AnswersConcepts in Probability and Statistics ABox Plots

Box Plots — Cumulative exam Answers

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Eighty members of a bike club were asked whether they like touring bikes and whether they like mountain bikes. A total of 70 like touring bikes, 47 like mountain bikes, and 5 do not like either. What are the correct values of a, b, c, d, and e?

Question illustration
A
a = 42, b = 28, c = 33, d = 5, e = 10
B
a = 42, b = 5, c = 28, d = 33, e = 10
C
a = 5, b = 42, c = 28, d = 10, e = 33
D
a = 5, b = 10, c = 28, d = 33, e = 42
2
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What is the greatest common factor of 8m, 36m3, and 12?

A
4
B
8
C
4m
D
8m
3

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 9x2 – 36x?

A
The graph of f(x) = x2 is widened.
B
The graph of f(x) = x2 is shifted right 4 units.
C
The graph of f(x) = x2 is shifted down 36 units.
D
The graph of f(x) = x2 is reflected over the x-axis.
4

Which is the graph of the function f(x) = x2 + 2x + 3?

A
On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (negative 1, 2), and goes through (0, 3).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 4, 3), has a vertex at (negative 2, negative 1), and goes through (0, 3).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (2, negative 1), and goes through (4, 3).
Option D
5

The graph represents a distribution of data.

Question illustration
A
5
B
10
C
30
D
50
6

Consider the plot created from the residuals of a line of best fit for a set of data.

Question illustration
A
Yes, the points have no pattern.
B
No, the points are evenly distributed about the x-axis.
C
No, the points are in a linear pattern.
D
Yes, the points are in a curved pattern.
7

Which function has a vertex on the y-axis?

A
f(x) = (x – 2)2
B
f(x) = x(x + 2)
C
f(x) = (x – 2)(x + 2)
D
f(x) = (x + 1)(x – 2)
8

Which is the graph of the sequence defined by the function f(x + 1) = f(x) when the first term in the sequence is 375?

Question illustration
A
Option
B
Option
C
Option
D
Option
9

What is the y-value of the vertex of the function f(x)=−(x−3)(x+11)?

A
−8
B
−4
C
33
D
49
10

Find the residual values, and use the graphing calculator tool to make a residual plot.

Question illustration
A
Yes, the points have no pattern.
B
No, the points are evenly distributed about the x-axis.
C
No, the points are in a linear pattern.
D
Yes, the points are in a curved pattern.
11

Which is a solution to the equation?(x − 3)(x − 5) = 35

A
x = −8
B
x = −5
C
x = 2
D
x = 10
12

The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form.

Question illustration
A
f(x) = (x + 2)2 + 3
B
f(x) = (x2 + 2x)2 + 3
C
f(x) = (x + 1)2 + 2
D
f(x) = (x + 3)2 + 2x
13

Which is the graph of ?

Question illustration
A
Option
B
Option
C
Option
D
Option
14

The table shows the approximate height of an object x seconds after the object was dropped. The function h(x) = –16x2 + 100 models the data in the table.

Question illustration
A
–2.75
B
0.25
C
1.75
D
2.25
15

A group of 120 people were asked whether their income level is above or below $25,000 and whether they subscribe to a movie channel. The data from the survey is shown in the Venn diagram. Use the Venn diagram to find the missing values in the frequency table.

Question illustration
A
a = 18, b = 34, c = 65
B
a = 34, b = 18, c = 68
C
a = 34, b = 68, c = 47
D
a = 47, b = 18, c = 68
16

The graph of an exponential function and a linear function are shown below. Exponential Linear Which statement is true about the functions?

Question illustration
A
The exponential function is generally growing slower than the linear function.
B
The exponential function is generally growing faster than the linear function.
C
The linear function is generally growing faster than the exponential function.
D
The exponential function and the linear function are generally growing at the same rate.
17

The equation for the line of best fit is f(x) ≈ 1.8x − 5.4 for the set of values in the table.

Question illustration
A
14
B
20
C
45
D
54
18

Which is equivalent to , and what type of special product is it?

Question illustration
A
; a perfect square trinomial
Option A
B
; the difference of squares
Option B
C
; a perfect square trinomial
Option C
D
; the difference of squares
Option D
19

Which statements are true about the graph of the function h(x) = –5x2 + 60x – 200? Select three options.The axis of symmetry is the line x = –6.The graph of h(x) will not intersect the graph of the parent function, f(x) = x2.The vertex of the graph is at (6, –20).The parabola has a maximum.The value of k, when the equation is written in vertex form, is –200.

A
The axis of symmetry is the line x = –6.
B
The graph of h(x) will not intersect the graph of the parent function, f(x) = x2.
C
The vertex of the graph is at (6, –20).
D
The parabola has a maximum.
E
The value of k, when the equation is written in vertex form, is –200.
20

Which function represents exponential decay?

A
f(x) =
Option A
B
f(x) =
Option B
C
f(x) = 4
Option C
D
f(x) = 4
Option D

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