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# 8th Semester Review

Front | Back |
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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