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Real Numbers and Functions
Arithmetic Sequences
Lines
Linear Models
Geometric Sequences
100
For the function f(x) = 1.5x - 4.2, what is f(8)?
7.8
100
What is the common difference in the sequence {-35, -42, -49, -56, ...}?
d = -7
100
What is the slope of the line 3x + 12y = 8?
m = - 1/4
100
True or False: When modeling data, the linear regression equation (y = ax + b) represents the "line of best fit".
True
100
Find the common ratio of the geometric sequence {3/4, 3/2, 3, ...}
r = 2
200
Is this relation a function? Inputs: 1 -1 1 -1 Outputs: 2 -2 -2 2
No. Each of the input values of 1 and -1 correspond to more than one output value.
200
Write the arithmetic sequence with u(sub 3) = 4 and a common difference of d = 2 in explicit form for u(sub n).
u(sub n) = 2n - 2
200
What is the slope of the line through the points (4, -2) and (9, 6)?
m = 8/5
200
Put the following keystrokes in order of how you would find the linear regression equation on your calculator. a) CALC menu b) ENTER c) STAT d) 4: LinReg(ax+b)
In order: 1) STAT 2) CALC menu 3) 4: LinReg(ax+b) 4) ENTER
200
Find the common ratio of the geometric sequence with u(sub 1) = 27 and u(sub2) = -9.
r = - 1/3
300
What is the smallest subset of real numbers that contains the number 0?
Whole numbers
300
Find the sum of the first 9 terms of the sequence {6n - 2}.
252
300
Compare the line through A(-6, 4) and B(4, -2) with the line through C(5, 4) and D (3, 6). Are these lines parallel, perpendicular, or neither? Hint: Find and compare the slopes of each line.
Neither. The slope of the line through AB is -6/10 and the slope of the line through CD is -1.
300
When using your calculator to find the linear regression equation, what does "r" represent?
r = correlation coefficient
300
List the first four terms of the geometric sequence with u(sub 1) = 27 and u(sub2) = -9.
27, -9, 3, -1
400
What is the smallest subset of real numbers that contains the number 1/3?
Rational numbers
400
What is the recursive formula for the sequence? {-9, -5, -1, 3, ...}
u(sub1) = -9 and u(sub n) = u(sub n-1) + 4 for all n >= 2
400
Find an equation for the line satisfying the given conditions. y-intercept = -4, slope = 1/5
y = 1/5 x - 4
400
What can the value of "r" tell you in terms of your line of best fit?
Take the absolute value of r. When the absolute value of r is close to 1, you can say that the line of best fit is a good model of the data. When the absolute value of r is closer to 0, then the line is a less reliable model.
400
Write the recursive form of the geometric sequence with u(sub 1) = 27 and u(sub2) = -9.
u(sub n) = (- 1/3) u(sub n-1)
500
What is the smallest subset of real numbers that contains the number -1.2?
Rational numbers
500
Find the kth partial sum of the arithmetic sequence where k = 12, u(sub 1) = -2, d = -3.
-222
500
Find an equation for the line satisfying the given conditions. through (5, -2); slope = 0
y = -2
500
Which of the following lines is a better model for some data? a) G = -9.7754H + 1.6746, with r = -0.995 b) G = -9.7754H + 1.6746, with r = 0.915
a) is better since the absolute value of -0.995 is closer to 1 than the absolute value of 0.915.
500
Write the explicit form of the geometric sequence with u(sub 1) = 27 and u(sub2) = -9.
u(sub n) = 27(- 1/3) ^ (n-1)