Category Archives: Math 10

Summary blog post

June 21, 2016 Angus Wai Leave a comment

Most important things in each chapter:

Chapter I:
Prime numbers – a whole number that has only 2 factors
Composite number – a whole number that has more than 2 factors
Prime factorization – there are 2 ways to do it: division table & tree diagram
Lowest Common Multiple – a number that is a multiple of two or more numbers
Greatest Common Factor – the greatest factor that divides two numbers
Repeating decimals – decimals that have a recurring pattern of digits
Non-repeating decimals – decimals that have no recurring pattern of digits
Terminating decimals – decimals with a finite amount of digits
Non-terminating decimals – decimals with an infinite amount of digits
Real number system – it includes R, , Q, I, W, N
How to simplify roots – $\sqrt[3]{24} = \sqrt[3]{3\cdot8} = 2\sqrt[3]{3}\\\sqrt[3]{32} = \sqrt[3]{4\cdot8} = 2\sqrt[3]{4}$
MOST IMPORTANT THING – flower power, root is always on the bottom

Chapter II:
Multiplication $x^{12}\cdot x^8=x^{20}$
Division $\frac{x^{30}}{x^{10}}=x^{x^{20}}$
Power $(x^4)^5=x^{20}$
Negative $\frac{1}{x^{-20}}=x^{20}$
Fraction $x^\frac{100}{5}=\sqrt [5]{x^{100}}=x^{20}$

Chapter III:
How to convert a number to scientific notations – $2345=2.4\cdot 10^3\\0.089567=9.0\cdot 10^{-2}$
How to convert to another unit – 6780cm = 67.8m, 0.91km = 910m, etc.
How to calculate surface area and volume –
Volume of prism: volume = area of base x height
Surface area of prism: add all the surfaces
Volume of cylinder: volume = area of base x height
Surface area of cylinder: area of side + 2 x area of base
Volume of pyramid: $\frac{1}{3}$ x volume of prism
Surface area of pyramid: area of base + area of triangular faces
Volume of cone: $\frac{1}{3}$ x volume of cylinder
Surface area of cone: area of base + area of curved surface

Chapter IV:
Sine ratio – opposite side/hypotenuse
Cosine ratio – adjacent side/hypotenuse
Tangent ratio – opposite side/adjacent side
20160401_171415 20160401_171433

Chapter V:
Variable – a letter that represents one or more numbers
Algebra expression – 2a-b+4
Numerical coefficient – the number that multiplies the variable
Monomial – polynomial with 1 term
Binomial – polynomial with 2 terms
Trinomial – polynomial with 3 terms
Polynomial – polynomial with 4 or more terms
Degree of a monomial – the sum of exponents of its variable(s)
Degree of a polynomial – the degree of the term with highest degree
Constant term – a term of degree zero(no variable present)
Leading coefficient – coefficient of the term with highest power of variable
Simplifying – $(3-a-2a^2)+(9-4a+5a^2)\\=-2a^2+5a^2-a-4a+3+9\\=3a^2-5a+12$

Chapter VI:
Factoring polynomials – $12x-8y+16z\\=4(3x-2y+4z)$

Chapter VII:
Relation – the mathematical relationship between 2 quantities
Independent variable – the variable used for inputs in a relation
Dependent variable – the variable used for outputs in a relation
Domain – the set of all possible values for x
Range – the set of all possible values for y

Chapter VIII:
positive slope – goes up from left to right
negative slope – goes down from left to right
zero slope – horizontal line
undefined – vertical line
Slope – $\frac{rise}{run}$
positive slope piggy

Chapter IX:
y-intercept form – y = mx+b
Slope-point form – m(x-x) = y-y
General form – ax+by+c = 0
Standard form – ax+by = c

Chapter X:
Substitution – a simple way to solve two equations if there is coefficient of 1
Step 1: Choose the simpler equation and express one variable in terms of other
Step 2: Substitute the expression from step 1 into the other equation
Step 3: Solve the single variable equation
Step 4: Substitute the solution from step 3 into the equation in step 1 to find the value of the other variable
Elimination – a way that you can always use, especially without coefficient of 1
Step 1: If necessary, multiply each equation by a constant to obtain coefficients for x or y that are identical
Step 2: Add or subtract the two equations to eliminate one of the variables
Step 3: Solve the resulting equation to determine the value of one of the variables
Step 4: Substitute the solution into either of the original equations to determine the value of the other variable

Math 10

Letter graph

June 1, 2016 Angus Wai Leave a comment

Math 10

Week 14 review

May 23, 2016 Angus Wai Leave a comment

Things I have learned this week:

-How to find the distance between two points

examples:

(1,6), (1,9)
Subtract the y values then you will get 3 or -3, since this is a distance, there is no negative values so the answer is 3.

(20,2),(5,2)
Subtract the x values and the answer is 15.

(2,5),(3,9)
Find the difference between x values and then find the difference between y values. Then use pythagorean theorem to find the length of the line segment. So the answer is $\sqrt{(2-3)^2+(5-9)^2}=\sqrt{17}$

-How to find slopes

(2,5),(7,20)
You have to find the rise(difference between y values) and run(difference between x values), then do $\frac{rise}{run}$ . So the answer is $\frac{2-7}{5-20}=\frac{-5}{-15}=\frac{1}{3}$

REMEMBER: YOU HAVE TO DO THE SUBTRACTION IN ORDER $(\frac{y_1-y_2}{x_1-x_2})$

Important things about slopes:

$\frac{rise}{run}$
positive slope: goes up from left to right
negative slope: goes down from left to right
zero slope: horizontal line
undefined: vertical line

Math 10

Week 13 blog post

May 16, 2016 Angus Wai Leave a comment

Math 10

Week 9 review – Updated

April 21, 2016 Angus Wai 1 Comment

Things I have learned:

-Factoring polynomial expressions:
I did some simple questions

e.g.
$12x-8y+16z\\=4(3x-2y+4z)\\48y^2-72y^5\\=24y^2 (8-12y^3)$

The first one what I did was finding the greatest common factor that the equation has, which is 4. The second one is same as the first one, and the greatest common factor is $24y^2$ .

Here is another example I found in the internet:

For this example, 3 is the greatest common factor.

Even though these questions are not new for me, it still helps me. I didn’t do factoring for a while, so these questions allow me to practice more. I have to find the GCF in each question, it is similar to Chapter 1 (Number), it’s pretty much the same thing.

Math 10