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Geometry
Exponents
Equations
Variables
Stuff to Know
100
With similar shapes, we know the angles equal. But what about the lines?
They become larger or smaller by the same ratio.
100
the square root of 70 is between what 2 numbers and closer to which?
8 and 9, closer to 8 because 8 squared in 64 and 9 squared is 81.
100
When given two equations, you graph them the point that intersects is the solution. What if the graphed lines run parallel?
The systems of equations have no solution.
100
How would you write seven less than four times a number equals five?
4n-7=5
100
If the area of a square patio is 72.25 feet, what is the perimeter?
34 feet because each side would measure 8.5
200
If a triangle's interior angles = 180, and a square's = 360, how could we calculate a pentagon's interior angles total? What is it?
Count the angles. You know the first 3 = 180 degrees from a triangle. Now add 180 degrees for each additional angle. Pentagon 5 angles 360 + 180 + 180 = 720 degrees
200
If ten to the power of one is ten, what is ten to the power of negative 1?
.1 or 1/10 because the exponent is made positive by making it the denominator and then solved.
200
If a van rental company costs $42.50 for 50 miles driven, $65.00 for 100 miles driven, and $110.00 for 200 miles driven, which function is represented? C(m)=.85m C(m)=.85m + 10 C(m)=.45m + 20
.45m + 20 because it holds true when 50, 100, and 200 miles are substituted for m
200
If a line segment measures 3 inches and then is dilated to measure 6 inches, what is the scale factor?
2 because 3 x 2 = 6
200
I lean a 20 foot ladder against a wall. The base is out from the wall 6 feet. How far up the wall is the ladder? Round to nearest whole number.
About 19 feet because....6 squared is 36 plus ? squared = 20 squared which is 400 so 36 + ? square root = 400 so ? is the square root of 364 which is about 19 feet.
300
What is the distance between these two points (3,2) and (9,7).
First subtract the x from point 2 from x of point 1 (9-3) and square it (36). Subtract the y from point 2 from y of point 1 (7-2) and square it (25). Add those two (36 + 25 = 61) and approximate the square root (7 square is 49, 8 square is 64, so it is between 7 and 8 closer to 8). The actual answer is 7.81....
300
What number is this scientific notation: 3.84 x 10 to the 5th power?
384,000
300
What is the equation for a line that passes through (-2,17) and (3, -13)?
Find slope: -13 - 17= -30/ 5 so slope is -6 3-(-2)=5 Then find y intercept by plugging in points y=-6x + ? if y is -13 and x is 3....-13=-18 + ?.....? = 5 so equation is y=-6x + 5
300
Which is a horizontal lines when graphed? y=x y=-x+1 y=-12 x=5
y equals -12
300
If a cylinder is 6 feet tall and the radius is 2 feet, what is the total surface area?
100.48 feet squared for 2 circles.... pi x 2 squared or pi x 4=12.56 per circle (there is 2) and circumference is d x pi or 4 x 3.14=12.56 is top edge of rectangle x 6 = 75.36. Add 12.56 + 12.56 + 75.35 = 100.48
400
When enlarging a 3-d object by a factor of 4, what scale factor will the volume be scaled by?
Since it is volume, it is 4 x 4 x 4 or 64.
400
Which is NOT a rational number: -250 11/39 the square root of 60 12.0982 repeating
The square root of 60
400
What is the quadratic equation for a parabola that curves up and has a point at (0,-2)? y=x squared +2 y=x squared -2 y=2x squared
y = x squared -2 because the y intercept is at -2
400
What is the slope and the y intercept for this equation: y=-5x + 2
slope -5 and y intercept (0,2)
400
Find the x and y intercepts of this equation: 4x-5y=20
(5,0) (0,-4) plug in 0 for y....4x-0=20 so x=5 (5,0) and then plug in 0 for x.....0-5y=20 so y = -4 (0,-4).
500
A hemisphere has a diameter of 9 centimeters, What is the volume to the nearest whole number?
191 centimeters cubed
500
If Ohio's population was 11,500,000 people, the scientific notation for this number would be 1.15 times 10 to what power?
1.15 times 10 to the power of 7
500
What is the solution to this system of equations? 3x-2y=7 and -3x+5y=5?
3x- 2y=7 -3x+5y=5 0 +3y=12 so y = 4 Plug in 4 for y in first equation and solve for x....3x-8=7 n 3x=15 so x=5 (5,4)
500
5(n+6)=2(n-3)+4 Remove the parenthesis and combine like terms. No need to solve.
5n+30=2n-3
500
What is the distance of a diagonal line between a point at (-3,-4) and (5,2)? Think of Pythagorean.....
To travel from -3 to 5 is 8 jumps, 8 squared is 64 plus to get from -4 to 2 is 6 jumps squared is 36. 64 + 36 = 100. The squared root of 100 is 10 so the answer is 10 units