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
- Names of polynomials (types)
Monomial – 5x
Binomial – x + 4
Trinomial – 2x – 5 + 2
Polynomial – 5x + 5 – 3x – 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
- 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
- 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
- Dividing polynomials
(4x^2 + 4x – 10) / 2
2x^2 + 2x – 5
- 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
– When multiplying 2 powers with the same base you add the exponents.
2^3 * 2^5 = 2^8
– 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.
a) Displayed on a number line
In this photo I made the denominators out of 3 and I put the positive and negative fractions where there are supposed to be placed.
b) How you compare fractions
In this photo I had to compare fractions. The first one I compared was the 4/7 vs the 6/7. the 6/7 was the bigger fraction. The second one I had to make the denominator the same and the compare them.
c) Adding and subtracting fractions (where at least one negative)
In the first example I had to multiply -5/6 by 2 so the denominator was 12. Now you can add the 2 fractions which are now -10/12 x 7/12. You will end up with -3/12. After you just have to reduce which will make it -1/4.
d) Multiplication and division of fractions (where at least one negative)
With multiplication all you have to do is “just do it”. As you can see in my first example I have 4/9 x -8/10. And all I did was multiply the numerators together and the denominators together. So I ended up with -32/90 and the final step was to reduce.
Question 1: How might your digital footprint affect your future opportunities? Give at least two examples.
If you type or post something bad when you are young it might come back and bight you in the future. This might affect your future job. It is easy for things you post online to be misread or falsely interpreted.
Question 2: Describe at least three strategies that you can use to keep your digital footprint appropriate and safe.
Don’t post without thinking first. Know what’s out there, for example. Take some time and google your self and see what comes up, because you know potential employers or creditors. Make sure your private post are private.
Question 3: What information did you learn that you would pass on to other students? How would you go about telling them?
Be carful of what you post, think is it safe and is it appropriate before you do it.