Transcript Slide 1

1. Which function represents p, the water pressure in square inches, as
a function of d, the depth, in feet?
A. p  4.3d
B. p  0.43d
C. p  2.33d
D. p  23.3d
Depth in feet (d) Pressure in PSI (p)
The function is linear because the
change in d is constant and the
change in p is constant.
The slope of the linear function
is the change in p divided by the
change in d or
4.3
 0.43 .
10
Choice B is the only one
with a slope of 0.43.
10
4.3
20
8.6
30
12.9
40
17.2
50
21.5
Increases
by 10
Increases
by 4.3
An easier way to do this problem is to substitute the table values into the
formulas to see which one works.
2. For one child, a childcare facility charges $300 per month for preschool and
$3.50 per hour for each hour of childcare after preschool. The function below can be
used to determine the monthly fee for childcare and preschool, where h represents
the number of hours spent in childcare after preschool.
f ( h)  300  3.5h
If the one-month charges for one child totaled $637.75, what was the total number
of hours the child spent in childcare after preschool?
Since f(h) represents the total monthly fee, substitute $637.75 for f(h) and solve
for h.
637.75  300  3.5h
300  300
337.75  3.5h
337.75 3.5h

3.5
3.5
96.5  h
The child spent 96.5 hours in childcare after preschool that month.
3. An economics teacher plotted the value of a stock on 11 different days during a
500 day period and used line segments to connect them. In the graph shown, the
horizontal axis is in days and the vertical axis is measured in dollars.
Based on the graph, which of the following best describes the range of the value of
the stock for this 500-day period?
A. 0  x  500
B. 1  x  500
C. 10  y  60
D. 0  y  80
The y-axis displays the
values of the stock. The
lowest value is about 10
and the highest value is
about 60.
4. The set of ordered pairs shown below defines a relation.
{(0, 0), (1, 5), (2, 8), (3, 9), (4, 8), (5, 5), (6, 0)}
What is the value of the greatest element in the range of this relation?
The range is the set of all y-coordinates or {0,5,8,9}.
These numbers are in numerical order so the greatest element
in the range is 9.
5. Mario needs to cut three book shelves from a board that is 1.8 meters long.
The second shelf is 15 centimeters longer than twice the length of the first shelf.
The remaining shelf is 5 centimeters longer than the first shelf. The equation
below represents this situation, where x is the length of the first shelf in meters.
x  (2 x  0.15)  ( x  0.05)  1.8
Which of the following is the length, in meters, of the first shelf?
A.
B.
C.
D.
0.40
0.45
0.53
0.96
The problem states that
x denotes the length of
the first shelf so solving
for x will answer the
question.
x  (2 x  0.15)  ( x  0.05)  1.8
4 x 1.6
4 x  0.2  1.8

4
4
0.2  0.2
x  0.4
4 x  1.6
The length of the first
shelf is 0.4 meters.
6. Bill is planning to drive from his house to a baseball stadium and arrive in
time for the beginning of the championship game. His arrival time depends on
the traffic. If traffic is light, he will travel at an average speed of 50 miles per
hour and arrive 1 hour early. If traffic is heavy, he will travel at an average
speed of 30 miles per hour and arrive on time. The equation below can be used
to model this situation, where t represents Bill’s driving time, in hours.
50( t  1)  30t
What is the distance, in miles, from Bill’s house to the baseball stadium?
Solve the equation to
determine Bill’s
driving time if he
averages 30 mph.
50( t  1)  30t
50t  50  30t
30t
 30t
20t  50  0
50  50
20t  50
20t 50

20 20
t  2.5
The question askes for
the distance and distance
equals rate times time.
The rate is 30 mph and
the time is 2.5 hours.
d  rt
d  (30)(2.5)
d  75 miles
7. The Gross Domestic Product of a country for a given year is the sum of the
market values of all goods and services produced within the country during
that year. The Gross Domestic Product per capita is found by using the
followinig formula. C  I  G  N
Which of the following shows the
S
formula solved for C?
P
Where:
PS
S = Gross Domestic Product per capita
A. C 
I G  N
C = consumer spending
PS
I = Investment
B. C 
G = government purchases
I G N
N = net exports
C. C  PS  I  G  N
P = population
C  I G N
PS  P
P
PS  C  I  G  N
I  G  N  I  G  N
PS  I  G  N  C
or
C  PS  I  G  N
D. C  PS  I  G  N
8. Taylor has a total of $25 to spend on dinner, which includes a 6.5% sales tax and
a 20% tip. Taylor used the inequality shown below to calculate the amount in
dollars, a, she can spend before tax and tip.
1.2(a  0.065a )  25
Which of the following shows the solution to this inequality?
A. a  22.74
B. a  22.34
C. a  19.76
D. a  19.56
1.2(a  0.065a )  25
1.2a  0.078a  25
1.278a  25
1.278a
25

1.278 1.278
a  19.56181534...
9. Which graph shows the solution to the inequality shown below?
15  7n  2( n  10)  35
A.
 2 1
0
1
2
3
4
5
6
7
8
9
10 11 12
 2 1
0
1
2
3
4
5
6
7
8
9
10 11 12
 2 1
0
1
2
3
4
5
6
7
8
9
10 11 12
 2 1
0
1
2
3
4
5
6
7
8
9
10 11 12
B.
C.
D.
15  7n  2( n  10)  35
15  7n  2n  20  35
15  5n  20  35
20
 20  20
5  5n  15
5 5n 15


5
5
5
1  n  3
Since  requires a solid circle and <
requires an open circle, the answer is
D.
10. The out-of-pocket costs to an employee for health insurance and medical
expenses for one year are shown in the table below.
Type of Cost
Definition
Cost to Employee
Premium
Total amount employee pays insurance
company for the policy
$3,626
Deductible
Amount of medical expenses employee pays
before insurance company pays for anything
$500
Co-payment
Percentage of medical expenses after the first
$500 that employee has to pay
20%
According to the plan outlined in the table, total annual health care costs, C, depend
on the employee’s medical expenses for that year. If x represents the total medical
expenses of an employee on this plan and x  500 , which of the following equations
can be used to determine this employee’s total health care costs for that year?
This employee has paid the $500
A. C  3,626  500  0.20( x  500)
deductible plus 20% of the amount over
B. C  3,626  500  0.20 x
$500 which is 500  x . The employee has
also paid the premium. The sum of all
C. C  3,626  500  0.20( x  500)
three costs will determine the total cost C.
D. C  3,626  500  0.20 x
C  3,626  500  0.20( x  500)
11. Karen works as a salesperson for a local marketing company. Using the
equations shown below, the company calculates her monthly earnings based
upon her total sales for the month.
Total Sales for the
Month (s in dollars)
s  $5,000
s  $5,000
where:
Earnings Equation
E  1,600  0.1s
E  1,600  0.1s  0.15( s  5000)
E represents total monthly earnings before taxes and withholding
s represents the dollar amount of her total sales
Karen’s total sales were greater than $5,000 in October. If her total monthly
earnings for October were $3,000, what was the value of her total monthly
sales, s?
3,000  1,600  0.1s  0.15( s  5000)
3,000  1,600  0.1s  0.15s  750
Use the second row
3,000  0.25 s  850
of the table because
850 
 850
s > $5,000.
Substitute $3,000 for
2150  0.25s
E and solve for s.
2150 0.25 s

0.25 0.25
s  8600
12. Roger went to a garage sale where hardback books sold for $5 each and paperback
books sold for $2.50 each. He has $20 to spend. The equation below can be used to
find how many books of each type Roger can buy, where x is the number of hardback
books and y is the number of paperback books.
5 x  2.5 y  20
Which of the following shows the graph of this equation.
Use x and y intercepts.
y
9
9
(a) Let x = 0
8
8
7
7
5(0)+2.5y = 20
6
6
5
2.5 y  20
5
4
4
2.5 y 20
3

3
2
2.5 2.5
2
1
y=8
1
1 2 3 4 5 6 7 8 9 10 11 x
1 2 3 4 5 6 7 8 9 10 11
(0,8) is the y-int
A.
C.
(b) Let y = 0
9
9
5x + 2.5(0) = 20
8
8
7
5x = 20
7
6
6
5 x 20
5
5

4
4
5
5
3
x
=
4
3
2
2
(4,0) is the x-int
1
1
1 2 3 4 5 6 7 8 9 10 11
B.
1 2 3 4 5 6 7 8 9 10 11
D.
The answer is A.
13. An architect designed an outdoor staircase for a house. The relationship between
the height of the steps and the length of the tread is modeled by the equation
57 x  95 y  0.
Which of the following represents the slope of the line defined by this equation?
5
3
3
B.
2
2
C.
3
3
D.
5
A.
Solve for y to get the equation in the form
y = mx + b so that m will be the slope.
57 x  95 y  0
57 x
 57 x
95 y  57 x
95 y 57 x

95
95
57
x
95
57 19  3 3
m


95 19  5 5
y
14. An engineer needs to determine the
slope between two points on a gondola ride
in order to evaluate the power
requirements when the gondola is full of
passengers. A coordinate grid has been
placed over a diagram between the two
points, as shown below. For estimation
purposes, a straight line between the two
points can be used to find the slope.
x ,y 
2
2
x ,y 
1
1
Assuming the cable runs in a straight line, what is the slope of the line between the
two points shown?
m
y2  y1
x2  x1

70  30
180  20

1
40

4
160
15. In a technical drawing class, students
 x1 , y1 
are analyzing the side view of a house
that has been positioned on a coordinate
 x 2 , y2 
grid, as shown.
-2
Which of the following equations best
+5
represents the line that contains PQ ?
5
A. y   x  14.4 Determine the slope by using
the formula or by counting.
2
5
B. y  x  27 m  y2  y1  10  12  2   2
2
x2  x1 11  6
5
5
2
C. y   x  14.4 or m  rise   2
5
run
5
2
D. y  x  27 Now use the point-slope formula to determine the equation of the line.
5
y  y  m( x  x )
1
1
2
y  12   ( x  6)
5
2
y  12   x  2.4
5
12 
 12
2
y   x  14.4
5
Note that after determining the
slope of the segment, only choice C
has the correct slope.
16. On the coordinate grid, line l is
perpendicular to AB .
What is the slope of line l ?
Use the slope formula to find the
slope of AB . The slope of line l will
be the opposite reciprocal since the
lines are perpendicular.
y2  y1
2  0
2
1
m



x2  x1
0  ( 4)
4
2
The opposite reciprocal is 2.
 x1 , y1 
 x 2 , y2 
17. David is training for a marathon. He writes down the time and distance
for each training run and then records the data on a scatter plot. He has
drawn a line of best fit on the scatter plot, as shown below.
Which statement best expresses the
meaning of the slope as a rate of change for
this line of best fit?
A. It represents the number of miles he will
have to run to finish the marathon.
B. It represents the average speed, in miles
per hour, of his training runs.
C. It represents the number of hours he
will need to finish the marathon.
D. It represents the distances, in miles, that
he ran while he was training.
The slope of a line is vertical change over horizontal change or change in miles over
change in hours. Therefore, the units on the slope would be miles per hour.
18. Joel graphed the line shown on the coordinate plane shown.
What is the x-coordinate of the point at which this line intersects the x-axis?
First write an equation for the
line that is graphed. It is easiest
to use y = mx + b because the
y -intercept is 11 as shown on the
graph. The slope can be
determined by using the slope
formula.
m
y2  y1 7  11 4


 2
x2  x1
20
2
Using b = 11 and m = -2 and
substituting into y = mx + b gives
y = -2x + 11.
The x-intercept has a y-coordinate of 0, so
substitute 0 for y in the equation of the line
and solve for x to get the x-intercept.
 x1 , y1 
 x 2 , y2 
 ?,0 
y  2 x  11
0  2 x  11
11
 11
11  2x
11 2 x

2
2
11
x
or 5.5
2
19. Russ bought 3 medium and 2 large submarine sandwiches for a total of $29.95.
Stacy bought 4 medium and 1 large submarine sandwiches for a total of $28.45.
Which statement shows the cost of each medium and each large submarine
sandwich?
A.
B.
C.
D.
Each medium sandwich costs $5.69 and each large sandwich costs $6.89.
Each medium sandwich costs $5.69 and each large sandwich costs $6.39.
Each medium sandwich costs $5.39 and each large sandwich costs $6.89.
Each medium sandwich costs $5.39 and each large sandwich costs $6.39.
3m  2l  29.95
3(5.39)  2l  29.95
4m  1l  28.45
16.17  2l  29.95
2  4m  1l   2  28.45
2l  13.78
8m  2l  56.90
l  6.89
3m  2l  29.95
5m  26.95
5
5
m  5.39
A medium sandwich costs $5.39 but
we need to also determine the cost of
a large. Substitute in the top
equation and solve for l.
20. A website that sells songs for downloading increased its price per song from
$0.99 to $1.29. Macy spent $15.36 downloading songs during the month of the
price increase. She downloaded 4 more songs at $0.99 than at $1.29. The set of
equations below represents the situation where x is the number of songs Macy
downloaded at $0.99 and y is the number of songs she downloaded at $1.29.
x  y4
0.99 x  1.29 y  15.36
What is the exact number of songs Macy downloaded at the $0.99 price?
0.99( y  4)  1.29 y  15.36
0.99 y  3.96  1.29 y  15.36
2.28 y  3.96  15.36
3.96  3.96
2.28 y  11.4
2.28 y 11.4
But y represents the number

2.28
2.28
of songs downloaded at $1.29
and the question asks how
y5
many are downloaded at
x  y4
$0.99. Substitute the value of
x9
y and solve for x.
21. The expression
12
10
A. m n q
m n q 
6
5
3
2
is equivalent to which of the following?

 
m  n  q 
m 6 n5 q 3
6
B. m 36 n 25 q 9
2
6
2
2
5
C. 2m 8 n 7 q 5
3
2

m12n10q6
D. 2m 12 n10 q 6
22. Mina simplified the expression shown below:
 a b  a b 
3 6
m
n
2 2
Her final answer was in the form a b . If she simplified the
expression correctly, what is the value of n, the exponent of b?
Add exponents to get
 a b  a b  
3 6
Therefore, the value of n is - 4 .
2 2
a 5 b 4 .
23. Which expression is equivalent to the perimeter of the shaded portion of
the rectangle?
The consecutive sides of the
A. 2 x  10
rectangle are x + 3 and x + 4
x4
units in length. The
B. 2 x  12
x3
perimeter is
C. 4 x  14
2(x + 3) + 2(x + 4) =
D. 8 x  28
2 x + 6+ 2 x + 8=
x4
4x+14
24. New photo imaging techniques on computers allow artists to distort an image
from its original shape. Figure 1 is a square image. Figure 2 is stretched 4 units
wider and shrunk 4 units shorter than Figure 1. How many square units greater
is the area of Figure 1 than the area of Figure 2?
x 2  ( x 2  16) 
Area Figure 1 is x  x  x 2 .
x 2  x 2  16 
Area Figure 2 is ( x  4)( x  4)  x 2  16.
16
25. Members of the art club want to raise money for their next field trip. They plan
to decorate greeting cards with glitter and origami animals made of origami
paper. They wrote the expression below to help calculate their total expenses:
( np  ng )  nc
where c = cost of one greeting card, g = cost of glitter per card,
p = cost of origami animals per card, and n = number of cards.
Which of the following expressions is equivalent to the expression above?
A. n( p  g  c )
B. n( p  g )  c
C. 3n( p  g )  c
D. 3n( p  g  c)
( np  ng )  nc 
n( p  g )  nc 
n( p  g  c )
26. If x  3 , which of the following shows the expression below in simplest
form?
3 x 2  27
3 x 2  27
A. 3( x  3)
B. 3( x  3)
C. 3( x  9)
D. 3( x  9)
x3

x3
3( x 2  9)

x3
3( x  3)( x  3)
 3( x  3)
x3
27. Charlie needs to simplify the expression below before he substitutes values
for x and y.
18 12
9 8
x y x y
x3 y4
If x  0 and y  0 , which of the following is a simplified version of the
expression above?
9
A. x y
5
B. x 24 y16
x18 y12  x 9 y 8

3 4
x y
x 18 y12 x 9 y 8
15 8
6 4
x
y

x
y


3 4
3 4
x y
x y
C. x 6 y 3  x 3 y 2
D. x 15 y 8  x 6 y 4
28. Tammy made similar
models of a building, with
dimensions, in inches, as
shown in the diagram
below. What is the value,
in inches, of x?
A.
B.
C.
D.
3
4
5
6
x5 x3

16
12
12( x  5)  16( x  3)
12 x  60  16 x  48
16 x
 16 x
4 x  60  48
60  60
4 x  12
x3
29. What is the solution of the equation below?
2
3

x  14 4 x
2
3

x  14 4 x
2(4 x )  3( x  14)
8 x  3 x  42
3 x  3 x
5 x  42
5 x 42

5
5
42
x
or  8.4
5
30. Neelam simplified the expression below for a homework assignment.
12  3 x  7 3
If Neelam simplified correctly, which of the following is her answer?
A. 9 3  3 x
12  3 x  7 3 
B. 11 3  3 x
2 2 3  3x  7 3 
C. 7 15  3 x
2 3  7 3  3x 
D. 8 15  3 x
9 3  3x
31. Jeannie solved the quadratic equation shown below by factoring.
x2  2 x  8  0
Which of the following shows a step in solving the equation shown?
A. ( x  2)( x  4)  0
B. ( x  2)( x  4)  0
C. ( x  2)( x  4)  0
D. ( x  2)( x  4)  0
The first step is to factor the quadratic.
x2  2 x  8  0
( x  4)( x  2)  0
32. Which of the following is the graph of y  x 2  2 x  8 ?
The graph is a parabola that
opens up because the leading
coefficient is positive. This
eliminates choices A and B.
Set y equal to 0 and solve
to find the x-intercepts.
x2  2 x  8  0
( x  4)( x  2)  0
x  4  0 or x  2  0
x  4 or x  2
The correct graph is C
because it has the correct
x-intercepts.
33. A ball is kicked from ground level into the air. Its height y, in feet, after x
seconds can be represented by the equation y  40 x  16 x 2 . What is the total
elapsed time, in seconds, from the time the ball is kicked until it reaches ground level
again?
Set y = 0 and solve because when the ball is on the ground its height, y, is 0.
y  40 x  16 x 2
0  40 x  16 x 2
0  8 x(5  2 x )
8 x  0 or 5  2 x  0
8x 0
 or  2 x  5
8 8
2 x 5
x  0 or

2
2
x  0 or
x  2.5
The ball is on the ground for a total of 2.5 seconds.
34. The set T represents several Tauring breeds of cattle.
T = {Angus, Devon, Shorthorn, Texas Longhorn}
The set Z represents several Zebu breeds of cattle.
Z = {Boran, Nelore, Ponwar}
What is the total number of elements in the set T  Z ?
The number of elements in the cross product of two sets
A. 7
is the number of elements in one set multiplied by the
B. 9
number of elements in the other.
C. 12
4 x 3 = 12
D. 20
35. Set D lists the ages of Dianna’s grandchildren.
D = {2, 5, 6, 8, 10, 11}
Set K lists the ages of Karen’s grandchildren.
K = {2, 10, 18}
Set P lists the ages of Patrick’s grandchildren.
P = {10, 11, 14}
What is the greatest age in the set ( K  P )  D ?
The set K  P contains any
element in either set K or set
P which is {2, 10, 11, 14, 18}
The intersection of this set
with set D is elements that
the sets have in common
which is {2, 10, 11}
The greatest element in this set is 11.
36. The universal set contains only sets R, S, and T. These sets are related as shown
in the Venn Diagram below:
Which set represents
(~ R  S )  (~ T  S )?
A.
B.
C.
D.
{d, e, f, j}
{d, j, k, m, n}
{d, e, f, j, k, m, n}
{d, e, f, g, j, k, m, n}
~ R  S denotes elements not in R and in S .
The elements in S, the yellow circle, that are
NOT in R make up the set {j, k, m, n}.
~ T  S denotes elements not in T and in S .
The elements in S, the yellow circle, that are NOT in T make up the set
{d, k, m, n}.
The union of {j, k, m, n} and {d, k, m, n} contains all elements that are in
either set. Therefore, the union of the sets is {d, j, k, m, n}.
37. The Venn diagram below shows the number of students who chose to participate
in each of the three sports offered at Sports Camp.
Based on the diagram, what is the
Total number of students who
did NOT participate in
Volleyball?
Students who did NOT
participate in volleyball are
represented by the areas that
lie outside the highlighted
circle that represents
Volleyball.
15 + 9 + 11 = 35