Tools of the Trade
Linear Relationships
Statistics
Models of Change
Graphical Models
100
Bananas cost $3 a bunch and apples cost $0.50 each. If b represents the number of bunches of bananas and a represents the number of apples, which of the following expressions represents the total cost?
3b + 0.5a
100
Use the reciprocal property to rewrite
x/6 = 28/3
6/x = 3/28
100
Define mean, median and mode
mean = the average. Add all of our values and divide by the number of values.
Median = the middle number (of our ordered set)
Mode = the value that appears most often
100
What is the defining characteristic of a function.
For every input in our domain, there is exactly one output.
100
Is this graph a function?
Yes, it passes the vertical line test
200
Which of the following (could be more than 1) are true about the number sqrt(2)
It is real, rational, irrational, whole, and an integer
It is real and irrational
200
find x:
8/12 = (x-4)/15
15 cdot 8 = 12(x-4)
120 = 12x-48
160 = 12x
x=14
200
Name the three key differences between a bar chart and histogram
1.) Bars touching or not touching
2.) Intervals or no intervals for bars
3.) Categorical vs Numerical data
200
What are domain and range?
Domain - all possible x values
Range - all possible y values
200
How do we plot the point (-4, 2)
We go left 4 and up 2
300
Simplify and write in exponential form:
2^2 \cdot 2^3
What does this equal?
2^5 = 32
300
There are 32 marbles in the box. There are 12 red marbles, 14 blue marbles, and 6 yellow marbles. What percent of the marbles are NOT yellow?
_% of ___ is ____
x% of 32 is 32-6
32x = 26
x = 26/32 = .8125 = 81.25%
300
What does standard deviation tell you?
how spread out our data is
300
Using the equation y = 3x – 5, what would the output be for an input of -4?
y = 3(-4) - 5
y = -12-5
y = -17
300
What is the slope of the line through the points (2, 5) and (6, 13)
(rise)/(run)
(13-5)/(6-2)
8/4
2
400
Rewrite (2g)^5 as a product
2g cdot 2g cdot 2g cdot 2g cdot 2g
400
The cost of a pair of jeans was changed from $78 to $68.64. What was the percent change?
Percent change =
(chang e)/(o rignial)
= (78-68.64)/78
= -0.12 = -12% = 12% decrease
400
If the outlier is excluded from the following data set, what happens to the mean?
{250, 200, 308, 275, 32, 199, 220, 268, 290}
It increases
400
Is the sequence 1, 0.1, 0.01, 0.001,... arithmetic? Why or why not?
(bonus 1000 points if you can calculate the sum of this sequence)
No it is not, because there is not a common difference between terms
sum is 10/9. Mr. Sanders can prove
400
What is the equation for the following graph?
x = 4
500
What is the additive inverse of -32
32
500
Solve 6x=48 for x
x=8
500
What is the general form for relative frequency?
(observed)/(t otal)
500
What are the first 3 terms of the sequence
a_n = 12-2n
(Hint: we technically start at the "0th" term)
12, 10, 8,......
500
Where does the line y = 2x + 7 cross the y-axis?
at y=7
600
Simplify (32/4) cdot (4/2) cdot 2
32
600
Solve
8r-12 = 12r+8
8r-12 = 12r+8
-12 = 4r + 8
-20 = 4r
r = -5
600
Draw a perfect negative correlation
600
Calculate the rate of change for the following data:
-3
600
Calculate the equation of the following line:
y = -3/2x+7/2
700
What is the mathematical definition of the distributive property?
a(b+c) = ab + ac
700
Solve 2(a + 6) – 3(a – 5) = 18
2(a+6)-3(a-5)=18
2a+12-3-3a+15=18
-a + 27 = 18
-a = -9
a = 9
700
What are the three types of sampling methods we learned about in class? How do they work? Which one is biased?
Simple random sample - everyone has an equal chance of being selected, people are chosen randomly.
Systematic - every nth person is selected
Convenience - we select the people easiest to reach. This is biased.
700
What type of transformation is caused by:
f(x) rightarrow f(-x)
A reflection over the y-axis
700
Find the slope of a line parallel and perpendicular to
y=-4/3x-5
parallel: y=-4/3
perpendicular: 4=3/4
800
What is the definition of like terms? What can we do with them?
2 terms with the same variable AND exponent. We are able to combine like terms by adding their coefficients.
800
Solve 2(3c + 3) < 6c + 9 for c
2(3c+3) < 6c+9
6c+6 < 6c+9
This is always true, so our solution is "all real numbers"
800
What are the steps needed to calculate standard deviation?
Hint:
sqrt(1/(N-1)sum_(i=1)^N(x_i - barx)^2
1.) Find the mean
2.) subtract the mean from every value in your set
3.) Square the differences
4.) Add these all up
5.) Divide this sum by either N or N-1 based on whether you're taking the standard deviation of a population or a sample (we didn't cover the difference so I'll accept either)
800
What type of transformation is caused by:
f(x) rightarrow f(x-3)
A translation to the right by 3 units
800
Calculate the equation of the line through the points (-1, 1), (4, 0), and (24, -4)
y=-1/5x+4/5