Equal and Equivalent
Expressions with Exponents
Relationships between Quantities
Equations in One Variable
100
t + t + t is equivalent to what expression when you can only use the t once?
3t
100
What is the value of 42?
16
100
Plot these points on a coordinate plane.
(3, 4), (5, 6), (4, 1)
100
What is the value of x in the equation 2x = 10?
x = 5
200
What is the equivalent unit rate of apples to 1 orange if I have the ratio 10 apples and 5 oranges?
2 apples to 1 orange
200
What is the value of x3 when x is 5?
125
200
Here is a coordinate grid. What is the name of the variable that goes on the bottom line (the x-axis)?
The independent variable goes on the horizontal (x-axis)
The dependent variable goes on the vertical (y-axis)
Dependent = independent x (something)
200
What is the value of y in the equation y + 40 = 41
y = 1
300
What is x equal to if 5x + 10 = 30?
x = 4
300
What is the value of 4x3 - 10 if x is 2?
4 (23) - 10
4 (2 x 2 x 2) - 10
4 (8) - 10
32 - 10 = 22
300
The equation f = 1/2 x s shows the relationship between flour and sugar in a brownie recipe.
What's a point that could show this equation works if s is the independent variable and f is the dependent variable?
(1, 2) (3, 6)
(2, 4) (5, 10)
(4, 8) etc.
300
Solve the equation for x.
2/5 = 1/2x
2/5 ÷ 1/2 = x
2/5 x 2/1 = x
x = 4/5
400
Distribute to make an equivalent expression.
4 (6x + 5 - y)
24x + 20 - 4y
400
What are the names of the big and small numbers in an exponent, respectively?
xy
x = base
y = exponent
400
Mai uses the equation d =25t to find the what?
If we assign the independent variable the value 8 hours, what is the value of the dependent variable in kilometers?
Mai uses the equation to find the dependent variable (in this case the distance).
d = 25t
d = 25 x 8
d = 200 kilometers
400
40% of x is 100.
Solve for x.
40% * x = 100
40% = 2/5
2/5 * x = 100
x = 100 ÷ 2/5
x = 100 * 5/2
x = 250
500
Factor the expression to make it equivalent.
40x + 12y - 8
4(10x + 3y - 2)
500
What is the value of (2/3)3?
2/3 x 2/3 x 2/3 = 8/27
500
The equation s = (1/4)P relates the perimeter P of any square and its side length s. A graph of the equation includes the point (12, 3).
What does the point (12, 3) represent in this situation?
3 is the length of a side of the square
12 is the perimeter of the square
This equation states that the length of a side can be found by multiplying the perimeter by (1/4).