diff --git a/Grade 9/Math/MFM1P1/Final_Exam_Study_Sheet.md b/Grade 9/Math/MFM1P1/Final_Exam_Study_Sheet.md index 00d72f6..3054960 100644 --- a/Grade 9/Math/MFM1P1/Final_Exam_Study_Sheet.md +++ b/Grade 9/Math/MFM1P1/Final_Exam_Study_Sheet.md @@ -348,9 +348,9 @@ ## Line Of Best Fit - A line that represents the `trend` in a graph. ### How To Find The Line of Best Fit - 1. Simply draw the line according to the properties of the line below. - 2. Use a ruler when drawing the line. - 3. Make sure the line of best fit represents the trend. +1. Simply draw the line according to the properties of the line below. +2. Use a ruler when drawing the line. +3. Make sure the line of best fit represents the trend. ### Properties Of Line Of Best Fit - Shows the trend for the data in a scatter plot. @@ -361,9 +361,10 @@ ## Curve Of Best Fit - A curve that represents the `trend` in a graph. + ### How To FInd The Curve Of Best Fit - 1. Simply draw a curve that connects all the points. - 2. You can also use an online graphing calculator, like [DESMOS](https://www.desmos.com/calculator). +1. Simply draw a curve that connects all the points. +2. You can also use an online graphing calculator, like [DESMOS](https://www.desmos.com/calculator). ## Time - Distance Graph @@ -395,5 +396,52 @@ |9|300| |12|400| - First label the x and y axis, since time is the **independent variable**, the `Hours Worked` will be `x-axis`. The `Pay in dollars` will be our y-axis. - - + +## Graphing Non-Linear Relations +- Plot the points in a scatter plot. +- Use one smooth curve to connect all the points. + + +# Unit 7: Linear Relations +- Cartesian Coordination System: its a coordinate system that has 4 grids, with x and y values. +- +- `Direct Variation`: A line that passes through or from the `origin`. Simply put, there is a point where the x and y values both equal to 0. +- `Partial Variation`: A line that does not pass through or from the `origin`. Simply put, there isn't a point where the x and y values both equal to 0. + +## Recognizing Linear Relations +- Use either `table of values` or a graph to determine it. +- If the `first differences` in the table of value is constant, it is a linear relation. +- If the line that connects all the points is a straight line, it is a linear relation. + +## Average Speed As Rate Of Change +- $` \text{average speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}}`$ +- The average speed, is simply equal to the rate of change. + +## Solving Equations +- `Equation`: When the alegebraic expression are set to equal to each other. +- `Variable`: A number that can change (varies) $`\rightarrow`$ unknown. +- `Constant`: A number that always stays the same (doesn't vary). +- `To solve an equation is`: fidn the value of the variable (unknown), so that the left side of the equation and the right side of the equation are equal. + +### Tips +- Remember if you do something to one side, you must do it to the other. +- Make sure to flip the negative/positive sign when moving an value to the other side. + +## Deteriming Values in a Linear Relation + +### Steps + +1. Enter the data given in the question into this table. +2. Graph the data, Join the points with a line. +3. Determine the rate of change. +4. Extend the line on the graph to the left until it intersects the vertical axis. +5. Simply use the graph, by either looking at the x or y axis to solve the questions that are given. + +## Two Linear Equations +- Plot the points and draw the lines for all the equations. +- The point where they intersect is called the point of intersection, and is when the equations equal to one another (the x and y values). +- In terms of money, the less steep the line, the better the deal is. + +## Unit 8: Polynomials + \ No newline at end of file