Exam Notes: Circle Formulas

• Circumference: C=πd or C=π2r
• Diameter: D=2r
• Radius: R=d/2
• Area: πr2

Exam Notes

-Perpendicular Bisector: line that bisects a different line segment into 2 equal parts.

-Perpendicular: 2 lines that intersect at a 90 degree angle.

-Parallel Lines: 2 lines on the same plane that never meet. (same distance apart)

-Intersecting: 2 lines that cross, 'intersect', at any point.

-Angle Bisector: dividing the angle into 2 equal parts. 
eg. 90 degrees divided into two is 45 degrees.

 

Exam Notes: Divisibility Rules

Divisible means when a number can be divided by another number, with no remainder or decimal. 

1- All numbers. 

2- Numbers that are even, ending with 0, 2, 4, 6 or 8. (eg. 18, 18÷2=9)

3- Sum of the digits is divisible by 3. (eg. 33, 3+3=6, 6÷3=2)

4- Divisible by 2 twice. (eg. 24, 24÷2= 12, 12÷2=6)

5- Ends with a 0 or 5. (eg. 25, 25÷5=5)

6- Divisible by 2 and 3. (eg. 12, 12÷2=6, 12÷3=4)

8- Divisible by 2, thrice. (eg. 48, 48÷2=24, 24÷2=12, 12÷2=6)

9- Sum of the digits is divisible by 9. (eg. 81, 8+1=9, 9÷9=1)

10- Ends with a 0. (eg. 100, 100÷10=10)

Exam Notes

• Variable: an unknown number.

• Expressions contain variables, operations (+, -, x, ÷), and numbers, in any combination. (there is no equals sign = in an expression)

• Mean: add up all the values and divide by how many values there are.
• Median: the middle number in a set of ordered values, might be the mean of two middle values.
• Mode: the value that shows up the most. 
• Range: positive difference between largest and smallest values.
• Outlier: values too big or small compared to other values. 

Transformations

Translation: to slide along a straight line.
Rotation: to turn about a fixed point.
Reflection: a mirror image. 

What is a Numerical Coefficient?

A Numerical Coefficient is when a number multiplies the variable.

~For example: 2t
-2 is the numerical coefficient, t is the variable.

What is a Constant?

A Constant is when the number doesn't change, and it increases/decreases the value of the expression.

What is a Value?

The Value is any known or calculated amount.

What is an Expression?

An Expression is any single number or variable, or a combination or operations (-, +, x, ÷) involving numbers and variables.

~For example: 5, n, 8t, x+1, 2y-7, etc.

What is a Variable?

A Variable is a letter that represents an unknown number.

For example: x, a, n, etc.

Divisibility Rules

Divisibility Rules:

1- all whole #'s are divisible by 1
2- all even #'s are divisible by 2 (2, 4, 6, 8, 0)
3- the sum of the digits of the # is divisible by 3
4- all #'s divisible by 2 twice
5- all #'s ending in 5 or 0
6- all #'s divisible by 2 and 3
8- all #'s divisible by 2 thrice
9- the sum of the digits of the # is divisible by 9
10- all #'s ending in 0

Multiples

Multiple- the product of any given natural number like 1, 2, 3, etc.

eg. multiples of 3 are 3, 6, 9, 12, 15, 18, etc.

Find the first 5 multiples of each #;
2- 2, 4, 6, 8, 10
3- 3, 6, 9, 12, 15
4- 4, 8, 12, 16, 20
5- 5, 10, 15, 20, 25
8- 8, 16, 24, 32, 40
12- 12, 24, 36, 48, 60

Divisibility Rules: #5

Divisibility Rule for 5 - the last digit of a whole number has to be either 0 or 5. (The quotient has to be a whole number).
eg. 5, 10, 15, 20, 25, 30, etc.

Textbook pg. 146 #4

Use a ratio table to figure out the questions.
Remember; whatever you do to one side, has to be done to the other side as well.

a). 10% of 25:









10% of 25 is 2.5

b). 25% of 84:









25% of 84 is 21

c). 50% of 98:








50% of 98 is 49

d). 75% of 124:








75% of 124 is 93

Order of Operations

Here is how to do today's Order of Operations (BEDMAS) question.

4x3+12÷2=

First, you check for Brackets, and since there are none, you move on to the next step.

Next, you check for Exponents, there are none again so you go to the next step.

Third, you check for Division and Multiplication, and you have to calculate from left to right, so in this equation, you multiply first.

So you have...

4x3+12÷2=

12+12÷2=

Then you do the division...

4x3+12÷2=

12+12÷2=

12+6=

Then, you check for Addition and Subtraction, and then you solve.

So now you have...

4x3+12÷2=

12+12÷2=

12+6=

18=

Your answer should be 18.

Here's a video to help you with BEDMAS.

Click here to practice your BEDMAS skills.