exam review 2 nd semester algebra i. topics covered essential questions from first semester chapter...

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