STEM 9 Algebra 2 Summer Assignment 2013
Welcome to STEM 9!
I am Ms. Blasko and I will be your STEM Algebra 2 teacher. This coming
school year we will build on the skills you learned in Algebra 1 and Geometry.
The purpose of this summer assignment is to remind you and reinforce what
you learned in previous math classes. Also, I hope to reinforce the practice of
showing your work! To receive full credit you must show the steps taken to
reach your final answer.
Note that there is a mini lesson and a link to an online resource for each
topic. If you do not remember how to complete a problem you are expected to
research and review the topic.
Have a wonderful summer, see you in August!
Ms. Blasko
Name____________________
Great Mills High School Math Department Summer Review
STEM Algebra 2 Honors
This packet contains review material. You have been taught and tested on this material
in prior math courses. However, math is a cumulative study; it builds upon itself.
Recalling these prerequisite mathematical concepts and processes is critical to your
success in this class.
The purpose of this review packet is three-fold:
1. Review/refresh prerequisite skills
2. Reinforce the expectation that you are prepared to take this course
3. Provide a smooth transition into a higher-level math course
This material will be graded as follows:
1. Completion of this packet is a process grade for the class.
2. This packet will be returned to you and each problem will be reviewed.
Following review, you will take a process-grade group quiz.
3. Lastly, there will be a product-grade individual quiz on this material.
For each topic addressed, there are examples, explanations, and/or references,
followed by a short set of practice problems. You are expected to complete this packet
on your own. Be sure to show your work. If you need additional space, use lined
notebook paper and staple it to this packet.
This packet is due on August 21, 2013, the first day of school.
Topics:
1.
2.
3.
4.
5.
6.
7.
8.
Fractions
Simplify Polynomial Expressions
Solve Equations
Rules for Exponents
Radicals
Slope/Rate of Change
Graphing Lines
Right Triangles
1. Fractions
Multiplying fractions:
a
b
c
d
ac
bd
2 5
3 7
10
21
Dividing fractions:
a
b
c
d
a d
b c
ad
bc
1
4
2
7
1 7
4 2
7
8
Adding or subtracting fractions without a common denominator:
a
b
c
d
d a
d b
3
4
2
3
3 3
3 4
c b
d b
2 4
3 4
da
db
9
12
cb
db
8
12
da cb
db
9 8
12
17
12
Practice Set I: Perform the following operations. Write answers in the lowest terms.
1.
12 x 3 xz
5y 4y
2.
3a
5b
7b
5c
3.
5
x
4.
4a
b
6a
c
6
y
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut3_fractions.h
tm
2. Simplify Polynomial Expressions
Combine like terms. “Like” terms have the same variable to the same power.
Example: 8x2 + 10x3 – 5x2 + 3x3
8x2 – 5x2 + 10x3 + 3x3
3x2 + 13x3
Apply the Distributive Property:
Example: 5(4x – 6)
5 • 4x – 5 • 6
20x – 30
Combine Like Terms and Apply the Distributive Property
Example: 4(6x – 3y) + 5(2x + 7y)
4 • 6x – 4 • 3y + 5 • 2x + 5 • 7y
24x – 12y + 10x + 35y
34x + 23y
Practice Set 2. Simplify. Show all work.
1. 3(5a – b) + 4(2a – 2b)
2. -5(4x – 7) + 13 – 6x
3. 8(3x + 5y – 6z) – 2(2x + 4z).
4. 2(3x – 4) – (12x + 3)
http://www.khanacademy.org/math/algebra/polynomials/polynomial_basics/v/simply-apolynomial
3. Solve Equations
Simplify both sides of the equation.
Use addition/subtraction to move variables to one side, constants to the other.
Use multiplication/division to solve for the variable.
Example:
4(x + 7) = 22 – 2x
4x + 28 = 22 – 2x
distribute the 4
+2x
add 2x to both sides
+2x
6x + 28 = 22
- 28 -28
6x
subtract 28 from both sides
= -6
x = -1
divide both sides by 6
Problem Set 3. Solve each equation. Show all work.
1. 45x – 720 + 15x = 60
2. 8(3x – 4) = 232
2. -131 = -5(3x – 8) + 6x
4. – 7x – 22= 18 + 3x
5.
6.
http://www.purplemath.com/modules/solvelin.htm
http://www.purplemath.com/modules/solvelin3.htm
4. Rules for Exponents
Practice Set 4. Simplify each expression.
1. (-3m2n)4
12a 6 b 9
3.
6a 4 b 3 c
2. (x2y4)(x3y5)
4.
3x 2
12 x 4
3
http://www.mathsisfun.com/algebra/exponent-laws.html
5. Radicals
Practice Set 5. Simplify each radical. Show your work.
1.
486
3.
475
2.
500
http://hotmath.com/help/gt/genericalg1/section_8_1.html
6. Slope/Rate of Change
The slope of a line describes its steepness, or how it angles away from the horizontal.
The slope of a line is a rate of change and can expressed as a relationship between two
variables, such as miles per gallon or cost per pound.
slope m
change in y
change in x
vertical change
horizontalchange
y2
x2
rise
run
y1
x1
Find the slope of the line passing through points (3, -1) and (-2, 5)
5 ( 1)
2 3
m
6
5
Practice Set 6.
Find the slope of the line passing through each pair of points. Show your work.
1. (7, -9) (-1, 5)
2. (4, 0) (-6, 6)
F ind the slope of the lines represented on the graphs below.
3.
y
4.
9
y
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
x
1
2
3
4
5
6
7
8
9
1
2
3
4
http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/Rate.htm
http://www.purplemath.com/modules/slopyint.htm
5
6
7
8
9
7. Write Linear Equations/Graph Lines
You can find the equation of a line from two points, or from one point and the slope.
Slope-intercept form, y = mx +b, where m Is the slope and b is the y-intercept, is one
form of a linear equation that is particularly easy to graph.
Example: Write the equation of a line with a slope of 3 and passing through the point
(5, 7)
y = mx + b
7 = 3(5) + b
Equation: y = 3x – 8
-8 = b
Example: Write the equation of a line that passes through (2, 9) and (-1, 3)
3 9
1 2
m
6
3
2
y
mx b
9
2(2) b
b
5
y
2x 5
Problem Set 7. Write an equation, in slope-intercept form, using the given information.
1.
m = -⅓
(-3, 6)
2. (-4, -1) (4, 5)
Graph the lines.
3. y = (2/3)x - 4
4. y = -3x + 3
y
y
6
5
4
3
2
1
6
5
4
3
2
1
x
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
x
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut14_lineargr.htm
8. Right Triangles
Pythagorean Theorem : a 2 b 2
c2
SOHCAHTOA
opp
cos
hyp
a
sin A
cos A
c
b
sin B
cos B
c
sin
adj
opp
tan
hyp
adj
b
a
tan A
c
b
b
b
tan B
c
a
Example: Given that a = 6 and b = 8, find the length of the hypotenuse.
c2
a2
b 2 so c 2
62
82
36 64 100 c 2
100, c 10
Problem Set 8. Given right triangle ABC, where C = 90º, solve for the missing side.
Show all work.
1. a = 12, b = 5, find c.
2. b = 15, c = 17, find a.
Given that a = 9, b = 40, and c = 41, find the trig ratio.
3. sin B
4. tan A
http://www.mathsisfun.com/algebra/trig-finding-angle-right-triangle.html
http://www.purplemath.com/modules/basirati.htm