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8th Semester Review

A number written in scientific notation must be greater than or equal to 1 but less than 10
A positive exponent in scientific notation means it represents a very large number. Move the decimal to the right.
A negative exponent in scientific notation means it represents a very small number. Move the decimal to the left.
m represents the slope of a line when written as an equation. Rate of change; constant; unit rate; rise over run.
+ b represents the y-intercept of a line when written as an equation. Initial value; starting point; where the line crosses the y-axis.
-b represents a negative number as the y-intercept. On a graph, crosses the y-axis below the x-axis.
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.
Unit rate the unit rate is the rate per unit. Slope; m; k; rate of change.
In an equation: Proportional v. Nonproportional Proportional: y=mx+b Nonporportional: y=kx The difference is "+b" m=k
On a graph: Proportional v. Nonproportional Proportional relationships go through the origin (0,0)
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.
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.
Identify a function: x cannot repeat each x can only go to one y, although each y can come from multiple x's
Exterior angle theorem The exterior angle of a triangle is equal to the sum of the two remote interior angles.
B means "area of the base"
Surface area - Total The area of all sides. IE: The precise amount of wrapping paper it would take to cover a package .
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.
Finding surface area - alternate route Find the area of each side, remembering the sides you cannot see, and add them together.
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
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),
Surface area - nets A net is essentially an unrolled cylinder or an unfolded prism. The process for finding the surface area is the same.
Pythagorean Theorem * can be used to find a missing side length * can be used to prove that a triangle is a right triangle
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.
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.
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
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)
Created by: fitzpatrickt