accelerated algebra 1 & geometry summer work algebra 1 & geometry summer work we hope you...
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Accelerated
Algebra 1 & Geometry
Summer Work We hope you have a great summer. Since it would be in your
best interest to review some mathematics this summer in
preparation for this challenging and fun class, we’re providing
you with a few review problems for you to complete this
summer. These are all problems that you will need to know how
to do before the school year starts. These are concepts that
were covered in your 7th or 8th grade math classes. We will
collect these problems on the first day of school. They may be
graded for accuracy. You will have a quiz over this material
during the first week.
If you have any questions, we have included websites at the end
of the packet that can help you in completing it.
Start your year off on the right track by completing these
problems before school starts! Once again, the packet is due
when you walk through the door the first day of class. We look
forward to seeing you in August!
Please feel free to email me:
You will receive an email invite to join the Accelerated
Algebra 1/Geometry Google Classroom website. Please join as
soon as possible. If you don’t receive an email please join the
AAG Google Classroom website using the following code:
end0pt.
DUE 8/7/2017
Name: __________________________
Know the following terms:
a. variable b. rational numbers c. irrational numbers d. real numbers
e. integers f. function g. exponent h. perfect squares
i. perfect cubes j. average rate of change k. Pythagorean Theorem l. hypotenuse
m. parallel lines n. transversal o. supplementary angles p. complementary angles
q. corresponding <’s r. alternate interior <’s s. alternate exterior <’s t. consecutive interior <’s
u. vertical angles
For all of the following problems you must show your work. If only answers are given NO CREDIT
will be given. Some questions only require you to look at a graph and get a value, but most require
work.
#1 - 3 Evaluate the algebraic expressions below (no decimal answers):
1. n2 - 25 a) when n = -10 b) when n = 1/2
2. 2
147 d a) when d = -2 b) when d = 6/7
3. 2 x - x a) when x = 16 b) when x = 1/4
4. Write an algebraic expression for the situation. Define the variable, then evaluate the expression
for the amount given. Andrea wants to buy a photo book from an online photo printing service.
The book costs $14.98 plus $0.39 for each photo printed in the book. How much will she pay if
she wants to have 35 photos in the book?
5. Use the graph to the right, to answer the following
questions. What will the fine be for a book that is
a) 3 days overdue b) 10 days overdue?
6. Operations with Fractions – Simplify the following fractions:
a) 1 3
2 5 b)
4 3
9 8 c)
14
2 d)
5 7
8 4 e)
3 5 1
10 2 4
7. Solve the equations for x: a) -x - 20 = 14 b) 13 - 7
x = 6 c) 8
7
2
x
Name: __________________________ 8. Solve the equations for x: SHOW WORK!
a) 3(2x+7) - 3x = 18 b) -14 = -2(5-x) + 16 c) 5
2
10
7
5
3x
9. Solve the inequality 21 - 9x > - 6
10. Solve the graph of each linear inequality:
a) b)
11. Answer the questions about the graph to the right that
represents a dieter's weight loss over a year’s period.
a) Describe what happens between months 3 and 5.
b) Circle where the graph increases and interpret the meaning.
c) During which months did the dieter lose weight the fastest?
d) What is the rate of change that occurs between
months 10 and 12?
12. Identify the slopes and y-intercepts of the linear equations below.
a) y = -2x - 8 b) y = 3 c) x = 9 d) y = x e) 2x + 3y = 5
13. Identify the x and y-intercepts: 3x - 4y= 12 and graph the equation.
Name: __________________________ 14. Write the equation for a line that has a slope of -2 and passes through the point (4,7).
15. Write the equation of the line given the points (3,25) and (4, 31).
16. Write an equation of the line shown in the graphs below: (The graph’s scale is 1 unit)
a) b)
17. Solve the system of equations by graphing (Remember to write your answer as an ordered pair)
a)
xy
y
2
4 b)
22
1
4
xy
x
18. Solve the system of equations using the substitution method
a)
xy
yx
7
169 b)
63
3242
yx
yx
19. Solve the system of equations using the elimination method.
a)
39
97
yx
yx b)
3534
4952
yx
yx
Radicals:
20. Approximate the answer to the nearest tenth and explain your answer (no calculators):
a) 11 b) 48 c) 300
Name: __________________________ Exponents:
21. Identify the parts of the expression 5x4 as either the base, coefficient, or exponent.
22. Simplify each expression
a) (m4)2 b) (2x3y)4 c) a-3 b-2 d) 52
1x
Pythagorean Theorem:
23. How far up a wall will an 11m ladder reach, if the foot of the ladder must
be 4m from the base of the wall?
24. How long is the hypotenuse, if two sides of a right triangle are 3 and 4?
These three numbers (the lengths of the two sides and hypotenuse) are called a Pythagorean
triple, define and find another example of a Pythagorean triple.
Parallel Lines, transversals and their angles:
25. If m ll n ll o and p is a transversal, find the following:
(Use the diagram to the right for #33 – 38)
a) State a pair of corresponding angles:
b) State a pair of alternate interior angles:
c) State a pair of alternate exterior angles:
d) State a pair of same-side interior angles:
e) State a pair of corresponding angles:
f) State a pair of vertical angles:
g) State a pair of supplementary angles:
Name: __________________________ 26. What is the measurement of angle L?
27. What is the measurement of angle M?
28. What is the measurement of angle S?
29. If the m<J is 2x, what is x?
30. If the m<K is 4y – 7, what is y?
31. Write down at least two questions you have for me about this math class.
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
Resources:
Fractions:
http://www.purplemath.com/modules/fraction4.htm
http://www.purplemath.com/modules/fraction3.htm
Solving equations:
http://regentsprep.org/Regents/math/ALGEBRA/AE2/LSolvEq.htm
Inequalities:
http://www.regentsprep.org/regents/math/algebra/ae8/compoundlinequal.htm
http://www.mathsisfun.com/algebra/inequality-solving.html
Linear equations:
http://www.purplemath.com/modules/strtlneq.htm
Solving Systems of Linear Equations:
http://math.about.com/od/linearequations/tp/leje2.htm
Radicals:
http://www.gaston.k12.nc.us/schools/cramerton/faculty/kllasky/Course%20Outline%20and%
20Syllabus/Textbook/Ch%2011/Text%2011.2%20Approximating%20Square%20Roots.pdf
Exponents:
http://www.coolmath.com/algebra/01-exponents/06-exponent-rules-putting-rules-1-4-
together-01.htm
Pythagorean Theorem:
http://www.mathsisfun.com/pythagoras.html
Parallel Lines and Transversals:
http://www.studyzone.org/mtestprep/math8/g/8parallelanglepairsl.cfm