Download CP Algebra / Honors Algebra

2013-2014 Algebra 1 Summer Math Packet
Dear Students and Parents:
The purpose of this packet is to review pre-algebra concepts as you look forward to Algebra 1 next
year. All concepts in this packet have been previously covered in Pre-Algebra. Following the
review of this packet, there will be an assessment on these skills in the first couple weeks when you
return in September. Please use this summer to assure all pre-requisite concepts have been
understood. You will have access to the online Holt series through summer, if needed. Show all
your work for each problem.
Have a wonderful summer!
Ms. Weil
[email protected]
Order of Operations
1)
2
2)
5 – (12 ÷ 2 x 3) ÷ 9 + 15
(18 − 9)
0
+15
3•12 − 6 • 4
3)
3
4[3 – 5(8 – 6)] ÷ 2 + 11
Adding/Subtracting/Multiplying/Dividing Positive and Negative Numbers
4) 5 – 3 + 12 – (-9)
5)
7) -4 + -9 – 3(-6)
8)
−4
⎛ 3 ⎞
⎜ ⎟
⎝ 4 ⎠
1 7
2 −
3 9
6)
(−2)(4) − (−5)(−1)
9)
⎛ 2 ⎞ ⎛ 5 ⎞
⎜ ⎟ ÷ ⎜ 1 ⎟
⎝ 3 ⎠ ⎝ 9 ⎠
1
Evaluating Expressions
10)
12)
7b – 2a, when a = -3 and b = 4
11)
2r
+ 7 , when r = 12 and t = 3
t
3x2 + 5x + 1, when x = -2
13) (3x)2 – 7y2, when x = 3 and y = -2
Solving Equations
Check:
3b + 2 = 6(3 – b)
3b + 2 = 18 – 6b
-2 -2
3b = 16 – 6b
+6b
+ 6b
9b = 16
9
9
16
b=
9
16)
22 − 6x ≤ −63− x
19)
2a 2
=
7 3
16
16
) + 2 = 6(3 – ( ))?
9
9
16
11
+ 2 = 6( )
3
9
16
6
22
+ =
3
3
3
22
22
=
✓
3
3
Does 3(
17)
Here is an example: The
check is a required step
Solve the equation &
inequalities. Include a check.
1
15)
d +2=3
4
5(g − 7) + 2"# g − 3(g − 5)$% = 0
3
18) 1− (v + 2) = −5
4
20) 7x + 6 ≤ 14(x – 4)
2
Properties of Real Numbers
Match each equation on the left with the property it illustrates on the right.
21) 4 + (9 + 6) = (4 + 9) + 6
A.
Identity Property of Addition
22) x + 12 = 12 + x
B.
Associative Property
23) (3 + y) + 0 = 3 + y
C.
Distributive Property
24) x Ÿ 1 = x
D.
Identity Property of Multiplication
25) 5(x + y) = 5x + 5y
E.
Commutative Property
Classification of Real Numbers
26) Explain the difference between a rational and an irrational number.
27) Classify the following numbers as rational or irrational.
a) ½
b) 8
c)
6
d)
16
e) π
28) List the set of all natural numbers.
29) List the set of whole numbers less than 4.
30) List the set of integers such that –3 < x < 5.
31) Classify the following numbers as real, rational, irrational, natural, whole and/or integer. (A number
may belong to more than one set)
a) –3
c)
3
b) 4
2
3
d) 0
True or False?
32) All whole numbers are rational numbers.
33) All integers are irrational numbers.
3
34) All natural numbers are integers
Properties of Exponents
35)
38)
d7 • d9 =
5 6 4
( −c h )
=
36)
x 2 e • x8 e =
39)
417
=
414
Monomials and Polynomials
41) What the difference between.
a monomial and polynomial?
43)
(3p2 - 2p + 3) - (p2 - 7p + 7)
42)
44)
37)
(7q ) (12q r ) =
40)
⎛ −4s 6 ⎞
⎜ 3 5 ⎟ =
⎝ t r ⎠
5
3 5
3
(d2 - d + 5) - (-d2 + d + 5)
(x3 - 3x2y + 4xy2 + y3) - (7x3 - 9x2y + xy2 + y3)
2x - 2
3x -10
45) Find the length of each side of the triangle if the perimeter is 33 cm.
3x + 5
Slope and Linear Equations
45) Find the slope of the line through the given points.
a) (-1, 2) and (-5,10)
b) (-7, 10 ) and (1, 10)
47) Rewrite 3y = 2x – 7 in slope-intercept form. Identify the slope and y-intercept.
4
Translating Expressions and Equations
Set up an algebraic expression or equation to represent each verbal expression. DO NOT SOLVE.
Example: 18 less than the quotient of a number and 3. à let n = a number ;
n
− 18
3
48)
The sum of six times a number and 25
49)
7 less than fifteen times a number
50)
Four times the square of a number
increased by five times the same number
51)
The sum of a number and 23 is 78.
52)
The sides of a rectangle are a number and
4 less than that same numbers. The
perimeter is 56 meters.
53)
If a number is decreased by 6, and the
result is multiplied by 3, then the answer
is 15. Find the unknown number.
Consecutive Number Problems
Include a let statements and checks for each problem.
54) The sum of two consecutive integers is 61.
55) The sum of three consecutive even integers is
156.
56) Find two consecutive odd whole numbers whose sum is 2 less than 6 times the first number.
5
Miscellaneous Word Problems
Write an equation to mode each word problem. Include let statements and checks for each
problem.
57) Joelle had $24 to spend on seven pencils.
After buying them she had $10. How much did
each pencil cost?
Example:
Let x = cost per pencil
7x + 10 = 24
-10 -10
7x = 14
7
7
x=2
58) Sarah already has 45 stamps in her collection,
and she gets 7 new stamps each month. How
long will it take before she has 129 stamps in her
collection?
Check:
Does 7(2) + 10 = 24?
14 + 10 = 24
24 = 24 ✓
Each pencil cost 2
dollars.
59) The perimeter of a trapezoid is 90 cm. The
parallel bases are 24 cm and 38 cm long. The
lengths of the other two sides are consecutive odd
integers. What are the lengths of these other two
sides?
60) Lynn took a cab from her office to the airport.
She had to pay a flat fee of $2.05 plus $0.90 per
mile. The total cost was $5.65. How many miles
was the taxi trip?
61) Luke has $5 more than Sam. Together they
have $73. How much money does each have?
62) The length of a rectangle is 3 inches more
than the width. Find the length and width if the
perimeter of the rectangle is 98 in.
64) A ladder is leaning against the side of a 10m house. If the base of the ladder is 3m away
from the house, how tall is the ladder? Round your answer to the nearest hundredth. Please draw a
diagram and show all work.
6
67) In any triangle the sum of the measures of the
angles is 180 degrees. In Triangle ABC, ∠ A is
twice as large as ∠B. ∠B is 4 degrees larger than
∠C. Find the measure of each angle.
69) Four times a number increased by 25, is 13
less than 6 times the number. Find the number.
68) The sum of 38 and twice a number is 124.
Find the number.
70) 15% of what number is 12? (Set up a
proportion).
Put an X on in the box where you think you belong:
I was not at all confident
completing this packet
in my own.
I found this packet to be
extremely easy to
complete on my own.
Here are some websites you might find useful in completing your summer assignment.
1.
2.
3.
4.
5.
6.
7.
8.
9.
9.
10.
my.hrw.com (use your 7th grade log-in)
http://www.regentsprep.org – use the Math A site
http://www.math.com – use both Algebra and Pre-Algebra
http:// library.thinkqest.org
http://www.mathgoodies.com/lessons/toc_vol5.html –
http://www.teacherschoice.com.au/Maths_Library/Algebra/Alg_1.htm
http://education.jlab.org/solquiz
http://w3.fiu.edu/math/cine_math/fast/pie.htm -- solving equations
http://www.algebrahelp.com/worksheets/
http://www.math.com/homeworkhelp/Algebra.html
http://www.math.com/homeworkhelp/PreAlgebra.htm
My child completed this packet over the summer and will be ready to submit it by the end of the first
week back to school in September.
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Parent Signature _______________________________
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