Algebra I Unit

Algebra 1 Unit 1

Overview

By Paige Roberts

Table of Contents

1.1 Properties of Rational & Irrational Numbers​ Slides 3 - 14

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​1.2 Quantitative Reasoning/Dimensional Analysis Slides 15 - 22

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1.3 Structure of Expressions Slides 23 - 28

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​1.4 Operations of Polynomials​ Slides 29 - 36​

1.1 Properties of Rational & Irrational Numbers

Rational vs Irrational

• CANNOT be written in the form of p/q where p & q are integers​.

• Non-terminating or "unpatterned" decimals.

• Examples: pi, -0.74839201​

Irrational

• Can be written in the form ​p/q where p & q are both integers.

• Terminating or Repeating decimals​

• Examples: 3/8, -5, .3333​

Rational

Draw

Separate the following numbers into rational and irrational groups.

$$\sqrt[]{36}$$  , -9 , .78379251 , 1/3 , $$\sqrt[]{2}$$

• Find a PERFECT SQUARE that will divide evenly into the radicand.

  • perfect square: 4

  • radicand: 48

  • 4 divides into 48 evenly 12 times. 4 * 12 = 48​

• Simplify the perfect square.

  • the square root of 4 is 2​​

• Repeat the process until the radicand is either prime or cannot be divided by a perfect square.​

  • Continue to break down 12

  • 4 divides evenly into 12 and is a perfect square.

Simplifying Radicals:

Perfect Squares​​

Draw

Simplify $$\sqrt[]{24}$$  

​Radicals can only be added or subtracted if the radicands are the same.

​

1. Simplify your radicals.

2. Add/Subtract the coefficients.

3. Keep the radicands the same.​

Adding/Subtracting Radicals​

Draw

Show the sum of $$\sqrt[]{20}-\sqrt[]{180}$$  

1.1 Quiz

4 questions​

​Be sure to check each question for calculator allowances.

Multiple Choice

NON-CALCULATOR

What is the rewritten form of the radical $$-6\sqrt[]{32}$$  ?

• $$-96\sqrt[]{2}$$  

• $$-2\sqrt[]{2}$$  

• $$-24\sqrt[]{2}$$  

• $$-192$$  

Multiple Choice

NON-CALCULATOR:

Which sum is rational?

• $$\pi+18$$  

• $$\sqrt[]{25}+1.75$$  

• $$\sqrt[]{3}+5.5$$  

• $$\pi+\sqrt[]{2}$$  

Multiple Select

NON-CALCULATOR:

Select the product(s) that are rational.

• $$\sqrt[]{2}\cdot\sqrt[]{50}$$  

•   $$\sqrt[]{10}\cdot\sqrt[]{8}$$  

• $$\sqrt[]{9}\cdot\sqrt[]{49}$$  

•   $$\sqrt[]{64}\cdot\sqrt[]{4}$$  

Multiple Choice

NON-CALCULATOR:

Which of these is equivalent to the expression $$3\sqrt[]{28}\cdot\sqrt[]{12}$$  ?

• $$3\sqrt[]{336}$$  

• $$3\sqrt[]{40}$$  

• $$12\sqrt[]{28}$$  

• $$12\sqrt[]{21}$$  

1.2 Quantitative Reasoning & Dimensional Analysis

If you need to move to the right, you will multiply by 10 at each move.

Example: Going from Deci to Milli, I would multiply by 100.​

Multiply by 10...

​If you need to move to the left, you will divide by 10 at each move.

Example: Going from Deca to Kilo, I would divide by 100.​

Divide by 10...

Draw

Change 10 cm into hm.

Determine factors that are equal.

This will help to form fractions that are equal to 1.

​​1) Conversion Factors

​Remember, "What goes up, must come down."

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​2) Set Up Special 1's

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Once a unit is on top and bottom, it cancels out.

Leaving you with the desired units.​

Multiply everything on the top of your fractions.

Multiply everything at the bottom of you fractions.​

​​4) Multiply!

​​3) Cancel Out Units

​

Draw

Convert 20 miles per hour into inches per second.

1.2 Quiz

2 questions​

​Be sure to check each question for calculator allowances.

Multiple Choice

How many centimeters is 5 meters?

• .005

• .05

• 50

• 500

Fill in the Blank

Daniel took a run on the track to record his speed. One lap around the track is 1/4 of a mile. It takes him 1 minute and 20 seconds to run one lap. How many seconds will it take him to do one mile?

1.3 Structure of Expressions

Anything separated by a plus or minus sign.

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Examples: 5x², -x², 4x²​

Term

A number that doesn't have a variable with it.​

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​Example: 3

Constant

The number before a variable.

Tells you what to multiply by.

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Examples: 5, -1/5, 4, -1​

Coefficient

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It tells you how many times to multiply a number or variable by itself.​ They are raised above the other letters and numbers​

Examples: 5, 2, 3​

​​Exponent

​

Draw

Create a polynomial that has 4 terms; coefficients of -1, 3 & 1/5; Exponents of: 1, 2 & 3; and a constant of -7

1.3 Quiz

2 Questions​

​Be sure to check each question for calculator allowances.

Multiple Choice

NON-CALCULATOR:

In which expression is the constant 5?

• $$3n^5+4n-1$$  

• $$-n^2+5n+4$$  

• $$-2n^2-n+5$$  

• $$4n^2+n-5$$  

Multiple Choice

NON-CALCULATOR:

The expression $$s^2$$  is used to calculate the area of a square, where s is the side length of the square. What does the expression $$\left(9x\right)^2$$   represent?

• The area of a square with a side of 9.

• The area of a square with a side length of 18.

• The area of a square with a side length of 3x.

• The area of a square with a side length of 9x.

1.4 Operations of Polynomials

• ​Be sure to add/subtract like terms by adding/subtracting the coefficients of those terms.

• Like terms are terms with the same variables raised to the same power.​

• Use the vertical method by stacking the like terms and them combining them.​

Adding & Subtracting Polynomials

​

Draw

$$\left(5x^2+4x+1\right)+\left(2x^2+5x+2\right)$$  

• You can multiply terms that are not like.

• Be sure to apply the exponent rules to terms with variables.

  • When multiplying terms with variables, you will add the exponents.​

• Use the area model to assist with multiplying polynomials with 2 or more terms.​

• After multiplying, be sure to simplify by​ adding like terms.

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Multiplying Polynomials

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Draw

Determine the product of $$x+3$$  and $$x+2$$  .

1.4 Quiz

2 Questions​

​Be sure to check each question for calculator allowances.

Multiple Choice

NON-CALCULATOR:

What is the product of $$3x+2$$  and $$-4x-5$$  ?

• $$-12x^2-15x-8x-10$$  

• $$12x-10$$  

• $$-12x^2-23x-10$$  

• $$-12x^2-15x-8x-10$$  

Multiple Choice

What is the perimeter of the model given the expression measurements?

• $$22x+4$$

• $$33x+1$$  

YOU HAVE NOW COMPLETED THE LESSONS FOR UNIT 1!

Please complete the Unit 1 Review Questions. The answers are provided at the bottom of the last page so that you can check your work.