Transformations
Functions and Volume
Linear Equations
Pythagorean Theorem
Exponent Rules
100
What type of transformation preserves size and shape?
Rigid Transformations (also acceptable to say any of the following:translations, reflections, rotations)
100
What is the volume of a cube with side length 4 cm
4 times 4 times 4=64
100
What is the slope of the line: y=3x+2?
3
100
What is the formula for the Pythagorean Theorem and what is it used for?
The formula is used to find the missing side length of a right triangle.
a^2+b^2=c^2
100
What does the product rule of exponents tell me?
When you are multiplying exponent terms with the same base, keep the base and add their exponents .
200
A triangle is flipped over the x-axis. What type of transformation is this?
Reflection
200
Determine whether the relation below is a function:
(1, 2), (2, 3), (1, 4)
Not it is not a function because the x repeats with a different y. Each input does not have its own output.
200
Solve: 2x+4=12
x=4
200
Find the hypotenuse: legs are 3 and 4 units.
Answer: 5
200
Simplify:
z^0
1. Anything raised to the 0 power equals 1.
300
What characteristics of a shape are preserved during a dilation?
ratio of side lengths and angle measures.
300
What is the output of the function f(x)=2x+1 when x=4?
f(x)=9
300
Give an example of a non linear equation and explain why it is non linear.
a non linear equation will have x in the denominator of a fraction, the exponent on the input variable is something other than 0 or 1
(y=x^2 +4)
300
A right triangle has one leg 6 and hypotenuse 10. Find the missing leg.
8
300
Simplify:
x^2 times x^3
x^5
400
If a pre-image is currently in quadrant 1 and was rotated 270 degrees clockwise, which quadrant would the image be in?
Quadrant 2
400
If the slope of a line is two thirds, what would the slope of a perpendicular line be?
negative 3 over 2
400
Write the equation of a line with slope 4 passing through (2, 3).
Answer: y=4x-5 or y=4x+-5
m=4 (given in the problem)
3=4(2)+b
3=8+b
-5=b
400
A ladder leans against a wall. The base is 6 ft from the wall, and the top reaches 8 ft high. How long is the ladder?
10 ft
400
Simplify:
frac(a^-2b^4)(a^3b^-1)
frac(b^5)(a^5)
500
If a pre image of a triangle has the coordinate points A (2,3) B (6, 3) C (4,6) and was reflected over the y-axis AND dilated by a scale factor of 2, what would the new coordinates be?
After reflection
A(-2,3)
B(-6,3)
C(-4,6)
After Dilation (Final coordinates)
A (-4,6)
B(-12,6)
C (-8,12)
500
Does the table below represent a function?
No. The inputs of 1 repeat and the output is not the same.
500
A line passes through (0, 2) and (4, 10). Find the slope and write the equation.
Equation: y=2x+2
m=10-2 over 4-0
m=8 over 4
m=2
b=2 (when x is zero, the y value is the y-intercept)
500
The diagonal of a square is 10 units. What is the side length?
a=sqrt 50
since the sides of a square are equal, that means A and B are equal. so a^2 + a^2 must equal 10^2(hypotenuse). if you combine like terms, you get 2a^2=10^2. Then use inverse operations to isolate a.
500
Simplify:
(frac (x^4)(x^-1))^-2
frac 1(x^10