exam review 2 nd semester algebra i. topics covered essential questions from first semester chapter...
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Exam Review
2nd Semester
Algebra I
Topics Covered
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
The Pythagorean Theorem Rational and Irrational Numbers Calculating with Radicals Multiplying Monomials and Binomials Special Products
Chapter 7 –Solving Systems of Equations
Solving systems of equations Substitution method Elimination method Graphing method
Solving systems of inequalities
Chapter 8 – Quadratic Functions and Equations
Graphing quadratic functions y-intercept x-intercepts vertex symmetry
Solving quadratic equations The quadratic formula
Chapter 9 – Exponential Functions
Graphing simple exponential functions Applications of exponential functions Simplifying expressions with exponents
Positive exponents Negative exponents
Scientific Notation
Chapter 10 – Polynomial Functions and Equations
The Discriminant Factoring Solving quadratic equations Simplifying polynomial expressions
Involving multiplication and/or division Involving addition and/or subtraction
Chapter 11 – Rational Functions and Equations
Graphing simple rational functions Solving rational equations Simplifying rational expressions
Involving multiplication and/or division Involving addition and/or subtraction
Unit 12 – Probability and Trigonometry
Counting principle Permutations and combinations Probability Special right triangles Simple trigonometry Applications of trigonometry
Order of Operations
27 7 85
2
Solving Equations
64)3(5 xx
Writing the Equation of a Line
Find an equation of a line passing through the points (-1, 3) and (-2, -5).
Probability
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
Find the area of the shaded region.
Pythagorean Theorem
Find the missing leg length.
48
Pythagorean Theorem
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
162
Simplify the radical
72
Simplify the radical
3 12
Simplify the radical
3 125 2 80
Add/Subtract
75 27
Add/Subtract
3 8 4 6
Multiply
( 3 1)( 3 1)
Multiply
Find the product.
(2x + 1)(2x + 3)
Find the product.
(4 3)(2 3)
Find the product.
(3 7)(4 2 7)
Expand.
(x + 2)2
Solving systems of equationsSubstitution method
4
2 13
y x
x y
Solving systems of equationsElimination method
3 2 1
5 2 1
x y
x y
Solving systems of equationsGraphing method
2 1
2 4 2
y x
y x
Solving systems of inequalities
2 3
4 2 8
y x
y x
Graphing quadratic functions
State the vertex, the x- and y-intercepts. Show all work to find the vertex and the x- and y-intercepts.
2( ) 2 3f x x x
Solving quadratic equations
22 32 0x
Solving quadratic equations
22 21x x
Solving quadratic equations
24 12 9x x
The quadratic formula
2 5 18 0x x
22 6 3x x
The quadratic formula
22 6 3x x
Graphing simple exponential functions
Determine whether the following is exponential growth or decay. Graph.
16(0.5)xy
Graphing simple exponential functions
Determine whether the following is exponential growth or decay. Graph.
x
y
2
38
Applications of exponential functions
Alyisha is saving for her college tuition. She has $2000 in a savings account that pays 6% annual interest. 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
222
453
6
2
zyx
zyx
Simplifying expressions with exponents
22 1
2 3
3
2
xy z
x y z
Scientific Notation
Write in scientific notation.
12,030,000,000
0.00000001254
The Discriminant
Determine the number of x-intercepts for each of the following.
23 2 3y x x
2 3 12y x x
Factoring
Factor completely, if possible.
2 5 14x x
225 16x
22 14 24x x
Solving quadratic equations
230 25 0b b
Solving quadratic equations
5 2 7 0r r
Solving quadratic equations
214 30 2 8x x x
Simplifying polynomial expressions – (+ and - )
7 3 6 2 9 5x y x y
2 2 2 22 8 3 2a b a ab b
Simplifying polynomial expressions ( and )
3 6 2 9x y x
Simplifying polynomial expressions ( and )
2 2c d c cd d
Simplifying polynomial expressions ( and )
25 6 2(3 2)x x x
Graphing simple rational functions
Graph
1y
x
Graphing simple rational functions
Graph
1
1y
x
Solving rational equations
3 4
2 3x x
Solving rational equations
2
2 3 1
2 4 2x x x
Simplifying rational expressions ( and )
Simplify2
2
6 2
5 15
x x
y y
Simplifying rational expressions ( and )
Simplify22
4 4
y y y
y y
Simplifying rational expressions ( and )
Simplify2 29 2 1
2 2 3
n n n
n n
Simplifying rational expressions (+ and - )
3 2
5x x
Simplifying rational expressions (+ and - )
2
2 2
n n
n n
