Download STEM 9 Algebra 2 Recommended Review

STEM 9 Algebra 2 Summer Review 2016
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 the summer
review is to remind you and reinforce what you learned in previous math classes. I suggest
working on this review in the few weeks before returning to school.
This material will not be graded. I will provide an answer key and can review your work with
you the first week of school.
For each topic addressed, there are examples, explanations, and/or references, followed by
a short set of practice problems.
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
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 and see you in August!
Ms. Blasko
[email protected]
1. Fractions
Multiplying fractions:
a c ac
 
b d bd
2 5 10
 
3 7 21
Dividing fractions:
a c a d ad
   
b d b c bc
1 2 1 7 7
   
4 7 4 2 8
Adding or subtracting fractions without a common denominator:
a c  d  a c  b  da cb da  cb
     


b d  d  b d  b  db db
db
3 2  3 3 2  4 9
8 9  8 17
     



4 3  3  4 3  4  12 12
12
12
Practice Set I: Perform the following operations. Write answers in the lowest terms.
1.
12 x 3xz

5y 4y
2.
3a 7b

5b 5c
3.
5 6

x y
4.
4a 6a

b
c
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut3_fractions.htm
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-a-polynomial
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
2. (x2y4)(x3y5)
12a 6 b 9
3.
6a 4 b 3 c
 3x 2
4. 
4
 12 x



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
vertical change
rise y 2  y1



change in x horizontal change run x2  x1
Find the slope of the line passing through points (3, -1) and (-2, 5)
m
5  (1)
6

23 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.
y
3.
9
4.
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. Slopeintercept 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)
m
39
6

2
1 2  3
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  c 2
SOHCAHTOA
opp
adj
opp
cos 
tan 
hyp
hyp
adj
a
b
a
sin A 
cos A 
tan A 
c
c
b
b
b
b
sin B 
cos B 
tan B 
c
c
a
sin 
Example: Given that a = 6 and b = 8, find the length of the hypotenuse.
c 2  a 2  b 2 so c 2  6 2  8 2  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