Division by Binomials Part 2



Unit: Algebra and # Notes

Name ________________________ Dates Taught _________________

|General Outcome | | | |

|10I.A.2 |Demonstrate an understanding of irrational numbers by representing, identifying, and | | |

| |simplifying irrational numbers and ordering irrational numbers. | | |

|10I.A.2 |Express a radical as a mixed radical | | |

|10I.A.2 |Express a mixed radical as an entire radical | | |

|10I.A.3 |Demonstrate an understanding of powers with integral and rational exponents | | |

Comments : ________________________________________________

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

Outcome 10I.A.3: Integral Exponents

Note: a,b and x are rational and variable basis while m and n are integral exponents.

|Law: |Example: |

|Converting Negative Powers |[pic] [pic] |

| | |

|[pic] | |

|Product of Powers |[pic] |

| | |

|[pic] | |

|Quotent of Powers |[pic] |

| | |

|[pic] | |

|Power of a Power |[pic] |

| | |

|[pic] | |

|Power of a Product |[pic] |

| | |

|[pic] | |

|Power of a Quotient |[pic] |

| | |

|[pic] | |

|Zero Exponent |[pic] [pic] |

| | |

|[pic] | |

More Examples: Simplify. Your answer should contain positive exponents only.

a) [pic] b) [pic]

c) [pic] d) [pic] e) [pic]

f) [pic] g) [pic] h) [pic]

Homework: Handout: Kuta Software: Properties of Exponents

Outcome 10I.A.3: More Integral Exponents

Examples: Simplify. Your answer should contain positive exponents only.

a) [pic] b) [pic]

c) [pic] d) [pic]

e) [pic]

Homework: Handout: Kuta Software: More Properties of Exponents

Outcome 10I.A.3: Rational Exponents

Note: a,b and x,y are rational and variable basis while m and n are integral exponents.

|Law: |Example |

|Product of Powers |[pic] |

| | |

|[pic] | |

|Quotent of Powers |[pic] |

| | |

|[pic] | |

|Power of a Power |[pic] |

| | |

|[pic] | |

|Power of a Product |[pic] |

| | |

|[pic] | |

|Power of a Quotient |[pic] |

| | |

|[pic] | |

|Zero Exponent |[pic] [pic] |

| | |

|[pic] | |

Note: A power with a rational exponent can be written with the exponent in decimal or fractional form. Eg. [pic].

Extra Examples:

|Example: | | |

|a) [pic] |b) [pic] |c) [pic] |

| |e) [pic] |f) [pic] |

|d) [pic] | | |

| |

|g) [pic] |h) [pic] |i) [pic] |

Homework: Page 72, Q #

Outcome 10I.A.2: Number Systems and Approximating Irrationals

numbers, , are all . ie. N = {1, 2, 3, . . . }

numbers, , are all positive integers and .

ie. W = {0, 1, 2, 3, . . . }

, , are whole numbers and their .

ie. I = {. . . -2, -1, 0, 1, 2, . . . }

numbers, , are any numbers written in the form of a

[pic], where a & b are and b . ie. [pic]

numbers, , are any number that be written in the form [pic], where a & b are and b ( 0. ( [pic]Q = Set of irrational numbers

numbers, , are the of the number set and the number set.

ie. R = Q U Q

| |

|Word bank: cannot fraction integers integers integers integers |

|irrational irrational natural opposites positive rational |

|rational real union whole zero |

Examples:

1. Which Number System best represents the following numbers?

a) 2 b) 0.25

c) [pic] d) –5

e) ( f) 0.131313…

g) [pic] h) 0

i) 0.123456789… j) ¾

2. Write each number in decimal form (round to 2 decimal places). Some may already be written in decimal form.

a) 3 b) 1.41

c) [pic] d) –3

e) ( f) 0.171717…

g) [pic] h) 0

i) 0.5123456789… j) ¾

Place the above numbers on a horizontal number line (below). Clearly label the number line and use an appropriate scale.

Homework: MPC20S, Exercise 20

Outcome 10I.A.2&3 Rational Exponents

A is the proper name for the of a number. The parts of a radical are as follows:

where, r is the root ,

x is the ,

p is the of the radicand, and

[pic] is the sign.

| |1 |2 |3 |4 |5 |6 |

|Perfect Squares | | | | | | |

|Perfect Cubes | | | | | | |

|Perfect 4th | | | | | |

|Perfect 5th | | | |

Example: Simplify:

a) [pic] Why?

b) [pic] c) [pic] d) [pic]

e) [pic] f) [pic] g) [pic]

Radicals may be written as numbers with exponents.

Example: The square root of 5, , could also be written as .

o The 1 represents the exponent or of 5.

o The 2 represents the second or root of 5.

o When there is root index shown as part of the radical, the root index is understood to be .

Examples 1: Write the following using a fractional exponent:

a) [pic] = b) [pic]= c) [pic] =

Examples 2: Write the following in radical form:

a) [pic] = b) [pic] = c) [pic]

Example 3: Evaluate without using a calculator:

Hint: Always evaluate the radical first, then apply the power (Make the expression before you make it bigger)

a) [pic]= b) [pic]= c) [pic]=

d) [pic]= e) [pic]=

Homework: Next Page of this booklet & Page76, Q # 1, 2

Homework:

1.Write as a rational exponent:

a) [pic]= b) [pic]= c) [pic]=

d) [pic]= e) [pic]= f) [pic]=

2.Write as a radical:

a) [pic]= b) [pic]= c) [pic]=

d) [pic]= e) [pic]= f) [pic]=

3.Evaluate without using a calculator;

a) [pic]= b) [pic]= c) [pic]=

d) [pic]= e) [pic]= f) [pic]=

g) [pic] = h) [pic] =

Key 1.[pic] [pic] [pic] [pic] [pic] [pic]

2. [pic] [pic] [pic] [pic] [pic] [pic]

3. a) -15 b) 125 c) 16 d) 1024 e) 4 f) 4 g) -4 h) 4

Outcome 10I.A.2: Operations on Radicals (Simplifying)

➢ [pic], [pic], [pic],[pic], etc. are in form.

➢ [pic]is because it contains a (integer) factor.

( [pic]

To simplify a radical (also known as writing as a mixed radical):

• Depending on the of the radical, look for a perfect (cube, etc.) hidden in the factors of the .

• . the perfect square (cube, etc.) by placing its root in of the radical sign.

• . any constants in front of the radicand.

• Leave any without integer roots the radicand.

Examples:

1. Simplify (express as a mixed radical) each radical:

a) [pic] b) [pic] c) [pic]

d) [pic] e) [pic] f) [pic]

2. Express each mixed radical as an entire radical:

a) [pic] b) [pic] c) [pic]

Homework: Page76, Q #

-----------------------

Irrationals

Naturals

Wholes

Integers

Rationals

Reals

[pic]

[pic]

Word bank: combine factors front inside not numbers radicand remove simplest square square

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download