Category: Math 10

NUMBER AND MONEY APPLICATIONS

• step 1: within the question you will need to find what X and Y are supposed to represent. With this information you will state the variables
• step 2: read the question carefully and decide what your two equations will be. usually in a number problem the word is will be the equal sign.
• step 3: solve the equations fully and check your work

ex:

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This week i learned how to turn an y intercept equation into a general form equation

step 1: with the y intercept equation Y= mX+b you will move the Y to the other side

step 2: This will Give you the answer 0= -Y+mX+B and this is your answer

example:

Slope:

• to find a slope there are two methods but the one I use is Method 1- Slope formula

Method 1- Slope formula

1. take the coordinates of the two points.
2. use the formula: M= yb-ya/xb-ax

Ex:

 

 

Functions and relations

• all Functions are relations but not all relations are functions
• For each relation to be a function:

Each input must have have only output

• Visually this means:

There are no two points that are vertically alligned

The graph passes the “vertical line test”

 

Ex:

source: https://www.slideserve.com/july/relations-and-functions

Vocabulary on relationships between two quantities

• relation: mathematical relationship with two quantities/values
• Indapendent variable: used for inputs in a relation
• Dependent variable: used for outputs in a relation
• ordered pairs: used to locate points on a cartesian plane
• coordinate: the location of numbers on a grid

Finding a missing side of a triangle

• To find the missing side of a triangle you need to have the length on one side and an angle.
• you name all the sides and find out if you need to use sin, cos or tang.
• to make the equation you take the angle and put is after your sign then put equals sign for the variable and the length of the side.
• depending on if the length is on the top of the fraction or not you will multiply or divide the length by the sign of the angle.
• once you do this you will have your missing side.

Ex:

scientific notation

• scientific notation is used represent a very long number in a shortened way. For example 19 000 000 would become 1.9 x 10 to the power of 7
• To convert a large number into scientific notation you count how many times you would have to move the decimal over until you reach the last number. With the number you just came up with you will times the decimal version of the large number with 10 to the power of the fist number you came up with. I find this method a very useful method for me.

an example of a way to do this with positives is shown in this image:

another example but with negatives:

citation:

https://study.com/skill/learn/how-to-use-scientific-notation-with-negative-exponents-explanation.html

The GCF

This week in math I learned how to find the Greatest common factor of two different numbers. I learned two different ways that i could find the GCF:

1. Use a factor tree.

To find the GCF using the factor tree you take the first number and you write how you multiply to get the number. If the numbers you chose are prime numbers then you circle that number. If the number is not a prime number you repeat the process until you get all prime numbers. With each set of prime numbers you would cross out all matching numbers and place them somewhere else on your page. multiply these prime numbers together and you have your GCF

Ex:

2. division table

To find the GCF using a division table you must take the number and divide it by a prime number going from least to greatest. Repeat this process until you are left with a 1. With each set of prime numbers you would cross out all matching numbers and place them somewhere else on your page. multiply these prime numbers together and you have your GCF.