any questions regarding this packet, please email
kcouvillion@ecisd.org
or
dhamman@ecisd.org
Below are listed topics in the review. You can certainly do Google searches for any of these topics. But we
have given you several sites that will cover pretty much all of these topics.
Here are good sites for most algebra topics:
http://www.purplemath.com/modules/index.htm
http://www.sosmath.com
http://www.freemathhelp.com
Beginning Algebra topics
Exponents
Negative and fractional exponents
Intermediate Algebra topics
Domain
Solving inequalities: absolute value
Solving inequalities: quadratic
Special Factoring formulas
Function transformation
Factor theorem (p over q method)
Even and odd functions
Solving quadratic equations and quadratic formula
Advanced Algebra topics
Asymptotes
Complex fractions
Composition of functions
Solving Rational (fractional) equations
Reference Sheet
Use the following formulas in the coordinate plane when given two points x1 , y1  and x2 , y 2  .
x2  x1 2   y 2  y1 2
Distance Formula:
d
Midpoint Formula:
 x  x 2 y1  y 2 
( x, y )   1
,

2 
 2
m
Slope Formula:
y 2  y1
x 2  x1
Pythagorean Theorem for right triangle side lengths
a2  b2  c2
c
a
b
Applications involving distance (d), speed/rate (r), and time (t).
d  rt
Use the following formula when solving an equation in the form ax 2  bx  c  0 .
Quadratic Formula:
x
 b  b 2  4ac
2a
ORDER OF OPERATIONS
Evaluate the expression without using a calculator.
1. 2 4  3  16  4
2. 6  2 2  2  11
SIMPLIFACATION
Simplify by using the distributive property and combining all like terms. Simplify as much as possible.
3. 3mn  2m  2n(2m  3n)
4. 2a  5  4a  6  7  2a
5.
1 5 a
 7
6.  3  a     3  
6 2
2
 4
3a 2 2ab

 ab  a 2
4
3

 
7. 2 x 2  5x  7  3x 3  x 2  2


 
8. 4 x 2  3x  7  2 x 2  4 x

LAWS OF EXPONENTS
Simplify by using the laws of exponents. Simplify as much as possible.
2
9.  2 
12. y 3  y 4  y
13.
3x y 
14.
8x5 y 3
2 xy4
16.
 16a 3 b 2 x 4 y
 48a 4 bxy 3
17.
 3x y  (4 x)


15.  4a 2 x  5a 3 x 4

4
 3
11.   
 5
3
1
10.  
2
2
2 2
3
2
3
WORKING WITH RADICALS
Simplify these radicals. Do not give decimal answers. Leave answers in simplest radical form. Rationalize
the denominator when necessary. Problems with a * may be more challenging.
18. 144
19. 24
20. 108
21.
*24.
 8
2
3 3
 
22. 2 5
2
*23.
*25. 4 27  8 48
2
6
*26. 7 6  24
2
BINOMIAL (& more) MULTIPLICATION
Find each product. Simplify result as much as possible.
27. x  5x  4
28. 4n  33n  4
30. 2 x  9 y 3x  y 


31. 8  7 1  7


29. a  4 a 2  5a  7
32. 2 x  y 
2

FACTORING
Factor completely by using an appropriate factoring method.
33. 5a 2 b 2 c  15abc 2
34. x 2  7 x  6
35. 2r 2  3r  20
36. 6 x 2  5 x  6
37. 3 x 2  9 x
38. y 2  25
39. 16m2  1
40. y 3  2 y 2  81y  162
SOLVING EQUATIONS
Solve these linear equations. Do not give decimal answers. Leave answers as simplified fractions.
1
41. 5a  2a  6  4a  5
42. x  5  6 x  5
3
43.
8  5r
3
6
45.
y4 4

y 1 3
44.
 4a  1 3

 10a
8
Solve these equations for the indicated variable. Problems with a * may be more challenging.
8a 2b 3
 4a
46. Solve for y. 4 x  2 y  z
47. Solve for k.
3k
*48. Solve for m.
2m  a  3
Solve these quadratic equations. Find all possible solutions.
49. x  8x  4  0
50. x 2  8 x  20  0
NUMBER LINE
Solve and graph the solution on the number line.
51. 3(5w  4)  12w  11
COORDINATE PLANE & GRAPHING
Graph the linear equations.
53. y  3x  2
54. 3 x  2 y  10
52.  5  2  h or 6h  5  71
55. y  2
Determine if these lines are parallel, perpendicular, or neither.
56. y  2 x  6 and 3x  6 y  4
57. 4 y  10 x  3 and
58. Write an equation of a line in the form
y  mx  b that passes through the points
(-4, -1) and (2, -4).
5x  7  2 y
59. Find the slope of a line that passes
through the points (-6, 4) and (3, 5).
60. In the graph below, the axes and the origin are not shown. If the scale of the axes is 1 unit per box and
point P has coordinates (4, 2), what are the coordinates of point Q?
P
Q
61. Find the coordinates of the midpoint of
segment AB if A (6, 0) and B (-4, 1).
63. Find the length of PR if P (8, -2)
and R (5,2).
62. The midpoint of segment CD
3

 16

is  3,  . If C  ,2  find the
5

 3

coordinates of D.
SYSTEMS OF LINEAR EQUATIONS
Solve the system by the indicated method. State the solution as an ordered pair.
64. The graphing method.
65. The substitution method.
3 x  y  6
 x  y  11


 x y 2
x  3y  1
66. The elimination (linear combination)
method.
 6x  5 y  9

9 x  7 y  15
PYTHAGOREAN THEOREM
Use the Pythagorean Theorem to solve for the value of x in each right triangle.
67.
68.
x
10
x
8
2 13
2 3
VERBAL EXPRESSIONS
Translate each verbal expression into an algebraic expression or equation and solve.
69. The sum of six less than a number and five more than the same number is 9. Find the number.
70. The product of the square of a number and 7 is the same as the sum of the cube of 3 and 1. Find the
number.
71. 12 decreased by the square of a number is equal to 3. Find the number.
APPLICATIONS
Solve each problem. Show all work and any diagram necessary.
72. The length of a rectangle is 3 feet less than twice the width. If the area of the rectangle is 54 ft2, find the
dimensions of the rectangle. Solve by using a solving a quadratic equation.
73. A rectangular field is twice as long as it is wide. A golf cart traveling at 12 miles per hour takes 7.5
minutes to travel the perimeter of the field. What is the length and width (in miles) of the field?
74. A mountain bike park has a total of 48 trails, 37.5% of which are beginner trails. The rest are divided
evenly between intermediate and expert trails. How many of each kind of trail is there?
75. The perimeter P (in feet) of each of the two rectangles below is given. What are the values of c and d.
Solve by using a system of linear equations.
P = 24 ft d ft
c ft
P = 42 ft
(c + 4) ft
2d ft