What I have learned about grade 9 solving equations

 

• An equation is a statement that contains one or more variables. Solving the equations consists of determining which values of the variables make the answer true.
• An equivalent equation are algebraic equations that have identical solutions

 

 

Equation: a statement that the values of two mathematical expressions are equal

Equivalent: Equal in value

Solution: Solving a problem for the correct answer

Coefficient: The number before a variable

Zero Pairs: a pair of numbers whose sum is zero, e.g. +1, -1

Variable: a variable is a symbol, commonly a single letter, that represents a number, called the value of the variable

Common denominator: The same number on the bottom of a fraction

What I have learned about grade 9 polynomials

 

1. Names of polynomials (types)

Monomial – 5x

Binomial – x + 4

Trinomial – 2x – 5 + 2

Polynomial – 5x + 5 – 3x – 2

 

2. Adding polynomials

Adding polynomials is just combining like terms

2x^2 + 6x + 5  +  3x^2 – 2x – 1

2x^2 + 3x^2   +  6x – 2x   +   5 – 1

5x^2   +    4x   +  4

 

3. Subtracting polynomials

Subtracting polynomials is combing like terms after you have flipped the sign of the terms that are being subtracted

(x^3 + 4x – 2) – (2x^3 + 5x)

x^3 + 4x – 2 – 2x^3 – 5x

-x^3 – x – 2

 

4. Multiplying polynomials

Multiply each term in one polynomial by each term in the other polynomial. Add those answers together, and simplify

(x + 2y) (3x – 4y +5)

3x^2 – 4xy + 5x + 6xy – 8y^2 + 10y

3x^2 + 2xy + 5x – 8y^2 +10y

 

 

 

5. Dividing polynomials

(4x^2 + 4x – 10) / 2

2x^2 + 2x – 5

 

 

6. How to find degree of polynomials

It is the largest exponent of its terms

Example: 2x^3 + x^2 – 7

The degree of the polynomial is 3 because it is the largest exponent of its terms

 

 

 

 

 

 

 

 

 

What I have learned about grade 9 exponents

What is and exponent?

–        An exponent refers to the number of times a number is multiplied by itself

 2^3 = 2x2x2

What is the difference between evaluating and simplifying?

–        Evaluating is when substitute values for variables to solve the expression and simplifying is reducing an expression to a simpler form that is easier to work with.

Evaluating = x^3, if x equals 2 than 2^3 = 8

Simplifying = 2^4 x 2^7 = 2^11 

Multiplication law

–        When multiplying 2 powers with the same base you add the exponents.

2^3 * 2^5 = 2^8

Division law

–        When dividing 2 powers with the same base you subtract the exponents.

4^6 / 4^3 = 4^3

Power of a power law

–        When you raise a power to a power you multiply the exponents.

(x^5)^4 = x^20

Exponents on variables

–       An unknown number is raised to a power.

x^5       The variable x is raised to a power of 5.