Benchmark Review
the slope
What does this formula find?
1/3
What is 0.333.. as a fraction?
2/3
What is 0.6666... as a fraction?
5 8/33
What is 5.242424... as a fraction?
quotient rule
When dividing two powers that have the same base, you can subtract the exponents.
product rule
When multiplying two powers that have the same base, you can add the exponents.
power to a power rule
When you have an exponent raised to another exponent you keep the base and multiply the exponents.
A
Which function has a greater initial value (y-intercept)?
B
Which function has a greater initial value (y-intercept)?
A
Which function has a greater rate of change (slope)?
B
Which function has a greater rate of change (slope)?
9.8
Which of the following is the greatest number?
terminating decimal
a decimal that ends
irrational number
a number that cannot be written as a fraction
Rate of change
a ratio that describes, on average, how much one quantity changes with respect to a change in another quantity
Cube Root
a value which when multiplied by itself thrice or three times produces the original value
Scientific Notation
a way of writing very large or very small numbers
Function notation
f(x)=y
input
the first coordinate of an ordered pair in a relation (x,y)
output
the second coordinate of an ordered pair in a relation (x, y)
Square Root
the value, which gives the number when it is multiplied by itself
y-intercept
the y-coordinate of a point where a graph crosses the y-axis
(x⁴)³
x¹²
(x²)⁵
x¹⁰
x² ⋅ x³
x⁵
x⁵⋅x
x⁶
x² ⋅ x⁵
x⁷
x² ⋅ x⁶
x⁸
5.3 × 10⁻⁶
0.0000053
4 × 10⁻⁴
0.0004
5.72 × 10⁻⁴
0.000572
7.8 × 10⁻³
0.0078
5.3 × 10⁻²
0.053
10⁰
1
4⁰
1
a⁷/a⁷
1
³√1
1
10⁻²
1/100 or 1/10²
5⁻³
1/125 or 1/5³
15⁻²
1/225 or 1/15²
2⁻²
1/4 or 1/2²
5⁻¹
1/5 or 1/5¹
2⁻³
1/8 or 1/2³
√100
10
10²
100
10³
1000
What is the square root of 121
11
√121
11
√144
12
11²
121
5³
125
What is the square root of 169?
13
√169
13
What is the side length of a square that covers an area of 196?
14
√196
14
12²
144
√225
15
4²
16
13²
169
14²
196
³√8
2
How many times greater is 4 x 10⁸ than 2 x 10⁵?
2,000
√400
20
How many times greater is 4 x 10³ than 2 x 10¹?
200
6³
216
15²
225
The side length of square is 15, how much area can be covered?
225 units²
2.4327 × 10⁴
24,327
2.4327 × 10⁷
24,327,000
5²
25
How many times greater is 5 x 10³ than 2 x 10¹?
250
3³
27
(3x)³
27x³
(3x⁵)³
27x¹⁵
³√27
3
How many times greater is 6 x 10⁶ than 2 x 10³?
3,000
3 × 10¹
30
3 × 10²
300
3 × 10⁵
300000
7³
343
6²
36
2²
4
³√64
4
7²
49
(24a²) / (6a)
4a
(2x²)²
4x⁴
What is the square root of 25?
5
³√125
5
5.72 × 10⁹
5,720,000,000
8³
512
5.72 × 10⁴
57,200
5.72 × 10²
572
5x⁴/x²
5x²
³√216
6
4³
64
8²
64
(2x²)(3x²)
6x⁴
What is the side length of a square that has an area of 49?
7
√49
7
9³
729
√64
8
9²
81
³√729
9
√81
9
121
A cube shaped box has a volume of 1,331 cm. What is the area of one side of the box?
Linear function
A function can can be written in the form y=mx+b, its graph is a line
exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself.
rational number
A number that can be written as fraction.
Standard Form
A number written out in expanded form. (A rtegular number)
Constant
A value that does not change
Scientific Notation
An easier way to write a very large or very small number.
zero power property
Any nonzero number raised to the power of zero equals 1.
7.4
Approximate to the nearest tenth
9.7
Approximate to the nearest tenth
Standard form of a linear function
Ax+By=C
13
Emily wants to buy a tablecloth for a square table. If she knows the area of the table is 169 square feet, what is the minimum length and width the tablecloth needs to be?
Function
Function or Not a Function?
Not a Function
Function or Not a Function?
8
George is building a cube shaped shed for his dirtbike. If the shed has a volume of 512 cubic feet, what is the length, width, and height of the shed?
A perfect cube
How would you classify the number 125?
12
Identify the initial value (y-intercept) of the function:
20
Identify the initial value (y-intercept) of the function:
4
Identify the initial value (y-intercept) of the function:
5
Identify the initial value (y-intercept) of the function:
3
Identify the initial value (y-intercept) of the function: y = 4x + 3
-2
Identify the initial value (y-intercept) of the function: y = 6x - 2
2
Identify the rate of change (slope) of the function:
4
Identify the rate of change (slope) of the function:
4/3
Identify the rate of change (slope) of the function:
4
Identify the rate of change (slope) of the function: y = 4x + 3
6
Identify the rate of change (slope) of the function: y = 6x - 2
Yes, this relation is a function because every input has exactly one output.
Is this relation a function? If not, explain why. (10,1) (11,6) (12,11) (13,16)(14,21)
No, this relation is not a function because the ordered pair (5,3) and (5,4) have the same input but different outputs.
Is this relation a function? If not, explain why. (-2,-2) (2,-1) (3,0) (5,3) (5,4)
Irrational; It is not a perfect square so its root is irrational.
Rational or Irrational?
Irrational; this decimal does not terminate or repeat.
Rational or Irrational?
Rational: this is a repeating decimal.
Rational or Irrational?
Rational; It is a perfect square root.
Rational or Irrational?
Rational; this is a fraction.
Rational or Irrational?
Rational; this is a terminating decimal.
Rational or Irrational?
Rational; this is an integer.
Rational or Irrational?
+4, -4
Solve for x
Base
The number that is going to be raised to a power/exponent.
base
The number that is multiplied by itself
Scientific Notation with a positive exponent means...
The number will be greater than one.
Scientific Notation with a negative exponent means...
The number will be smaller than one (number begins with 0).
Exponent
The power to which a given number or expression is to be raised.
Negative Exponents
To make a negative exponent positive do one of the following: If the negative exponent is in the numerator position, shift the power to the denominator position. OR If the negative exponent is in the denominator position, shift the power to the numerator position.
5.72 × 10⁻¹
0.572
7.8 × 10⁻¹
0.78
repeating decimal
- a decimal that has a repeating pattern and never ends
(10y⁵)/(-2y²)
-5y³
y-intercept
"b" in y = mx + b stands for
slope
"m" in y = mx + b stands for