Download Algebra 1H Summer Packet

1
Algebra I Honors Summer Assignment
Algebra I Honors is a rigorous course designed for mathematically talented
students who have the conceptual and computational background and maturity
to pursue an honors-paced subject. Topics are covered in depth and at an
accelerated pace. The curriculum covers algebraic skills and concepts necessary for an understanding of all
future mathematics to be studied. Abstract and numerical reasoning are emphasized. Topics include: the Real
Number System, absolute value, linear, quadratic, polynomial, radical, rational and exponential equations,
functions, systems of equations and inequalities. Graphing calculators are employed to extend concepts.
Students learn a variety of problem solving techniques and will apply arithmetic principles to specific algebraic
topics. Standardized test preparation is integrated throughout the course. The completion of a summer
assignment is required.
If you want to preview the course, the book and the supplementary materials, you can go to the textbook website:
www.pearsonsuccessnet.com
choose the link for Pearson High School Mathematics Common Core © 2012
username: Alg1Honors
password: Westessex15
**you must turn off pop-up blockers
To be successful in Algebra 1, you will need:
 A lot of pencils
 A binder with loose-leaf paper
 A red pen (or any other color besides black/blue)
 A TI-84+ graphing calculator
Over the summer, it is your responsibility to review and master the concepts in this packet.
 You will be required to hand in the answers on THE FIRST DAY OF SCHOOL. No exceptions.
 This assignment is worth 5 homework grades.
 You will have a quiz on these topics.
 This packet should be done WITHOUT a calculator.
 Work should be done on the answer sheets provided.
Topic
Suggested date of completion
Part 1 – pages 3-5:
Fractions (Add/Subtract)
Fractions (Multiply/Divide)
8/1/2016
Part 2 – pages 6-8:
Comparing Numbers
Evaluating Expressions
8/8/2016
Part 3– pages 9-11:
Distributive Property
Combining Like Terms
Solving Equations
8/15/2016
Part 4– pages 12-14:
Solving Inequalities in One Variable
Rewriting Equations in Slope-Intercept Form
Graphing Equations in Slope-Intercept Form
8/24/2016
Part 5 – pages 15-16:
Percent Problems
Applications
8/29/2016
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Here are some other websites you might find useful in completing your summer
assignment.
1. http://www.math.com/homeworkhelp/PreAlgebra.html - for help with
adding/subtracting/multiplying/dividing integers, fractions, and decimals
2. http://www.math.com/homeworkhelp/Algebra.html - for help with order of
operations, combining like terms, solving equations
3. http://www.mathgoodies.com/lessons/ - for help with percentages, decimals,
fractions, probability, statistics, and PEMDAS
4. http://www.teacherschoice.com.au/mathematics_how-to_library.htm - for help
with evaluating and solving equations
5. http://www.algebrahelp.com/ - a great resource for help in all topics in algebra as
well as basic skills
6. http://www.freemathhelp.com/algebra-help.html - includes text and video lessons
includes text and video lessons from an array of algebra topics including
equations, inequalities, and polynomials.
7. http://mathforum.org/library/drmath/drmath.middle.html - An achieve of questions
and answers by Dr. Math
8. http://www.purplemath.com/modules/index.htm - excellent resource for topics
from pre-algebra to advanced algebra
9. www.brainpop.com – has a free trial version which includes video tutorials and
more
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PART 1
Find the reciprocal of the number.
1. 7
2.
3.
4.
4
Add or subtract without using a calculator. Write the answer as a fraction or mixed number in simplest form.
5.
6.
7.
8.
Add or subtract without using a calculator. Write the answer as a fraction or mixed number in simplest form.
9.
10.
11.
12.
5
Add or subtract without using a calculator. Write the answer as a fraction or mixed number in simplest form.
13.
15.
17.
19.
14.
16.
18.
20.
Multiply or divide without using a calculator. Write the answer as a fraction or mixed number in simplest form.
21.
24.
27.
30.
22.
25.
28.
31.
23.
26.
29.
32.
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Part 2
7
Compare the two numbers. Write the answer using <,>, or =.
1. -16.82 and -14.09
3.
5.
4.
6.
2. 0.40506 and 0.00456
Write the numbers in order from least to greatest.
7.
8.
10.
23.12, -23.5, -24, -23.08, -24.01
11.
9.
12.
13. You need a piece of trim that is
yards long for a craft project. You have a piece of trim that is
yards long. Is the trim you have long enough?
8
Remember:
P
E
M/D
A/S
Evaluate the expression without using a calculator.
14.
17.
15.
18.
16.
19.
20.
21.
22.
Evaluate the expression when x = 3 without using a calculator.
23.
24.
25.
26.
27.
28.
29.
30.
31.
2)
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PART 3
Use the distributive property to write the expression without parentheses.
1.
3.
5.
7.
2.
4.
6.
8.
Simplify the expression.
9.
10.
11.
9x + x
12.
15.
13.
16.
14.
17.
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Solving Equations with Variables on Both Sides
To solve equations with variables on both sides, you can use the properties of
equality and inverse operations to write a series of simpler equivalent equations.
Example 1:
Solve 2(m -2) + 5m = 13 – 2(3m + 2)
Solution:
2(m -2) + 5m = 13 – 2(3m + 2)
2m  4 + 5m = 13  6m  4
Distribute.
7m  4 = 6m + 9
Add the terms with variables together on the left side and
the constants on the right side to combine like terms.
7m  4 + 6m = 6m + 9 + 6m
To move the variables to the left side, add 6m to each
side.
Simplify.
13m  4 = 9
13m  4 + 4 = 9 + 4
13m = 13
13m 13

13 13
m=1
To get the variable term alone on the left, add 4 to each
side.
Simplify.
Divide each side by 13 since x is being multiplied by 13 on
the left side. This isolates x.
Simplify.
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Solving Equations with Infinite or No Solution
When solving an equation, if the variables cancel out, the equation will either have
no solution or infinite solutions.
Example 1:
Solve 2x + 6 = 3(x + 2) – x
Solution:
distribute
combine like terms
get all variables to one side
x’s cancel and you’re left with a true statement
You get an identity so the equation has infinite solutions. The solutions are all
real numbers, which means any value of x would make the equation true.
Example 2:
Solve 5x – 3 = 4(x + 2) + x
Solution:
distribute
combine like terms
get all variables to one side
x’s cancel and you’re left with a false statement
You get a false statement so the equation has no solution, which means there
are no values of x that would make the equation true.
Solve the equation.
25.
33. 5x + 9 = 3x + 1
26.
34. 14 + 7n = 14n + 28
18.
19.
27.
20.
21.
22.
7
4

6 n5
35. 22(g  1) = 2g + 8
36. d + 12  3d = 5d  6
28.
29. b  3   2
12
5
37. 4(m  2) = 2(3m + 3)
38. (4y  8) = 2(y + 4)
30.
39. 5a  2(4a + 5) = 7a
31.
40. 11w + 2(3w  1) = 15w
32.
41. 4(3  5p) = 5(3p +3)
23.
24.
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PART 4
Solving Inequalities in One Variable
 Remember:
o > means greater than
o < means less than
o > or < is an open circle
o ≥ or ≤ is a closed circle
o When you multiply or divide by a negative, the inequality symbol
must flip
EXAMPLES Solve each inequality and graph its solution.
Example 1:

First solve the inequality like you solve an equation.
a ≤ -18

**reverse the sign because you divided by a
negative
Then graph the solution
Example 2:

First solve the inequality like you solve an equation.

Then graph the solution
Solve and graph the inequality.
Write an inequality for each graph.
1. 11x + 13 ≥ -9
7. 3(2x – 4) -2(x + 1) > 10
2. 6x – 10 < 6 – 2x
8.
12.
9. -8x – 3 < 18 – x
13.
3. 3(x – 2) – 2x > 16
4. 6x + 10 > 8 – (x + 14)
5. -5x – 2(x + 3) ≤ 8
6. 3x + 8 ≤ 2(x – 4) – 2(1 – x)
10. 0.3(x – 2) > 0.4(1 + x)
11.
14.
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Rewriting Equations in Slope-Intercept Form
The equation of a line written in the form y = mx + b is in slope-intercept form. The slope of the
line is m and the y-intercept is the point (0, b).
Example 1:
Rewrite the equation 4x – 2y = 12 in slope-intercept form and identify the slope and y-intercept.
Solution:
4x – 2y = 12
-4x
-4x
-2y = -4x + 12
-2
-2 -2
y = 2x – 6
You want to solve for y.
Move the x-term to the right side.
Divide both sides by -2.
Simplify.
The slope of the line is m = 2 and the y-intercept is (0, -6).
Rewrite the equation in slope intercept form and identify the slope and y-intercept.
15. -2x + y = 1
18. 3x – 4y = 8
16. 2y = -x – 8
19.
y – 4 = -3(x – 3)
17. -2x + 3y = 15
20.
5x + 7y + 11 = 4x – 2y – 7
Graphing Equations in Slope-Intercept Form
Remember the equation of a line written in the form y = mx + b is in slope-intercept form. The
slope of the line is m and the y-intercept is the point (0, b).
Example 1:
Graph y = 2x + 1. Identify the slope and the y-intercept.
Step 1 Find the slope and y-intercept.
m=2
y-intercept: (0, 1)
Step 2 Graph the y-intercept (0, 1)
Remember: slope is rise over run!
Step 4 Draw the line.
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Example 2:
Graph 2x + 6y = 12.
Solution:
Step 1: Put 2x + 6y = 12 in slope-intercept form.
2x + 6y = 12
You want to solve for y.
-2x
-2x
Move the x-term to the right side.
6y = -2x + 12
Divide both sides by -2.
6
6
6
Simplify.
Step 2: Find the slope and y-intercept.
The slope of the line is
and the y-intercept is (0, 2).
Step 3: Graph the y-intercept (0, 2)
Step 4: Use the slope to plot another point.
Count 1 down (because the rise is negative)
and 3 right (because the run is positive) and plot another point.
Remember: the line should be decreasing because the slope is negative.
Step 5: Draw the line.
Graph the line. Identify the slope and y-intercept.
21. y = 3x + 5
22. y = -4x – 2
23. 3x – 4y = 12
24. 2x + 3y = 6
25. x - 5y = 20
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PART 5
Using the proportion method to solve Percent Problems
1. What is 25% of 80?
2. 9 is what percent of 200?
3. What is 55% of 600?
4. 5.4 is what percent of 9?
5. 90 is what percent of 40?
6. 120% of what is 60?
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Application Problems
Translate the following into an algebraic expression:
7.
a. 14 less than the quotient of 63 and a number “n”
b. The difference of q and 8
c. 9 more than the product of 51 and a number “t”
Show all work for each application problem.
8. You work for 4 hours on Saturday and 8 hours on Sunday. You also receive a $50 bonus. You
earn $164. How much did you earn per hour?
9. Online concert tickets cost $37 each, plus a service charge of $8.50 per ticket. The website also
charges a transaction fee of $14.99 for the purchase. You paid $242.49. How many tickets did
you buy?
10. An airplane has a wingspan of 25 feet and a length of 20 ft. You are designing a model of the
airplane with a wingspan of 15 inches. What will the length of your model be?
11. A drama club wants to raise at least $500 in ticket sales for its annual show. The members of
the club sold 50 tickets at a special $5.00 rate. The usual ticket price the day of the show is
$7.50. At least how many tickets do they have to sell the day of the show to meet their goal?
12. In a bird sanctuary, 30% of the birds are hummingbirds. If there are about 350 birds in the
sanctuary at any given time, how many are hummingbirds?
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NAME___________________________________________________
ALGEBRA 1 SUMMER PACKET 2015 Answer Sheet - Show ALL work for credit!
PART 1
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PART 2
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PART 3
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PART 4
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PART 5
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