Download Exam Review - The Westminster Schools

Exam Review
2nd Semester
Algebra I
Topics Covered
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Essential Questions from First Semester
Chapter 6 – Working with Radicals
Chapter 7 – Solving Systems of Equations
Chapter 8 – Quadratic Functions and Equations
Chapter 9 – Exponential Functions
Chapter 10 – Polynomial Functions and Equations
Chapter 11 – Rational Functions and Equations
Unit 12 – Probability and Trigonometry
Chapter 6 –
Working with Radicals
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The Pythagorean Theorem
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Rational and Irrational Numbers
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Calculating with Radicals
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Multiplying Monomials and Binomials
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Special Products
Chapter 7 –
Solving Systems of Equations
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Solving systems of equations
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Substitution method
Elimination method
Graphing method
Solving systems of inequalities
Chapter 8 –
Quadratic Functions and Equations
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Graphing quadratic functions
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y-intercept
x-intercepts
vertex
symmetry
Solving quadratic equations
The quadratic formula
Chapter 9 –
Exponential Functions
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Graphing simple exponential functions
Applications of exponential functions
Simplifying expressions with exponents
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Positive exponents
Negative exponents
Scientific Notation
Chapter 10 –
Polynomial Functions and Equations
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The Discriminant
Factoring
Solving quadratic equations
Simplifying polynomial expressions
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Involving multiplication and/or division
Involving addition and/or subtraction
Chapter 11 –
Rational Functions and Equations
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Graphing simple rational functions
Solving rational equations
Simplifying rational expressions
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Involving multiplication and/or division
Involving addition and/or subtraction
Unit 12 –
Probability and Trigonometry
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Counting principle
Permutations and combinations
Probability
Special right triangles
Simple trigonometry
Applications of trigonometry
Order of Operations
7  7  85
2
2
Solving Equations
5( x  3)  4 x  6
Writing the Equation of a Line
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Find an equation of a line passing through
the points (-1, 3) and (-2, -5).
Probability
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A six sided die was rolled 60 times.
1 came up 12 times, 2 came up 9 times,
3 came up 15 times, 4 came up 8 times,
5 came up 10 times. What is the
theoretical and the experimental
probability of getting an even roll?
Geometric Probability
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Find the area of the
shaded region.
Pythagorean Theorem
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Find the missing leg length.
8
4
Pythagorean Theorem
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Is a triangle with side lengths 4, 5, 6 a right
triangle? Justify your answer.
Rational or Irrational?
1
2
Rational or Irrational?
25
Rational or Irrational?
17
Rational or Irrational?

Rational or Irrational?
3.52
Simplify the radical
162
Simplify the radical
72
Simplify the radical
3 12
Add/Subtract
3 125  2 80
Add/Subtract
75  27
Multiply
3 8  4 6
Multiply
( 3  1)( 3  1)
Find the product.
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(2x + 1)(2x + 3)
Find the product.
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(4  3)(2  3)
Find the product.
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(3  7)(4  2 7)
Expand.
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(x + 2)2
Solving systems of equations
Substitution method
 y  x4
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2 x  y  13
Solving systems of equations
Elimination method
 3x  2 y  1

5 x  2 y  1
Solving systems of equations
Graphing method
 y  2 x  1

2 y  4 x  2
Solving
systems of inequalities
 y  2 x  3

4 y  2x  8
Graphing quadratic functions
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State the vertex, the
x- and y-intercepts.
Show all work to find
the vertex and the
x- and y-intercepts.
f ( x)  x  2 x  3
2
Solving quadratic equations
2 x  32  0
2
Solving quadratic equations
2 x  21  x
2
Solving quadratic equations
4 x  12 x  9
2
The quadratic formula
x  5 x  18  0
2
2x  6x  3
2
The quadratic formula
2x  6x  3
2
Graphing simple
exponential functions
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Determine whether the following is
exponential growth or decay. Graph.
y  16(0.5)
x
Graphing simple
exponential functions
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Determine whether the following is
exponential growth or decay. Graph.
3
y  8 
2
x
Applications of
exponential functions
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Alyisha is saving for her college tuition. She
has $2000 in a savings account that pays 6%
annual interest.
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Write an equation giving the amount of money in
Alyisha’s account at any time in the future
assuming she makes no deposits or withdrawals.
How much money will Alyisha have in her account
4 years from now?
Simplifying
expressions with exponents
3
5
4
2x y z
2 2 2
6x y z
Simplifying
expressions with exponents
 3 xy z 
 2 3 
 2x y z 
2 1
2
Scientific Notation
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Write in scientific notation.
12, 030, 000, 000
0.00000001254
The Discriminant
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Determine the number of x-intercepts for
each of the following.
y  3x  2 x  3
2
y   x  3x  12
2
Factoring
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Factor completely, if possible.
25 x  16
2
x  5 x  14
2
2 x  14 x  24
2
Solving quadratic equations
30b  25b  0
2
Solving quadratic equations
 r  5 2r  7   0
Solving quadratic equations
14 x  30 x  2  8  x
2
Simplifying polynomial
expressions – (+ and - )
 7 x  3 y  6   2  9 x  5 y 
a
2
 2b    8a  3ab  2b
2
2
2

Simplifying polynomial
expressions ( and )
 x  3 y  6 2  9 x 
Simplifying polynomial
expressions ( and )
c  d  c
2
 cd  d
2

Simplifying polynomial
expressions ( and )
5 x  6 x  2(3x  2)
2
Graphing simple rational
functions
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Graph
1
y
x
Graphing simple rational
functions
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Graph
1
y
x 1
Solving rational equations
3
4

x  2 x 3
Solving rational equations
2
3
1
 2

x2 x 4 x2
Simplifying rational expressions
( and )
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Simplify
2
6x 2x

2
5 y 15 y
Simplifying rational expressions
( and )
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Simplify
y
2y  y

y4
y4
2
Simplifying rational expressions
( and )
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Simplify
n  9 n  2n  1
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2n  2
n3
2
2
Simplifying rational expressions
(+ and - )
3
2

x 5 x
Simplifying rational expressions
(+ and - )
n
2n

n2 n2