Quantities
These are the two components necessary to define a quantity
What are numbers (numerical values/quantifiers) and units of measurements (units/qualifiers)?
This is the y-intercept for any equation of the form y=mx+b, where m and b are constants
What is "(0, b)" (or "y=b")?
This is a descriptive word for the rate of change of a linear function
What is "constant"?
This is the definition of a function
What is "a rule that pairs inputs and outputs such that each input has exactly one output"?
This equation tells us that the difference between two quantities is always 3
What is 'y-x=3'? (or similar)
True or False: A given quantity can be a constant and a variable simultaneously.
What is "False"?
In the equation d = 7t - 6, we might use this word to describe '7' in this context
What is 'slope'?
This number describes the constant rate of change in the equation u -5t = 4, where t depends on u
What is '1/5'?
True or False: The line "y=b" for any constant 'b' is a function.
What is "True"?
This equation tells us that two less than the square of x equals one more than y
What is 'x2-2=y+1'?
This famous quantity used to compute the ratio of a circle's circumference to its diameter is a classic example of a constant
What is "pi"?
In the equation y = 3 - t2, we would use this phrase to describe what kind of variable y is
What is 'dependent variable'?
This number describes the rate of change between x=1 and x=4 in the equation y = 2x-1 - 1.
What is '7/3'?
True or False: The line "x=a" for any constant 'a' is a function.
What is "False"?
If a business takes out a loan of $45,000 and brings in $4000 each week in profit, this is the number of weeks it will take until the loan is paid off (assuming no interest is accrued).
What is '11.25', or 'between 11 and 12, or '12' weeks?
In the standard form of a given quadratic equation y = ax2+bx+c, a, b, and c are all this kind of quantity
What is 'constant'?
In the equation y = 3 - t2, we would use this phrase to describe what kind of variable t is
What is 'independent variable'?
True or False: as x tends toward positive infinity, (1.1)x grows faster than x2
What is 'True'?
If f(x) = x2-1 and g(x) = 2x, this is the value of g(f(2))
What is "8"?
The number of tickets sold to a concert in Madison Square Garden (MSG) is equal to 3 times the square of the number of dinner reservations made within one block of MSG. If a 120,000 seat concert is completely sold out, how many dinner reservations were made within one block of MSG?
What is '200 reservations'?
True or False: A quantity is always a variable if you use a non-numerical symbol to describe it. To get the points, you must state the correct answer AND provide an example.
What is 'False'? (Many examples possible, such as: 'pi', 'e', 'x where x equals the number of bricks in Richardson Hall today', etc.)
This equation could describe the size of a population that starts at 400 people and increases by 10% every decade.
What is 'p=400(1.1)d', where d=# of decades and p=population after d decades (or similar)
True or False: If two quantities are proportional (e.g., inches/feet = 12), then there is a constant rate of change between the two quantities.
What is 'True'?
Let y = f(x), where f(x) = 7x - 4. This equation describes the same relationship as f, but where x is a function of y
What is "x = (y+4)/7"? (or similar)
Jay’s father is twice as old as Jay. In 20 years, Jay will be two-thirds as old as his father.
How old is each now?
What is 'Jay is 20, Jay's father is 40'?