Chapter 1: Numbers
Something that helped me greatly this year and I learned was all the different types of numbers there are. Despite numbers being such a vague word I learned this year that there are at least 5 types of numbers:
Natural Numbers – 1, 2, 3, 4, 5
Whole Numbers – 0
Integers – -5, -4, -3, -2, -1, 0 , 1, 2, 3
Rational Numbers – 1.25
Irrational Numbers- 6. 3476543234589892124…
These helped me lots with the vocabulary and understanding the unit.
Chapter 2: Exponents
While doing exponents one key thing that I learned during this unit was 3 big exponents laws that helped me most. They made understand when seeing these type of questions, know what to do in the moment.
Product Law – 8^3 X 8^2 = 8^5 3+2=5
Quotient Law – 8^3 / 8^2 = 8^1 3-2=1
Power of a Power – (8^3)^2 = 8^6 3×2=6
Chapter 3: Measurement
Something surprisingly I learned this year was knowing what to do when I was stuck on a test or even a question when doing homework. In the measurement unit a small thing that helped a whole lot was using referents in measurement. While measuring object especially, I used my thumb, pace etc, to use and most of the time it helped me figure out the question. You might think it is not important enough to include as something I learned but it really made the difference for me this year.
Chapter 4: Trigonometry
A major tip in the trig unit was SOH CAH and TOA . Despite it being quite a common tip it is for sure in my eyes the most valuable one too!
SOH- Sine
CAH- Cosine
TOA- Tangent
They are used differently depending on the clues given in the triangle, for example if we are using TOA, the opposite and adjacent angles or sides we should already have and we would TOA to figure out the missing side or angle.
Chapter 5: Polynomial Operations
My favourite method of multiplying two sets of Polynomials is to use an area diagram because it lays everything out infront of you and I find it the easiest. Using this method might take a bit of this but it always made me feel 100% in my answers. It was all infront of me and it was super simple.
Chapter 6: Factoring Polynomial Expressions
When factoring a polynomial, you need to remember that the last 2 terms in the equation have to multiply to equal the last term , and they must add to equal the middle term.
Ex. b² + 3b + 2, the b² will be the first terms in each bracket (b + ) and (b + ). Then you list all the factors for the last term (2). ( -2 x -1, and 2 x 1). Then you find the pair that equals to 3b. -2 + -1 does not equal 3, but 2 + 1 = 3. This lets you know to use 2 and 1. Then you input the numbers where they should go (b + 2) (b + 1). To check your answer you just expand the equation to how it was before if you did it correctly.
Chapter 7: Relations and Functions
Learning for this unit I wanted understanding how to find the x and y intercepts of equations. When you find the x and y intercept of the equation you have to understand that the x intercept will be equal to and they y intercept. So for the x intercept y will always be 0 and for the y intercept x will equal 0.
Ex. y = 6x + 2
1. 0=6x+2
2. -2=6x
3. x=1/3
Chapter 8/9: Equations of linear relations
A big part of this unit was know the formulas and when to use them. It helped me understand the unit greatly and solve most equations correctly.
y= mx + b
y – y1 = m (x – x1 )
