Unit Review PowerPoint - Weebly · Microsoft PowerPoint - Unit Review PowerPoint Author:...
Transcript of Unit Review PowerPoint - Weebly · Microsoft PowerPoint - Unit Review PowerPoint Author:...
Whiteboard ActivityUnit Review ‐ Polynomials
Math 9 – Mrs. Feldes
A POLYNOMIAL has one or more terms with whole number exponents.
One or more terms means…
A Polynomial can also be described as a Monomial, Binomial, Trinomial.
2
Whole number exponents means…• A variable cannot have a negative exponent, or
be in the denominator of a fraction.
• A variable cannot have a fraction exponent, or
be under a square root sign.
There can’t be a variable with a fraction exponent.
A number in front of a variable.A number, a variable, or the product of both a number & a variable.
A number without a variable.
The term with the greatest exponent is the degree of the polynomial. The exponent is the degree of each term.
TRY: Identify the number of terms, coefficient(s), constant, degree of the polynomial & of each term:
number of terms = 3 degree of poly. = 2constant = +2 degree of = 2coefficients (s) = +5,‐6 degree of = 1
degree of +2 = 0
SOLUTION:
TRY: Model with tiles the polynomial:
To simplify polynomials, we combine like terms or find zero pairs of like tiles.
Zero pairs of like tiles – cancel each other out!
TRY: Simplify the following polynomial:
Don’t forget the addition and subtraction signs make the coefficients
& constants positive or negative!
SOLUTION:
Note: Don’t forget to show your steps!
To add & subtract polynomials, we must remove the brackets before combining like terms.
TRY: Add:
SOLUTION:
Note: With addition, remove brackets and nothing happens to the terms!
Full marks are given when full steps are shown!
TRY: Subtract:
Remember, the subtraction sign is subtracting all the terms in the brackets!
SOLUTION:
)
Note: With subtraction, remove brackets and all the terms afterwards change to its opposite sign!
TRY: Write a simplified polynomial to represent perimeter.
Don’t forget to simplify the polynomial!
SOLUTION:
Don’t forget to simplify the polynomial!
What if b= 2cm….Determine the side length of each side & find the perimeter of the triangle.
SOLUTION:
9(2) + 8 = 26 cm and 12(2) – 8 = 16cm
P = 33(2) – 8 = 58 cm OR, P = 26 + 16 + 16 = 58 cm
To multiply by a constant, we can think about “equal groups”.
TRY: Model with Tiles:
SOLUTION:
Model with Tiles: 3 groups or 3 rows of 2x ‐ 1
All the tiles represent the answer!Answer = 6
To multiply by a monomial, we can think about “area”.
To multiply by a monomial using tiles, we can construct a rectangle using guiding tiles.
TRY: Model with Tiles:𝑙𝑒𝑛𝑔𝑡ℎ 𝑤𝑖𝑑𝑡ℎ 𝑎𝑟𝑒𝑎
SOLUTION:
Model with Tiles:
The area represents the answer!
Answer = 𝟐
The distributive property reminds us to multiply ‘ ’ to all the terms.
TRY: Multiply:
Note: Don’t forget to show your steps!
SOLUTION:
Multiply:
Note: Don’t forget to show your steps!
TRY: Multiply:
Note: Don’t forget to show your steps!
SOLUTION:
Multiply:
Note: Don’t forget to show your steps!
TRY: Multiply:
Note: Don’t forget to show your steps!
SOLUTION:
Multiply:
Note: Don’t forget to show your steps!
TRY: Model with Tiles:
SOLUTION: Model with Tiles:
Form 2 equal groups from all the tiles.
The tiles of one group represents the answer!
Answer = 𝟐
To divide by a monomial using tiles, we still construct a rectangle using guiding tiles.
TRY: Model with Tiles: 𝑎𝑟𝑒𝑎
𝑙𝑒𝑛𝑔𝑡ℎ 𝑤𝑖𝑑𝑡ℎ
SOLUTION:
Model with Tiles:The dimension represents
the answer!
Answer =
To divide, we write as a sum of fractions.
TRY:
a) b)
Note: Don’t forget to show your steps!
SOLUTION:
a) b)
Note: Don’t forget to show your steps!
Determine the unknown side length of a rectangle, if the area is and the other side length is .
SOLUTION: length = Areawidth
Note: Don’t forget to show your steps!