8th Semester Review
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| A number written in scientific notation must be | greater than or equal to 1 but less than 10
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| A positive exponent in scientific notation means | it represents a very large number. Move the decimal to the right.
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| A negative exponent in scientific notation means | it represents a very small number. Move the decimal to the left.
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| m | represents the slope of a line when written as an equation. Rate of change; constant; unit rate; rise over run.
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| + b | represents the y-intercept of a line when written as an equation. Initial value; starting point; where the line crosses the y-axis.
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| -b | represents a negative number as the y-intercept. On a graph, crosses the y-axis below the x-axis.
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| When reading a graph, rise over run tells us to | 1. Draw the two legs of a triangle to connect two points on a line.
2. Count the vertical units to find "rise".
3. Count the horizontal units to find "run".
4. Place rise/run in fraction form to represent the slope.
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| Unit rate | the unit rate is the rate per unit. Slope; m; k; rate of change.
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| In an equation: Proportional v. Nonproportional | Proportional: y=mx+b
Nonporportional: y=kx
The difference is "+b"
m=k
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| On a graph: Proportional v. Nonproportional | Proportional relationships go through the origin (0,0)
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| On a table: Proportional v. Nonproportional | What is y when x is zero? If it is zero, then the relationship is proportional. If it is anything else, it is nonproportional.
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| On a table: Slope | To find the slope:
1. Count how much x changes from one row to the next.
2. Count how much y changes from one row to the next.
To write the slope:
3. Place the change in y above the fraction bar.
4. Place the change in x below the fraction bar.
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| Identify a function: | x cannot repeat
each x can only go to one y, although each y can come from multiple x's
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| Exterior angle theorem | The exterior angle of a triangle is equal to the sum of the two remote interior angles.
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| B | means "area of the base"
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| Surface area - Total | The area of all sides. IE: The precise amount of wrapping paper it would take to cover a package .
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| Surface area - Lateral | The area of all sides EXCEPT FOR THE BASES. The siding on a house - you want to cover all of the outside walls, but not the roof or the floor.
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| Finding surface area - alternate route | Find the area of each side, remembering the sides you cannot see, and add them together.
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| Important! Spheres | * remember to CUBE the radius - (r) x (r) x (r)
* on the calculator: [r] [^] [3]
* to multiply by 4/3: divide the total by 3 and then multiply by 4
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| Important! Triangular prisms | * remember that there are two heights - the height you're using to find the area of the triangular base (the height of the triangle) & the height of the prism itself (the distance from one base to another),
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| Surface area - nets | A net is essentially an unrolled cylinder or an unfolded prism. The process for finding the surface area is the same.
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| Pythagorean Theorem | * can be used to find a missing side length
* can be used to prove that a triangle is a right triangle
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| Perfect squares | 1x1=1
2x2=4
3x3=9
4x4=16
5x5=25
6x6=36
7x7=49
8x8=64
9x9=81
10x10=100
11x11=121
12x12=144
etc.
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| Estimating a square root | Because we know that 7x7=49 and 8x8=65
We can safely assume that the square root of 55 is a number between 7 and 8.
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| Reading a graph | * Walk from one side to the other (left to right), are you walking uphill or downhill? Uphill = positive slope. Downhill = negative slope.
! +/- y-intercept does not affect +/- slope.
* Vertical center line - y-axis
* Horizontal center line - x-axis
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| Reading a graph | Sometimes you have to add or remove rows to find the constant rate of change. If your x column is counting all wild-like ( 1, 3, 5,6,7) , you can ignore the 6 so that your change in x is consistent (1,3,5,7 = change of +2)
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Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
fitzpatrickt
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