merp #71 - 77
TRANSCRIPT
Day 15Do Now Day 15
knowledge of polynomials to solve
open ended problems.
Nov 304:17 PM
Goal: Students will be able to apply knowledge of polynomials to solve open ended problems.
Notes and Examples
Practice
Goal: Students will be able to apply knowledge of polynomials to solve open ended problems.
Day 15
Homework #15 Study Island #3 Wed MERP Set #4 Friday
Goal: Students will be able to apply knowledge of polynomials to solve open ended problems.
Attachments
©A Q2i0D1K29 JKkultPau lSVoLfgtywEatr5ej VLALsCC.H 9 vApl0lx 6rliagchZtusm Tr2easheUrjv8eedF.4 n SMgaSdLek TwMiQtBh1 8IXnRffi3nmi0t4eQ RA7l2gWepbUrKa1 X1N.g Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Properties of Exponents
1)
2
17)
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Properties of Exponents
1)
2
17)
3
x7
yz
-2-
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
SMART Notebook
Multiplying Binomials to Find an Area
_______________(1) The dimensions of a rectangular garden can be represented by a width of feet and a length of feet. Write a polynomial expression for the area A of the garden.
_______________(2) The dimensions of a rectangular garden can be represented by a width of feet and a length of feet. Write a polynomial expression for the area A of the garden.
Find the area of the shaded region:
_______________(3) (3) (4)
(1) Page 453 #22 – 59 Left
(2) Page 453 #25 – 62 Right
(3) Page 459 #5 – 29 Odd
(4) Page 459 #14 – 42 First Column; Page 466 #3 – 27 First Column
(5) Page 459 #15 – 43 Second Column; Page 466 #6 – 30 Fourth Column
(6) Page 459 #16 – 44 Third Column; Page 466 #31 – 47 Left
(7) Page 459 #17 – 45 Right; Page 466 #33 – 48 Third Column
(8) Page 473 #16 – 44 Left *******Quiz Tomorrow********
(9) Page 580 #19 – 55 Left Every Other One
(10) Page 580 #21 – 52 Right Every Other One
(11) Page 587 #9 – 45 Left
(12) Page 587 #10 – 46 Middle
(13) Page 587 #11 – 47 Right *******Quiz Tomorrow*******
(14) Page 593 #16 – 40 Every Other Even
(15) Applications of Area Problems
(16) Practice Test for Test Tomorrow
(17) Page 498 #1 – 10; Page 638 #1 – 7
8.1 Multiplication Properties of Exponents (R,E/2)
Steps and Laws for Exponents 1. Power to Power - Look for an exponent on the outside of parenthesis
- Rule: i. Multiply the Exponents
2. Multiplying Monomials – Look for two terms being multiplied together - Rule:
i. Multiply the Coefficients ii. Re-write the Variables
iii. Add the Exponents 3. Dividing Monomials – Look for a fraction bar
- Rule: i. Divide the Coefficients
ii. Re-Write the Variables iii. Subtract the Exponents Down
4. Combining Like Terms – Look for a + or – sign between two terms - Rule:
i. Combine the Coefficients ii. Re-write the variable and exponent
Never: - Leave an answer in simplest form with a negative exponent (negative exponent property). - Leave an answer in simplest form with a zero as an exponent (zero exponent property E1) a. 5356 b. x2x3x4 c. 335 d. (-2)(-2)4 P1) a. 4543 b. y3y4y5 c. 226 d. (-5)(-5)3 E2) a. (35)2 b. (y2)4 c. [(-3)3]2 d. [(a+1)2]5 P2) a. (52)3 b. (x3)2 c. [(-2)3]4 d. [(a-2)3]2 E3) a. (65)2 b. (4yz)3 c. (-2w)2 d. –(2w)2 P3) a. (34)2 b. (3xy)4 c. (-3y)2 d. –(3y)2 E4) Simplify (4x2y)3x5 P4) Simplify (3x4y)2y5
8.2 and 8.3 Zero and Negative Exponents, Division Property of Exponents (R,E/4)
Steps and Laws for Exponents 1. Power to Power - Look for an exponent on the outside of parenthesis
- Rule: i. Multiply the Exponents
2. Multiplying Monomials – Look for two terms being multiplied together - Rule:
i. Multiply the Coefficients ii. Re-write the Variables
iii. Add the Exponents 3. Dividing Monomials – Look for a fraction bar
- Rule: i. Divide the Coefficients
ii. Re-Write the Variables iii. Subtract the Exponents Down
4. Combining Like Terms – Look for a + or – sign between two terms - Rule:
i. Combine the Coefficients ii. Re-write the variable and exponent
Never: - Leave an answer in simplest form with a negative exponent (negative exponent property). - Leave an answer in simplest form with a zero as an exponent (zero exponent property
E1) a. 2-2 b. (-2)0 c. 5-x d. (
)
)
e. 0-1
E2) a. 5(2-x) b. 2x-2y-3 P2) a. 4(3-k) b. 5g-3h-4 E3) a. 3-232 b. (2-3)-2 c. 3-4 P3) a. 4-343 b. (5-2)-3 c. 2-3
E4) a. (5a)-2 b.
P4) a. (4y)-3 b.
8.4 Scientific Notation (Multiply and Divide w/ Calculator) (I,E/1)
A number is written in ___________________________ if it is of the form c x 10n, where 1 ≤ c < 10 and n is an integer.
E1) Rewrite in decimal form. a. 2.834 x 102 b. 4.9 x 105 c. 7.8 x 10-1 d. 1.23 x 10-6
P1) Rewrite in decimal form. a. 3.128 x 103 b. 6.4 x 104 c. 3.9 x 10-1 d. 6.12 x 10-5 E2) Rewrite in scientific notation. a. 34,690 b. 1.78 c. 0.039 d. 0.000722 e. 5,600,000,000 P2) Rewrite in scientific notation. a. 52,314 b. 3.2 c. 0.0471 d. 0.0000428 e. 602,000,000
E3) Evaluate the expression. Write the result in scientific notation. a. (1.4 x 104)(7.6 x 103) b. (1.2 x 10-1)÷(4.8 x 10-4) c. (4.0 x 10-2)3 P3) Evaluate the expression. Write the result in scientific notation. a. (2.5 x 104)(5.8 x 102) b. (1.82 x 10-1)÷(1.4 x 10-3) c. (1.5 x 10-4)3 E4) Use a calculator to multiply 0.000000748 by 2,400,000,000. P4) Use a calculator to multiply 0.00000052 by 3,500,000,000.
10.1 Add and Subtract Polynomials (I,E/2)
An expression which is the sum of terms of the form axk where k is a nonnegative integer is a ______________. Polynomials are usually written in ________________ for, which means that the terms are placed in descending order, from largest degree to smallest degree.
Polynomial in standard form
2x3 + 5x2 – 4x + 7
The ________________ of each term of a polynomial is the exponent of the variable. The ___________________________________ is the largest degree of its terms. When a polynomial is written in standard form, the coefficient of the first term is the _____________________________.
A polynomial with only one term is called a _________________. A polynomial with two terms is called a __________________. A polynomial with three terms is called a _____________________.
E1) Identify the coefficients of -4x2 + x3 + 3 P1) Identify the coefficients of 4 – x + 2x3
E2)
Polynomial Degree Classified By Degree
Classified By Number Of Terms
a. 6 b. -2x c. 3x + 1 d. –x2 + 2x - 5 e. 4x3 – 8x f. 2x4 –7x3 – 5x + 1
P2)
Polynomial Degree Classified By Degree
Classified By Number Of Terms
a. -5 b. (1/4)x c. -9x + 1 d. x2 - 6 e. -x3 + 2x + 1 f. 3x4 +2x3 – x2+5x -8
Degree
E3) Find the sum. Write the answer in standard form.
a. (5x3 – x + 2x2 + 7) + (3x2 + 7 – 4x) + (4x2 – 8 – x3)
b. (2x2 + x – 5) + (x + x2 + 6)
P3) Find the sum. Write the answer in standard form.
a. (-8x3 + x - 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)
b. (6x2 - x + 3) + (-2x + x2 - 7)
E4) Find the difference. Write the answer in standard form.
a. (-2x3 + 5x2 – x + 8) – ( -2x3 + 3x – 4)
b. (x2 – 8) – (7x + 4x2) c. (3x2 – 5x + 3) – (2x2 –x – 4)
P4) Find the difference. Write the answer in standard form.
a. (-6x3 + 5x – 3) – ( 2x3 + 4x2 – 3x + 1)
b. (4x2 – 1) – (3x - 2x2) c. (12x – 8x2 + 6) – (-8x2 –3x + 4)
10.2 Multiply Polynomials (I,E/3)
E1) Find the product (x + 2)(x – 3) P1) Find the product (x + 8)(x – 7)
E2) Find the product (3x - 4)(2x + 1) P2) Find the product (2x +3)(5x + 1)
E3) Find the product (x – 2)(5 + 3x – x2) P3) Find the product (x – 4)(5x + 9 –2x2)
E4) Find the product (4x2 – 3x – 1)(2x – 5) P4) Find the product (5x2 – x – 3)(6x – 5)
10.3 Special Products of Polynomials (I,E/1)
E1) Find the product (5t – 2)(5t + 2) P1) Find the product (3b – 5)(3b + 5) E2) Find the product P2) Find the product
a. (3n + 4)2 b. (2x – 7y)2 a. (7a + 2)2 b. (2p – 5q)2
E3) Use mental math to find the product P3) Use mental math to find the product
a. 1723 b. 292 a. 1921 b. 382
Special Product Patterns Factored Form
(General) Product Form
(General) Factored Form
(Example) Product Form
(Example) (a + b)(a – b) a2 – b2 (3x – 4 )(3x + 4) 9x2 - 16
(a + b)2 a2 + 2ab + b2 (x + 4)2 x2 + 8x + 16 (a – b)2 a2 – 2ab + b2 (2x – 6)2 4x2 – 24x + 36
Exponent Applications (Including Area) (I,E/1)
E1) Find an expression for the area of the shaded region.
E2) Find an expression for the area of the shaded region.
E3) Keng creates a painting on a rectangular canvas with a width that is four inches longer than the height, as shown in the diagram below.
a. Write a polynomial expression, in simplified form, that represents the area of the canvas.
b. Keng adds a 3-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame.
c. Keng is unhappy with his 3-inch-wide frame, so he decides to put a frame with a different width around his canvas. The total area of the canvas and the new frame is given by the polynomial h2 + 8h + 12, where h represents the height of the canvas. Determine the width of the new frame. Show all work and explain each step.
1
knowledge of polynomials to solve
open ended problems.
Nov 304:17 PM
Goal: Students will be able to apply knowledge of polynomials to solve open ended problems.
Notes and Examples
Practice
Goal: Students will be able to apply knowledge of polynomials to solve open ended problems.
Day 15
Homework #15 Study Island #3 Wed MERP Set #4 Friday
Goal: Students will be able to apply knowledge of polynomials to solve open ended problems.
Attachments
©A Q2i0D1K29 JKkultPau lSVoLfgtywEatr5ej VLALsCC.H 9 vApl0lx 6rliagchZtusm Tr2easheUrjv8eedF.4 n SMgaSdLek TwMiQtBh1 8IXnRffi3nmi0t4eQ RA7l2gWepbUrKa1 X1N.g Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Properties of Exponents
1)
2
17)
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Properties of Exponents
1)
2
17)
3
x7
yz
-2-
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
SMART Notebook
Multiplying Binomials to Find an Area
_______________(1) The dimensions of a rectangular garden can be represented by a width of feet and a length of feet. Write a polynomial expression for the area A of the garden.
_______________(2) The dimensions of a rectangular garden can be represented by a width of feet and a length of feet. Write a polynomial expression for the area A of the garden.
Find the area of the shaded region:
_______________(3) (3) (4)
(1) Page 453 #22 – 59 Left
(2) Page 453 #25 – 62 Right
(3) Page 459 #5 – 29 Odd
(4) Page 459 #14 – 42 First Column; Page 466 #3 – 27 First Column
(5) Page 459 #15 – 43 Second Column; Page 466 #6 – 30 Fourth Column
(6) Page 459 #16 – 44 Third Column; Page 466 #31 – 47 Left
(7) Page 459 #17 – 45 Right; Page 466 #33 – 48 Third Column
(8) Page 473 #16 – 44 Left *******Quiz Tomorrow********
(9) Page 580 #19 – 55 Left Every Other One
(10) Page 580 #21 – 52 Right Every Other One
(11) Page 587 #9 – 45 Left
(12) Page 587 #10 – 46 Middle
(13) Page 587 #11 – 47 Right *******Quiz Tomorrow*******
(14) Page 593 #16 – 40 Every Other Even
(15) Applications of Area Problems
(16) Practice Test for Test Tomorrow
(17) Page 498 #1 – 10; Page 638 #1 – 7
8.1 Multiplication Properties of Exponents (R,E/2)
Steps and Laws for Exponents 1. Power to Power - Look for an exponent on the outside of parenthesis
- Rule: i. Multiply the Exponents
2. Multiplying Monomials – Look for two terms being multiplied together - Rule:
i. Multiply the Coefficients ii. Re-write the Variables
iii. Add the Exponents 3. Dividing Monomials – Look for a fraction bar
- Rule: i. Divide the Coefficients
ii. Re-Write the Variables iii. Subtract the Exponents Down
4. Combining Like Terms – Look for a + or – sign between two terms - Rule:
i. Combine the Coefficients ii. Re-write the variable and exponent
Never: - Leave an answer in simplest form with a negative exponent (negative exponent property). - Leave an answer in simplest form with a zero as an exponent (zero exponent property E1) a. 5356 b. x2x3x4 c. 335 d. (-2)(-2)4 P1) a. 4543 b. y3y4y5 c. 226 d. (-5)(-5)3 E2) a. (35)2 b. (y2)4 c. [(-3)3]2 d. [(a+1)2]5 P2) a. (52)3 b. (x3)2 c. [(-2)3]4 d. [(a-2)3]2 E3) a. (65)2 b. (4yz)3 c. (-2w)2 d. –(2w)2 P3) a. (34)2 b. (3xy)4 c. (-3y)2 d. –(3y)2 E4) Simplify (4x2y)3x5 P4) Simplify (3x4y)2y5
8.2 and 8.3 Zero and Negative Exponents, Division Property of Exponents (R,E/4)
Steps and Laws for Exponents 1. Power to Power - Look for an exponent on the outside of parenthesis
- Rule: i. Multiply the Exponents
2. Multiplying Monomials – Look for two terms being multiplied together - Rule:
i. Multiply the Coefficients ii. Re-write the Variables
iii. Add the Exponents 3. Dividing Monomials – Look for a fraction bar
- Rule: i. Divide the Coefficients
ii. Re-Write the Variables iii. Subtract the Exponents Down
4. Combining Like Terms – Look for a + or – sign between two terms - Rule:
i. Combine the Coefficients ii. Re-write the variable and exponent
Never: - Leave an answer in simplest form with a negative exponent (negative exponent property). - Leave an answer in simplest form with a zero as an exponent (zero exponent property
E1) a. 2-2 b. (-2)0 c. 5-x d. (
)
)
e. 0-1
E2) a. 5(2-x) b. 2x-2y-3 P2) a. 4(3-k) b. 5g-3h-4 E3) a. 3-232 b. (2-3)-2 c. 3-4 P3) a. 4-343 b. (5-2)-3 c. 2-3
E4) a. (5a)-2 b.
P4) a. (4y)-3 b.
8.4 Scientific Notation (Multiply and Divide w/ Calculator) (I,E/1)
A number is written in ___________________________ if it is of the form c x 10n, where 1 ≤ c < 10 and n is an integer.
E1) Rewrite in decimal form. a. 2.834 x 102 b. 4.9 x 105 c. 7.8 x 10-1 d. 1.23 x 10-6
P1) Rewrite in decimal form. a. 3.128 x 103 b. 6.4 x 104 c. 3.9 x 10-1 d. 6.12 x 10-5 E2) Rewrite in scientific notation. a. 34,690 b. 1.78 c. 0.039 d. 0.000722 e. 5,600,000,000 P2) Rewrite in scientific notation. a. 52,314 b. 3.2 c. 0.0471 d. 0.0000428 e. 602,000,000
E3) Evaluate the expression. Write the result in scientific notation. a. (1.4 x 104)(7.6 x 103) b. (1.2 x 10-1)÷(4.8 x 10-4) c. (4.0 x 10-2)3 P3) Evaluate the expression. Write the result in scientific notation. a. (2.5 x 104)(5.8 x 102) b. (1.82 x 10-1)÷(1.4 x 10-3) c. (1.5 x 10-4)3 E4) Use a calculator to multiply 0.000000748 by 2,400,000,000. P4) Use a calculator to multiply 0.00000052 by 3,500,000,000.
10.1 Add and Subtract Polynomials (I,E/2)
An expression which is the sum of terms of the form axk where k is a nonnegative integer is a ______________. Polynomials are usually written in ________________ for, which means that the terms are placed in descending order, from largest degree to smallest degree.
Polynomial in standard form
2x3 + 5x2 – 4x + 7
The ________________ of each term of a polynomial is the exponent of the variable. The ___________________________________ is the largest degree of its terms. When a polynomial is written in standard form, the coefficient of the first term is the _____________________________.
A polynomial with only one term is called a _________________. A polynomial with two terms is called a __________________. A polynomial with three terms is called a _____________________.
E1) Identify the coefficients of -4x2 + x3 + 3 P1) Identify the coefficients of 4 – x + 2x3
E2)
Polynomial Degree Classified By Degree
Classified By Number Of Terms
a. 6 b. -2x c. 3x + 1 d. –x2 + 2x - 5 e. 4x3 – 8x f. 2x4 –7x3 – 5x + 1
P2)
Polynomial Degree Classified By Degree
Classified By Number Of Terms
a. -5 b. (1/4)x c. -9x + 1 d. x2 - 6 e. -x3 + 2x + 1 f. 3x4 +2x3 – x2+5x -8
Degree
E3) Find the sum. Write the answer in standard form.
a. (5x3 – x + 2x2 + 7) + (3x2 + 7 – 4x) + (4x2 – 8 – x3)
b. (2x2 + x – 5) + (x + x2 + 6)
P3) Find the sum. Write the answer in standard form.
a. (-8x3 + x - 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)
b. (6x2 - x + 3) + (-2x + x2 - 7)
E4) Find the difference. Write the answer in standard form.
a. (-2x3 + 5x2 – x + 8) – ( -2x3 + 3x – 4)
b. (x2 – 8) – (7x + 4x2) c. (3x2 – 5x + 3) – (2x2 –x – 4)
P4) Find the difference. Write the answer in standard form.
a. (-6x3 + 5x – 3) – ( 2x3 + 4x2 – 3x + 1)
b. (4x2 – 1) – (3x - 2x2) c. (12x – 8x2 + 6) – (-8x2 –3x + 4)
10.2 Multiply Polynomials (I,E/3)
E1) Find the product (x + 2)(x – 3) P1) Find the product (x + 8)(x – 7)
E2) Find the product (3x - 4)(2x + 1) P2) Find the product (2x +3)(5x + 1)
E3) Find the product (x – 2)(5 + 3x – x2) P3) Find the product (x – 4)(5x + 9 –2x2)
E4) Find the product (4x2 – 3x – 1)(2x – 5) P4) Find the product (5x2 – x – 3)(6x – 5)
10.3 Special Products of Polynomials (I,E/1)
E1) Find the product (5t – 2)(5t + 2) P1) Find the product (3b – 5)(3b + 5) E2) Find the product P2) Find the product
a. (3n + 4)2 b. (2x – 7y)2 a. (7a + 2)2 b. (2p – 5q)2
E3) Use mental math to find the product P3) Use mental math to find the product
a. 1723 b. 292 a. 1921 b. 382
Special Product Patterns Factored Form
(General) Product Form
(General) Factored Form
(Example) Product Form
(Example) (a + b)(a – b) a2 – b2 (3x – 4 )(3x + 4) 9x2 - 16
(a + b)2 a2 + 2ab + b2 (x + 4)2 x2 + 8x + 16 (a – b)2 a2 – 2ab + b2 (2x – 6)2 4x2 – 24x + 36
Exponent Applications (Including Area) (I,E/1)
E1) Find an expression for the area of the shaded region.
E2) Find an expression for the area of the shaded region.
E3) Keng creates a painting on a rectangular canvas with a width that is four inches longer than the height, as shown in the diagram below.
a. Write a polynomial expression, in simplified form, that represents the area of the canvas.
b. Keng adds a 3-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame.
c. Keng is unhappy with his 3-inch-wide frame, so he decides to put a frame with a different width around his canvas. The total area of the canvas and the new frame is given by the polynomial h2 + 8h + 12, where h represents the height of the canvas. Determine the width of the new frame. Show all work and explain each step.
1