Middle Level Mathematics (Grades 5–8)
Subtest 1 Sample Items
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Question 1
1. Which of the following graphs could be used to represent the solution to (1 + 2i)(3 −
2i ) where i is the imaginary unit?




Answer to question 1
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0001) The product of (1 +
2i )(3 − 2i) = 3 + 6i − 2i − 4i^{2}
= 3 + 4i + 4 = 7 + 4i. On the complex plane, 7 + 4i is represented as an
arrow drawn from the origin to the point represented by the ordered pair (7, 4) for 7 indicated on the
real axis and 4 indicated on the imaginary axis.
Correct Response: A. (Objective 0001) The product of open parenthesis 1 plus 2
i close parenthesis open parenthesis 3 minus 2 i close parenthesis equals 3 plus 6
i minus 2 i minus 4 i squared equals 3 plus 4 i plus 4 equals 7
plus 4 i. On the complex plane, 7 plus 4 i is represented as an arrow drawn from the
origin to the point represented by the ordered pair open parenthesis 7 comma 4 close parenthesis for
7 indicated on the real axis and 4 indicated on the imaginary axis.
Question 2
2. If a is a real number, which of the following equations is valid?




Answer to question 2
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0001) For any real number
a, a^{2} ≥ 0. Since
must be greater than or equal to zero,
.
Correct Response: D. (Objective 0001) For any real number a, a
squared greater than or equal to 0. Since square root of a squared must be greater than or equal to
zero, square root of a squared equals absolute value of a.
Question 3
3. In base 3, 21 times which of the following numbers equals 22120?
 102
 1020
 2012212
 11100001
Answer to question 3
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0001) In base 3, 21 = 2 ×
3^{1} + 1 × 3^{0}, which equals 6 + 1 = 7 in base 10. In base 3, 22120 = 2 ×
3^{4} + 2 × 3^{3} + 1 × 3^{2} + 2 × 3^{1} + 0, which
equals 162 + 54 + 9 + 6 = 231 in base 10. In base 10, 231 ÷ 7 = 33, which equals 1 × 3^{3}
+ 0 × 3^{2} + 2 × 3^{1} + 0 × 3^{0} = 1020 in base 3.
Correct Response: B. (Objective 0001) In base 3, 21 equals 2 multiplied by 3 superscript
one plus 1 times 3 superscript zero, which equals 6 plus 1 equals 7 in base 10. In base 3, 22120 equals
2 times 3 superscript four plus 2 times 3 cubed plus 1 times 3 squared plus 2 times 3 superscript one
plus 0, which equals 162 plus 54 plus 9 plus 6 equals 231 in base 10. In base 10, 231 divided by 7 equals
33, which equals 1 multiplied by 3 cubed plus 0 multiplied by 3 squared plus 2 times 3 superscript one
plus 0 times 3 superscript zero equals 1020 in base 3.
Question 4
4. Let C equal the base10 equivalent of the sum of A and B.
A = 341 base _{8}
B = 2011 base _{5}
The digit that occupies the hundreds place of C is:
 0.
 2.
 3.
 4.
Answer to question 4
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0001) The base10 equivalent
of 341_{8} is 3 × 8^{2} + 4 × 8^{1} + 1 × 8^{0}= 192
+ 32 + 1 = 225. The base10 equivalent of 2011_{5} is 2 × 5^{3} + 0 × 5^{2}
+ 1 × 5^{1} + 1 × 5^{0} = 250 + 0 + 5 + 1 = 256. The sum of 225 and 256
is 481. The digit in the hundreds place is 4.
Correct Response: D. (Objective 0001) The base ten equivalent of three four one
base eight is three times eight squared plus four times eight to the first power plus one times eight
to the zero power which equals one hundred ninety two plus thirty two plus one which equals two hundred
twenty five. The base ten equivalent of two zero one one base five is two times five cubed plus zero
times five squared plus one times five to the first power plus one times five to the zero power which
equals two hundred fifty plus zero plus five plus one which equals two hundred fifty six. The sum of
two hundred twenty five and two hundred fifty six is four hundred eighty one. The digit in the hundreds
place is four.
Question 5
5. Which of the following expressions represents the multiplicative inverse of (2 + 3i)^{2} squared?




Answer to question 5
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0001) The product (2 + 3i)^{2}
= 4 + 6i + 6i + 9i^{2} = 4 + 12i + 9(–1) = 4 −
9 + 12i = –5 + 12i. The multiplicative inverse of –5 + 12i is
,
which is equivalent to
Correct response: C. (Objective 0001) The product open parenthesis two plus three
i close parenthesis the quantity squared equals four plus six i plus six i plus nine i squared which
equals four plus twelve i plus nine open parenthesis negative one close parenthesis which equals four
minus nine plus twelve i which equals negative five plus twelve i. The multiplicative inverse of negative
five plus twelve i is one over the quantity negative five plus twelve i, which is equivalent to open
parenthesis one over the quantity negative five plus twelve i close parenthesis times open parenthesis
the quantity negative five minus twelve i all over the quantity negative five minus twelve i close parenthesis
which equals the quantity negative five minus twelve i all over the quantity twenty five minus one hundred
forty four i squared which equals the quantity negative five minus twelve i all over the quantity twenty
five minus one hundred forty four open parenthesis negative one close parenthesis which equals the quantity
negative five minus twelve i all over the quantity twenty five plus one hundred forty four which equals
the quantity negative five minus twelve i all over one hundred sixty nine.
Question 6
6. A new sales representative will be paid by company X every 25 days, by company Y every 15 days, and
by company Z every 20 days. Based on this information, how many days will it be before all three companies
pay the representative on the same day?
 200 days
 250 days
 300 days
 350 days
Answer to question 6
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0002) The sales representative
is paid by Company X on multiples of 25 days, by Company Y on multiples of 15 days, and by Company Z
on multiples of 20 days. The first day all three companies pay the sales representative is the least
common multiple of 25, 15, and 20. The prime factorization of 25 is 5^{2}, of 15 is 3 × 5, and
of 20 is 2^{2} × 5, thus the LCM(25, 15, 20) = 2^{2} × 3 × 5 = 300. It will be 300 days
before all three companies pay the representative on the same day.
Correct Response: C. (Objective 0002) The sales representative is paid by Company
X on multiples of twenty five days, by Company Y on multiples of fifteen days, and by Company Z on multiples
of twenty days. The first day all three companies pay the sales representative is the least common multiple
of twenty five, fifteen, and twenty. The prime factorization of twenty five is five squared, of fifteen
is three times five, and of twenty is two squared times five, thus the L C M of twenty five comma fifteen
comma twenty close parenthesis equals two squared times three times five which equals three hundred.
It will be three hundred days before all three companies pay the representative on the same day.
Question 7
7. A farmer has 108 snap pea plants, 162 tomato plants, 270 green pepper plants, and 324 corn plants
that need to be planted in rows. If each row must contain the same number of only one kind of plant,
what is the smallest number of rows of vegetable plants needed?
 8
 16
 48
 54
Answer to question 7
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0002) The greatest common
factor (gcf) of 108, 162, 270, and 324 will ensure that each row will contain the same number of plants.
The prime factorization of 108 = 2^{2} × 3^{3}, of 162 = 2 × 3^{4},
of 270 = 2 × 3^{3} × 5, and of 324 = 2^{2} × 3^{4}. Thus,
the gcf (108, 162, 270, 324) = 2 × 3^{3} = 54. If there are to be 54 of each plant in
a row, then there will be 108 ÷ 54 + 162 ÷ 54 + 270 ÷ 54 + 324 ÷ 54 = 2 + 3 + 5 + 6 = 16 rows of plants.
Correct Response: B. (Objective 0002) The greatest common factor (g c f) of 108,
162, 270, and 324 will ensure that each row will contain the same number of plants. The prime factorization
of 108 equals 2 squared times 3 cubed, of 162 equals 2 times 3 superscript four, of 270 equals 2 times
3 cubed multiplied by 5, and of 324 equals 2 squared times 3 superscript four. Thus, the g c f open
parenthesis 108, 162, 270, 324 close parenthesis equals 2 multiplied by 3 cubed equals 54. If there
are to be 54 of each plant in a row, then there will be 108 divided by 54 plus 162 divided by 54 plus
270 divided by 54 plus 324 divided by 54 equals 2 plus 3 plus 5 plus 6 equals 16 rows of plants.
Question 8
8. The two instances of regrouping applied in the addition algorithm below require an understanding
of which of the following concepts?
6
+

9
5

4
8

6

14

12

6

15

2

7

5

2

 additive inverse
 commutative property
 distributive property
 place value
Answer to question 8
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0002) Analysis of the algorithm
reveals the regrouping of 1 × 10^{1p>1} + 4 × 10^{1} = 5 × 10^{1}
and 1 × 10^{2} + 6 × 10^{2} = 7 × 10^{2}, as they are digits
in partial sums that have the same place value. Thus, regrouping to obtain the final sum of 752 requires
an understanding of place value.
Correct Response: D. (Objective 0002) Analysis of the algorithm reveals the regrouping
of 1 multiplied by 10 superscript 1 p greater than 1 baseline plus 4 times 10 superscript one equals
5 multiplied by 10^{1} and 1 multiplied by 10 squared plus 6 multiplied by 10 squared equals
7 multiplied by 10 squared, as they are digits in partial sums that have the same place value. Thus,
regrouping to obtain the final sum of 752 requires an understanding of place value.
Question 9
9. Use the table below to answer the question that follows.
◊diamond

P

Q

R

P

R

R

R

Q

P

Q

R

R

R

R

R

Which of the following statements correctly characterizes operation ◊ over the elements P, Q, and
R?

 P is the identity element.

 Every element has an inverse.
Answer to question 9
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0002) (Q ◊ R) ◊ P
= Q ◊ (R ◊ P) and R ◊ P = Q ◊ R and R = R.
Correct Response: A. (Objective 0002) open parenthesis Q diamond R close parenthesis
diamond P equals Q diamond open parenthesis R diamond P close parenthesis and R diamond P equals Q diamond
R and R equals R.
Question 10
10. Use the diagram below to answer the question that follows.
The grid has a diagonal through each box from the upper right corner to the lower left corner and continues
a short way past the grid on the left and bottom. Above each column from left to right is two, four,
seven. Along the left side of each row from top to bottom is zero, nine. Along the right side of each
row from top to bottom is three, eight. Below each column from left to right is three, eight, six. The
upper diagonal half of the first row contains the values from left to right a, one, two. The bottom
diagonal half of the first row contains the values from left to right b, two, one. The upper diagonal
half of the second row contains the values from left to right one, c, e. The bottom diagonal half of
the second row contains the values from left to right six, d, f.
A student's work multiplying 247 by 38 using lattice multiplication is shown. Given that the student
carried out the steps correctly, what is the sum of the digits represented by b, c,
and e?
 8
 14
 15
 19
Answer to question 10
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0002) Lattice multiplication
is a tool for multiplying large numbers using a grid. The grid is filled in with the products of the
digits at the head of any row or column, with the tens digit of the product in the upper diagonal half
of the square and the ones digit on the bottom half. The product of 2 and 3 is 6, so the value of a
= 0 and b = 6. The product of 4 and 8 is 32, so c = 3 and d = 2. The product
of 7 and 8 is 56 so e = 5 and f = 6. The sum of b, c, and e
is 6 + 3 + 5 = 14.
Correct Response: B. (Objective 0002) Lattice multiplication is a tool for multiplying
large numbers using a grid. The grid is filled in with the products of the digits at the head of any
row or column, with the tens digit of the product in the upper diagonal half of the square and the ones
digit on the bottom half. The product of two and three is six, so the value of a equals zero and b equals
6. The product of four and eight is thirty two, so c equals three and d equals two. The product of seven
and eight is fifty six so e equals five and f equals six. The sum of b, c, and e is six plus three plus
five which equals fourteen.
Question 11
11. A reserved seat ticket, r, for a play costs $6 more than a general admission ticket, g.
The cost of 5 general admission tickets is $3 more than the cost of 2 reserved seat tickets. Which of
the following equations could be used to determine the cost of a general admission ticket?
 5g + 3 = 2(g − 3) five
g plus three equals two times the quantity g minus three
 2g + 6 = 5g + 3 two g plus
six equals five g plus three
 2(g + 6) = 5(3g) two times
the quantity g plus six equals 5 times the quantity three g
 5g − 3 = 2g + 12 five
g minus three equals two g plus twelve
Answer to question 11
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0003) The system of equations
r = g + 6 and 5g = 2r + 3 algebraically models the information in
the problem. Substituting the first equation into the second equation results in 5g = 2(g
+ 6) + 3. Distributing to simplify the right side of the equation results in 5g = 2g
+ 12 + 3. Subtracting 3 from both sides of the equation leaves 5g − 3 = 2g +
12.
Correct Response: D. (Objective 0003) The system of equations r equals g plus six
and five g equals two r plus three algebraically models the information in the problem. Substituting
the first equation into the second equation results in five g equals two open parenthesis g plus six
close parenthesis plus three. Distributing to simplify the right side of the equation results in five
g equals two g plus twelve plus three. Subtracting three from both sides of the equation leaves five
g minus three equals two g plus twelve.
Question 12
12. The table below contains U.S. census data for the years 1995 and 2005.
Year

U.S.
Population

U.S. National
Debt ($)

1995

262 million

4951 billion

2005

298 million

7912 billion

What is the difference in the national debt per person for the years 1995 and 2005?
 7.6 × 10^{1}7.6 times 10
superscript 1
 8.2 × 10^{1}8.2 times 10
superscript 1
 7.7 × 10^{3}7.7 times 10
superscript 3
 8.5 × 10^{3}8.5 times 10
superscript 3
Answer to question 12
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0003) The national debt per
person in 2005 minus the national debt per person in 1995 can be expressed as
Correct Response: C. (Objective 0003) The national debt per person in 2005 minus
the national debt per person in 1995 can be expressed as start fraction numerator seven thousand nine
hundred and twelve times ten superscript nine denominator two hundred and ninety eight times ten superscript
six end fraction minus start fraction numerator four thousand nine hundred and fifty one times ten superscript
nine denominator two hundred and sixty two times ten superscript six end fraction equals twenty six
point six times ten superscript three baseline minus eighteen point nine times ten superscript three
equals seven point seven times ten superscript three.
Question 13
13. A rectangular box without a cover is going to be made by cutting the four corners from a 10inch
by 14inch rectangular piece of cardboard and then folding up along the cuts. Which of the following
expressions could be used to model the volume of the box if the height, h, is unknown?
 h (10 + h)(14 + h)
 h (10h)(14h)
 4h (5 −minus h)(7
−minus h)
 4h (5h)(7h)
Answer to question 13
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0003) The piece of cardboard's
corners will be cut from each end of each side at a length of h. Thus, the volume of the box
can be expressed as h (10 − 2h)(14 − 2h) = h (2)(5 −
h)(2)(7 − h) = 4h (5 − h)(7 − h).
Correct Response: C. (Objective 0003) The piece of cardboard's corners will be
cut from each end of each side at a length of h. Thus, the volume of the box can be expressed
as h open parenthesis 10 minus 2 h close parenthesis open parenthesis 14 minus 2
h close parenthesis equals h open parenthesis 2 close parenthesis open parenthesis
5 minus h close parenthesis open parenthesis 2 close parenthesis open parenthesis 7 minus
h close parenthesis equals 4 h open parenthesis 5 minus h close parenthesis
open parenthesis 7 minus h close parenthesis.
Question 14
14. Use the problem below to answer the question that follows.
At a local high school, a total of 46 students are playing sports. There are 15 students participating
in soccer, 20 in volleyball, and 32 in basketball. Only 3 students participate in all 3 sports, 8 students
are in both soccer and volleyball, and 4 are in both soccer and basketball. How many students are playing
only one sport?

Which of the following strategies would be most appropriate for solving the given problem?
 drawing a diagram
 extending a pattern
 graphing on a set of axes
 making a systematic list
Answer to question 14
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0003) The best method for
solving this problem would be drawing a Venn diagram using three overlapping circles to represent the
sets of students playing soccer, basketball, and volleyball.
Correct Response: A. (Objective 0003) The best method for solving this problem
would be drawing a Venn diagram using three overlapping circles to represent the sets of students playing
soccer, basketball, and volleyball.
Question 15
15. Earth contains approximately 326 million cubic miles of water. One cubic mile is 5280^{3} cubed
cubic feet and one cubic foot of water has about 9.5 × 10^{26} to the twenty sixth power molecules of water. Approximately
how many molecules of water does Earth have?
 1.63 × 10^{35}1 point 63 times
10 to the thirty fifth power
 1.63 × 10^{39}1 point 63 times
10 to the thirty ninth power
 4.56 × 10^{40}4 point 56 times
10 to the fortieth power
 4.56 × 10^{46}4 point 56 times
10 to the forty sixth power
Answer to question 15
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0003) There are 326,000,000
× 5280^{3} cubic feet of water on Earth, each having 9.5 × 10^{26} molecules
of water. The total number of water molecules can be found by multiplying 326,000,000 × 5280^{3}
× (9.5 × 10^{26}) = (3.26 × 10^{8}) × (5.28 × 10^{3})^{3}×
(9.5 × 10^{26}) = (3.26 × 10^{8}) × (147.2 × 10^{9})
× (9.5 × 10^{26}) = (3.26 × 10^{8}) × (1.472 × 10^{11})
× (9.5 × 10^{26}) ≈ 45.58 × 10^{45} ≈ 4.56 × 10^{46}.
Correct Response: D. (Objective 0003) There are 326 million times 5,280 cubed cubic
feet of water on Earth, each having 9.5 times 10 to the twenty sixth power molecules of water.
The total number of water molecules can be found by multiplying 326 million times 5,280 cubed times
open parenthesis 9.5 times 10 to the twenty sixth power close parenthesis which equals open parenthesis
3.26 times 10 to the eighth power close parenthesis times open parenthesis 5.28 times 10 to the third
power close parenthesis the quantity cubed times open parenthesis 9.5 times 10 to the twenty sixth power
close parenthesis which equals open parenthesis 3.26 times 10 to the eighth power close parenthesis
times open parenthesis 147.2 times 10 to the ninth power close parenthesis times open parenthesis 9.5
times 10 to the twenty sixth power close parenthesis which equals open parenthesis 3.26 times 10 to
the eighth power close parenthesis times open parenthesis 1.472 times 10 to the eleventh power close
parenthesis times open parenthesis 9.5 times 10 to the twenty sixth power close parenthesis which approximately
equals 45.58 times 10 to the forty fifth power which approximately equals 4.56 times 10 to the forty
sixth power.
Question 16
16. After cashing a paycheck, a teenager paid $20 on a phone bill, then spent onethird of what was
left on a jacket, then bought 8 gallons of gas for $2.10 per gallon, and had $K left over.
Which of the following expressions represents the original amount of the paycheck?

(K − 20) − 8(2.10)two thirds (K minus 20)
minus 8(2 point 10)
 (K + 8 • 2.10) •
+ 20 (K + 8 multiplied by 2 point 10) multiplied by three halves
+ 20

(K − 20) − 8(2.10) one third (K minus 20)
minus 8(2 point 10)
 (K + 8 • 2.10) • 3 + 20
(K + 8 multiplied by 2 point 10) multiplied by 3 + 20
Answer to question 16
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0003) Let P represent
the amount of the paycheck. The amount remaining after paying the phone bill is P − 20.
After spending onethird of this value, the remaining value is
(P − 20). The amount left after buying gas is
(P − 20) − 8(2.10) = K. Working these steps backward from K results
in (K + 8 • 2.10) •
+ 20.
Correct Response: B. (Objective 0003) Let P represent the amount of the paycheck.
The amount remaining after paying the phone bill is P minus twenty. After spending onethird of this
value, the remaining value is two thirds open parenthesis P minus twenty close parenthesis. The amount
left after buying gas is two thirds open parenthesis P minus twenty close parenthesis minus 8 open parenthesis
two point one zero close parenthesis which equals K. Working these steps backward from K results in
open parenthesis K plus eight times two point one zero close parenthesis times three halves plus twenty.
Question 17
17. The pattern below shows the first 11 terms in a number sequence. If the pattern continues, what
will be the 87th term in the number sequence?
1, 5, 3, 8, 2, 1, 5, 3, 8, 2, 1, ...
 1
 2
 5
 8
Answer to question 17
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0004) A cyclic pattern in
which the numbers 1, 5, 3, 8, 2 repeat is shown. Since there are five numbers in the pattern, a_{n}
will be 2 for every value of n that is a multiple of 5. To find the value for a_{n}
for any value of n that is not a multiple of 5, look at the remainder when dividing n
by 5. The remainder when dividing 87 by 5 is 2. The 87^{th} term occurs two terms after a term
that has a value of 2, so the 87^{th} term is 5.
Correct Response: C. (Objective 0004) A cyclic pattern in which the numbers one,
five, three, eight, two repeat is shown. Since there are five numbers in the pattern, a subscript n
will be two for every value of n that is a multiple of five. To find the value for a subscript n for
any value of n that is not a multiple of five, look at the remainder when dividing n by five. The remainder
when dividing eighty seven by five is two. The eighty seventh term occurs two terms after a term that
has a value of two, so the eighty seventh term is five.
Question 18
18. A clock is set to strike one chime for each number of the hour on every hour and to strike a single
chime on the half hour. How many total chimes are struck in one full day?
 168
 180
 288
 324
Answer to question 18
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0004) The clock will strike
one chime on the hour of 1:00 a.m. and one chime on the half hour, two chimes on the next hour, and
one chime on the half hour. The pattern that forms is
This entire pattern repeats for the next 12 hours. Thus, the clock chimes 90 × 2 = 180 times in
one full day.
Correct Response: B. (Objective 0004) The clock will strike one chime on the hour
of 1:00 a.m. and one chime on the half hour, two chimes on the next hour, and one chime on the half
hour. The pattern that forms is one plus two plus three plus dot dot dot plus twelve plus twelve equals
start fraction numerator twelve open parenthesis one plus twelve close parenthesis denominator two end
fraction plus twelve equals ninety. This entire pattern repeats for the next 12 hours. Thus, the clock
chimes 90 multiplied by 2 equals 180 times in one full day.
Question 19
19. Which of the following expressions is equivalent to
five x plus two y minus start fraction numerator six x minus two y denominator three
end fraction?




Answer to question 19
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0004) Multiplying the first
two terms by
is multiplying by 1 and does not change any values, but it generates a common denominator. The minus
sign before the rational expression must be distributed. Thus,
.
Correct Response: D. (Objective 0004) Multiplying the first two terms by three
over three is multiplying by 1 and does not change any values, but it generates a common denominator.
The minus sign before the rational expression must be distributed. Thus, three over three left bracket
five x plus two y right bracket minus open parenthesis start fraction numerator six y minus two y denominator
three close parenthesis equals start fraction numerator fifteen x plus six y minus six x plus two y
denominator three end fraction equals start fraction numerator nine x plus eight y denominator three
end fraction.
Question 20
20. A hotel has 25 rooms on each side of a hallway numbered from 201 through 250. The evennumbered
rooms are in order on one side of the hallway and the oddnumbered rooms are in order on the other.
If room 201 is across the hall from room 250 and room 203 is across the hall from room 248 and so on,
which of the following rooms is across from room 215?
 232
 234
 236
 238
Answer to question 20
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0004) The placement of the
hotel rooms along the hallway forms a pattern that can be illustrated as follows:
Rooms on odd side of hallway: 201 203 205 … 215 … 249
Rooms on even side of hallway: 250 248 246 … 236 … 202
Thus, room 236 is across from room 215.
Correct Response: C. (Objective 0004) The placement of the hotel rooms along the
hallway forms a pattern that can be illustrated as follows:
Rooms on odd side of hallway: 201 203 205 ellipsis 215 ellipsis 249
Rooms on even side of hallway: 250 248 246 ellipsis 236 ellipsis 202
Thus, room 236 is across from room 215.
Question 21
21. A squirrel gathers 1 acorn on the first day of fall, 3 acorns on the second day, and 5 acorns on
the third day. If the squirrel continues to gather acorns in this pattern, how many acorns will it have
gathered altogether at the end of 12 weeks?
 3,570
 7,056
 11,660
 14,028
Answer to question 21
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0004) The acorns collected
generate a sequence of numbers as indicated in the table below:
Day

Total Number of
Acorns Gathered

1

1 = 1^{2}

2

1 + 3 = 4 = 2^{2}

3

1 + 3 + 5 = 9 = 3^{2}

n

1 + 3 + 5 + … + 2n − 1 = n^{2}

12 × 7 = 84

84^{2} = 7,056

On day 12 × 7 = 84, the squirrel will have collected a total of 84^{2} = 7,056 acorns.
Correct Response: B. (Objective 0004) The acorns collected generate a sequence
of numbers as indicated in the table below:
Day

Total Number of
Acorns Gathered

1

1 equals 1 squared

2

1 plus 3 equals 4 equals 2 squared

3

1 plus 3 plus 5 equals 9 equals 3 squared

n

1 plus 3 plus 5 plus ellipsis plus 2 n minus 1 equals n squared

12 times 7 equals 84

84 squared equals 7,056

On day 12 times 7 equals 84, the squirrel will have collected a total of 84 squared equals 7,056 acorns.
Question 22
22. The sum of A and B is
the quantity x squared minus twenty over the quantity x squared minus four
. Given that A =
4 over the quantity 2 minus x and the product of A
and B is C, which of the following expressions could represent the numerator of C?
 4x + 16
 4x + 24
 (2x − 8)(2x + 8)
 (x + 6)(x − 2)
Answer to question 22
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0004) B is the difference
between
and A, so
. The product of A and B
is
with numerator 4(x + 6) = 4x + 24.
Correct Response: B. (Objective 0004) B is the difference between the quantity
x squared minus 20 all over the quantity x squared minus 4 and A, so B equals open parenthesis the quantity
x squared minus 20 all over the quantity x squared minus 4 close parenthesis minus open parenthesis
4 over the quantity 2 minus x close parenthesis which equals the quantity x squared minus 20 plus 4
open parenthesis x plus 2 close parenthesis all over the quantity open parenthesis x minus 2 close parenthesis
open parenthesis x plus 2 close parenthesis which equals the quantity x squared plus 4 x minus 12 all
over the quantity open parenthesis x minus 2 close parenthesis open parenthesis x plus 2 close parenthesis
which equals the quantity open parenthesis x minus 2 close parenthesis open parenthesis x plus 6 close
parenthesis all over the quantity open parenthesis x minus 2 close parenthesis open parenthesis x plus
2 close parenthesis which equals the quantity x plus 6 all over the quantity x plus 2. The product of
A and B is open parenthesis 4 over the quantity 2 minus x close parenthesis times open parenthesis the
quantity x plus 6 all over the quantity x plus 2 close parenthesis with numerator 4 open parenthesis
x plus 6 close parenthesis which equals 4 x plus 24.
Question 23
23. The time it takes to empty a truck loaded with crates of oranges varies directly with the number
of crates in the truck and indirectly with the number of workers unloading the truck. It takes 4 workers
6 hours to unload a truck that is loaded with 180 crates of oranges. Under the same conditions, what
is the least amount of workers that should be assigned to unload a truck that is loaded with 310 crates
of oranges if the job must be finished in one shift of 8 hours?
 5
 6
 7
 8
Answer to question 23
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0005) The relationship between
the workers, the crates of oranges, and time can be expressed as w • h = 180
• k, where w equals the number of workers, h = the number of hours,
and k equals the constant of proportionality. Thus, 6 • 4 = 18 • k
and 8 • w = 180 •
w = 6.
Correct Response: B. (Objective 0005) The relationship between the workers, the
crates of oranges, and time can be expressed as w multiplied by h equals 180 multiplied
by k, where w equals the number of workers, h equals the number of hours,
and k equals the constant of proportionality. Thus, 6 times 4 equals 18 times k leads
to k equals two over fifteen and 8 multiplied by w equals 180 times two over fifteen leads
to w equals 6.
Question 24
24. Which of the following expressions is equivalent to b ^{7}
−superscript 7 minus b ^{
−7}superscript negative 7?

 −1negative 1

 2b^{7}2 b superscript 7
Answer to question 24
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0005) By applying rules for
negative exponents, the expression
.
Correct Response: A. (Objective 0005) By applying rules for negative exponents,
the expression b superscript seven baseline minus b superscript negative seven equals b superscript
seven baseline minus one over b superscript seven equals open parenthesis start fraction numerator b
superscript seven denominator b superscript seven end fraction close parenthesis b superscript seven
baseline minus one over b superscript seven equals start fraction numerator b superscript fourteen baseline
minus one denominator b superscript seven end fraction.
Question 25
25. A function is defined on the domain {1, 2, 3, 4} such that f (N) is the sum of
the divisors of N. Which of the following sets of ordered pairs represents this function?
 {(1, 0), (2, 1), (3, 1), (4, 2)}
 {(1, 1), (2, 1), (3, 1), (4, 3)}
 {(1, 1), (2, 2), (3, 2), (4, 3)}
 {(1, 1), (2, 3), (3, 4), (4, 7)}
Answer to question 25
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0005) The divisors of 1,
2, 3, and 4 are 1; 1 and 2; 1 and 3; and 1, 2, and 4; respectively. Thus, the sums of the divisors are
1, 3, 4, and 7, respectively. The set of ordered pairs {(1, 1), (2, 3), (3, 4), (4, 7)} represents this
function.
Correct Response: D. (Objective 0005) The divisors of 1, 2, 3, and 4 are 1; 1 and
2; 1 and 3; and 1, 2, and 4; respectively. Thus, the sums of the divisors are 1, 3, 4, and 7, respectively.
The set of ordered pairs left brace open parenthesis one comma one close parenthesis open parenthesis
two comma three close parenthesis open parenthesis three comma four close parenthesis open parenthesis
four comma seven close parenthesis close brace represents this function.
Question 26
26. The formula for luminosity of a star is given by L = 4πd^{2}b,
where L is luminosity measured in watts, d is distance in meters, and b is
brightness in watts per meter squared. Which of the following expressions represents the formula for
distance as a function of luminosity?




Answer to question 26
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0005) Beginning with the
formula for luminosity of a star and applying algebraic techniques results in the following representation
of distance as a function of luminosity:
Correct Response: A. (Objective 0005) Beginning with the formula for luminosity
of a star and applying algebraic techniques results in the following representation of distance as a
function of luminosity: l equals four pi d squared b leads to start fraction numerator l denominator
four pi b end fraction equals d squared leads to start square root start fraction numerator l denominator
four pi b end fraction end root equals one half start square root start fraction numerator l denominator
pi b end fraction end root equals d.
Question 27
27. The spreadsheet below is intended to calculate the slope of a nonvertical line using the coordinates
of two points. The slope will be displayed in cell B4.

A

B

1

x_{1} subscript 1

y_{1} subscript 1

2

x_{2} subscript 2

y_{2} subscript 2

3

= A2 − A1

= B2 − B1

4



If the coordinates of the points (x_{1}
subscript 1 , y_{1} subscript
1 ) and (x_{2} subscript
2 , y _{2} subscript 2
) are entered in the spreadsheet into cells A1, B1, A2, and B2, respectively, what formula
should be entered in cell B4?
 B3 × A3
 B3 + A3
 B3 ÷ A3
 B3 − A3
Answer to question 27
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0005) The slope of the line
through two distinct points is calculated as
. Here y_{2} − y_{1}
= B2 − B1, which is given in cell B3; and x_{2} − x_{1}
= A2 − A1, which is given in cell A3. Thus, the formula that calculates the slope should be entered
in B4 as B3 ÷ A3.
Correct Response: C. (Objective 0005) The slope of the line through two distinct
points is calculated as start fraction numerator y sub two baseline minus y subscript one denominator
x subscript two baseline minus x sub one end fraction. Here y subscript two minus y
subscript one equals B 2 minus B 1, which is given in cell B 3; and x sub two minus x
subscript one equals A 2 minus A 1, which is given in cell A 3. Thus, the formula that calculates the
slope should be entered in B 4 as B 3 divided by A 3.
Question 28
28. Given that f(x) =
f of x equals the quantity x plus one all over x,
which of the following intervals represents the domain of the inverse function f^{–}superscript negative^{1}(x)?
 (–∞, 1) ∪ (1, ∞)open
interval negative infinity comma one union open interval one comma infinity
 (–∞, –1) ∪ (–1, ∞)open
interval negative infinity comma negative one union open interval negative one comma infinity
 (–∞, 0) ∪ (0, ∞)open
interval negative infinity comma zero union open interval zero comma infinity
 (–∞, ∞)open interval negative
infinity comma infinity
Answer to question 28
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0005) The inverse of
f(x) can be found algebraically by replacing f(x) with y, switching
the x and y variables, and then solving the new equation for y in terms of
x. That is, x=
→ xy = y + 1 → xy − y = 1 → y(x −
1) = 1 → y =
→ f^{–1}(x) =
.
When x = 1, f^{–1}(x) =
,
which is undefined. For any other value of x, f^{–1}(x)
is a real number. The domain of f^{–1}(x) is any real number
except 1, or (–∞, 1) ∪ (1, ∞).
Correct Response: A. (Objective 0005) The inverse of f of x can be found algebraically
by replacing f of x with y, switching the x and y variables, and then solving the new equation for y
in terms of x. That is, x equals the quantity y plus one all over y becomes x y equals y plus one becomes
x y minus y equals 1 becomes y open parenthesis x minus one close parenthesis equals one becomes y equals
one over the quantity x minus one becomes f inverse of x equals one over the quantity x minus one. When
x equals 1, f inverse of x equals one over the quantity one minus one, which is undefined. For any other
value of x, f inverse of x is a real number. The domain of the f inverse of x is any real number except
1, or open interval negative infinity comma one union open interval one comma infinity.
Question 29
29. There are 3
hr.
left in the workday and a sales associate has 5 calls to make to potential customers and has a 45
min.
meeting to attend. If m equals the average number of minutes spent on each call, which of the
following inequalities could be used to determine the time the sales associate can spend talking with
each potential customer?
 180 ≥ 5m + 45 180 is greater than
or equal to 5 m plus 45
 3 – 0.75 ≥ 5m3 minus zero
point 75 is greater than or equal to 5 m
 3 + m ≤ 45(m + 5) 3 plus
m is less than or equal to 45 times the quantity m plus 5
 5m ≤ 45 + 180 5 m is less than
or equal to 45 plus 180
Answer to question 29
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0006) Since each call takes
an average of m minutes, it will take 5m minutes to complete 5 calls. Adding on the
number of minutes for the meeting, the sales associate has 5m + 45 minutes of work left to
do. The sales associate cannot exceed 3 hours, or 60 × 3 = 180 minutes, to complete the meeting
and calls. The inequality that best models this situation is 180 ≥ 5m + 45.
Correct Response: A. (Objective 0006) Since each call takes an average of m minutes,
it will take 5 m minutes to complete 5 calls. Adding on the number of minutes for the meeting, the sales
associate has 5 m plus 45 minutes of work left to do. The sales associate cannot exceed three hours,
or 60 times 3 which equals 180 minutes, to complete the meeting and calls. The inequality that best
models this situation is 180 is greater than or equal to 5 m plus 45.
Question 30
30. Two perpendicular lines, m and n, intersect at (–negative2, –negative3).
If line m has an xintercept of –negative9,
which of the following equations describes line n?
 x − 3y = 7
 3x − 7y = –negative15
 7x − 3y = –negative5
 3x − y = 9
Answer to question 30
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0006) Since line m
contains points (–2, –3) and (–9, 0), its slope is
. Since line n is perpendicular to
line m, its slope is
. Line n also contains point (–2,
–3). The equation of line n can be found by substitution:
.
Correct Response: C. (Objective 0006) Since line m contains points open
parenthesis negative 2 comma negative 3 close parenthesis and open parenthesis negative 9 comma 0 close
parenthesis, its slope is start fraction numerator negative three minus zero denominator negative two
minus open parenthesis minus nine close parenthesis end fraction equals start fraction numerator negative
three denominator seven end fraction. Since line n is perpendicular to line m, its
slope is negative start fraction numerator one denominator start fraction numerator negative three denominator
seven end fraction end fraction equals start fraction numerator seven denominator three end fraction.
Line n also contains point open parenthesis negative 2 comma negative 3 close parenthesis.
The equation of line n can be found by substitution: y equals m a plus b leads to negative
three equals seven over three open parenthesis negative two close parenthesis plus b leads to five over
three equals b and y equals start fraction numerator seven denominator three end fraction x plus five
over three leads to seven x minus three y equals negative five.
Question 31
31. A small catering company owns a van valued at $33,000. The company's accountant's recommendation
is to apply a firstyear depreciation of $5,000 and then 12% per year thereafter. Which of the following
functions could be used to find the depreciated value of the van for any year, t?
 f(t) = 24,640 − 3,360t
 f(t) = 28,000 − 3,360t
 f(t) = 28,000 − 3,300t
 f(t) = 31,360 − 3,360t
Answer to question 31
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0006) The depreciated value
of the van at the end of year 1 is represented by 33,000 − 5,000 = 28,000. At the end of year
2, it is 33,000 − 5,000 − (28,000 × 0.12 × 1) = 24,640. At the end of year 3,
it is 33,000 − 5,000 − (28,000 × 0.12 × 2) = 21,280. At the end of year t,
it is 33,000 − 5,000 − [28,000 × 0.12 × (t − 1)] = 28,000 −
3,360(t − 1) = 31,360 − 3,360t.
Correct Response: D. (Objective 0006) The depreciated value of the van at the end
of year 1 is represented by 33,000 minus 5,000 equals 28,000. At the end of year 2, it is 33,000 minus
5,000 minus open parenthesis 28,000 times 0.12 times 1 close parenthesis equals 24,640. At the end of
year 3, it is 33,000 minus 5,000 minus open parenthesis 28,000 times 0.12 times 2 close parenthesis
equals 21,280. At the end of year t, it is 33,000 minus 5,000 minus left bracket 28,000 times
0.12 times open parenthesis t minus 1 close parenthesis right bracket equals 28,000 minus 3,360
open parenthesis t minus 1 close parenthesis equals 31,360 minus 3,360 t.
Question 32
32. A mobile will balance if the product of the weight and the distance of the weight from a balance
point on one side equals the product of the weight and distance of the weight on the other side. If
the weight of the horizontal bars and connecting string is negligible, what is the weight of item b
in the mobile below?
straight line coming down, arm to the left five inches and an arm to the right nine inches. from the
five inch arm there is an arm going down connected to a weight labeled a. from the nine inch arm there
is a short arm then a weight labeled b then the arm continues down then splits to the left with a four
inch arm and then to the right six inches. on the four inch arm there is an arm down with a weight attached
labeled a. on the six inch arm there is another weight that is labeled three ounces.


 6 ounces
 10 ounces
Answer to question 32
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0006) The products of weight
and distance for equation 1 are represented by 5a = 9b. The products of weight and
distance for equation 2 are represented by 4a = 18, and 4a = 18
. By substitution into equation 1,
.
Correct Response: B. (Objective 0006) The products of weight and distance for equation
1 are represented by 5 a equals 9 b. The products of weight and distance for equation
2 are represented by 4 a equals 18, and 4 a equals 18 five open parenthesis nine over two close parenthesis
equals nine b leads to one ninths open parenthesis five close parenthesis open parenthesis nine over
two close parenthesis equals b leads to two and one half equals b. By substitution into equation 1,
five open parenthesis nine over two close parenthesis equals nine b leads to one ninth open parenthesis
five close parenthesis open parenthesis nine over two close parenthesis equals b leads to two and one
half equals b.
Question 33
33. At 9:00 a.m. a
hour weather delay
is announced at the MinneapolisSt. Paul International Airport. In addition to this, each flight will
be delayed another 15 minutes for every flight originally scheduled to depart between the time the delay
was issued and its originally scheduled time of departure. If there were n flights scheduled
between 9:00 and 10:00 a.m., which of the following models could airport personnel use to find the new
time of departure, t(n), for a flight that was originally scheduled for departure
at 10:00 a.m.?


 t(n) = 2 + 15n
 t(n) = 4 + 15n
Answer to question 33
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0006) The delay of
is added to 10:00 a.m., the original departure time, as well as
hour for each flight scheduled between the time the delay was issued (9:00 a.m.) and the original departure.
Thus,
.
Correct Response: A. (Objective 0006) The delay of two and one fourth is added
to 10:00 a m, the original departure time, as well as one fourth hour for each flight scheduled between
the time the delay was issued open parenthesis 9:00 a m close parenthesis and the original departure.
Thus, t open parenthesis n close parenthesis equals ten plus nine fourths plus one fourth n leads to
t open parenthesis n close parenthesis equals start fraction numerator forty nine plus n denominator
four end fraction.
Question 34
34. Use the system of equations below to answer the question that follows.
2x − ky = 12
3x + 5y = 8
In the system of linear equations shown, k is a constant. Given that the system has no solution,
what is the value of k?




Answer to question 34
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0006) For a system of linear
equations to have no solution, the lines must be parallel; that is, they have the same slope but different
yintercepts. Solving both equations for y in terms of x gives y
= and y =
. The slope and yintercept
of 2x − ky = 12 are and
,
respectively. The slope and yintercept of 3x + 5y = 8 are
and
, respectively.
For the slopes to be equal, =
,
so k =
. The
yintercepts are different because =
.
Correct Response: D. (Objective 0006) For a system of linear equations to have
no solution, the lines must be parallel; that is, they have the same slope but different yintercepts.
Solving both equations for y in terms of x gives y equals open parenthesis two over k close parenthesis
x minus twelve over k and y equals open parenthesis negative three fifths close parenthesis x plus eight
fifths. The slope and yintercept of two x minus k y equals twelve are two over k and negative twelve
over k, respectively. The slope and yintercept of three x plus five y equals eight are negative three
fifths and eighth fifths, respectively. For the slopes to be equal, two over k equals negative three
fifths, so k equals negative ten thirds. The yintercepts are different because negative twelve over
k which equals negative twelve over ten thirds which equals eighteen fifths which is not equal to eight
fifths.
Question 35
35. Which of the following functions, g(x), represents a translation
of the graph of f(x) =
four units to the left on the xaxis? Which of the following functions
g of x, represents a translation of four units to the left on the x axis of the graph of the equation
f of x equals the square root of the quantity x plus three?
 g(x) =
g of x equals the square root of
the quantity x plus seven
 g(x) =
g of x equals the square root of
the quantity x minus one
 g(x) =
+ 4g of x equals four plus the square root of the quantity x plus three
 g(x) =
− 4g of x equals negative four plus the square root of the quantity
x plus three
Answer to question 35
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0007) To translate a graph
b units to the left, add b to the x value in the equation representing the
function. To shift the graph of g(x) four units to the left, add 4 to x.
g(x) =
+ 4 =
.
Correct Response: A. (Objective 0007) To translate a graph b units to the left,
add b to the x value in the equation representing the function. To shift the graph of g of x four units
to the left, add four to x. g of x equals the square root of the quantity open parenthesis x plus four
close parenthesis plus three which equals the square root of the quantity x plus seven.
Question 36
36. Library A charges $0.05 for a book that is past due for one day and increases the fine by 50% for
each additional day the book is not returned. Library B charges $0.50 per day for a book that is past
due. Which library collects a larger fine for a book that is two weeks overdue and by how much?
 Library A by $2.73
 Library A by $7.59
 Library B by $3.25
 Library B by $5.95
Answer to question 36
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: A. (Objective 0007) The fine for the overdue
book at Library A is determined by 0.05(1.5)^{13} = 9.73. The fine for Library B is determined
by 0.50(14) = 7.00. The fine for Library A exceeds the fine for Library B by $9.73 − $7.00 = $2.73.
Correct Response: A. (Objective 0007) The fine for the overdue book at Library
A is determined by 0.05 open parenthesis 1.5 close parenthesis superscript thirteen equals 9.73. The
fine for Library B is determined by 0.50 open parenthesis 14 close parenthesis equals 7.00. The fine
for Library A exceeds the fine for Library B by $9.73 minus $7.00 equals $2.73.
Question 37
37. Which of the following expressions represents the range of the graph of y = x
^{2} − 4x + 9?
 [2, ∞)
 [5, ∞)
 [9, ∞)
 (∞, ∞)
Answer to question 37
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: B. (Objective 0007) Since y =
x^{2} − 4x + 9 is a parabola that opens upward, its range can be defined
using the ycoordinate of the vertex. The xcoordinate of the vertex is given by
. Thus, y = 2^{2} − 4(2)
+ 9 = 5 and the range of the graph of y = x^{2} − 4x + 9 is
given by [5, ∞).
Correct Response: B. (Objective 0007) Since y equals x squared
minus 4 x plus 9 is a parabola that opens upward, its range can be defined using the ycoordinate
of the vertex. The xcoordinate of the vertex is given by start fraction numerator negative
b denominator two a end fraction equals four over two equals two. Thus, y equals 2 squared
minus 4 open parenthesis 2 close parenthesis plus 9 equals 5 and the range of the graph of y
equals x squared minus 4 x plus 9 is given by bracket 5 comma infinity close parenthesis.
Question 38
38. In which of the following intervals of x is the function f(x) in the
graph below increasing?
starting on the left in the second quadrant decreasing passing the x axis at open parenthesis negative
nine comma zero close parenthesis decreasing into the third quadrant down to a trough at open parenthesis
negative six comma negative five close parenthesis then increasing back up past the x axis at open parenthesis
negative two comma zero close parenthesis increasing into the second quadrant to a crest up to open
parenthesis zero comma eight close parenthesis then decreasing into the first quadrant passing the x
axis at open parenthesis four comma zero close parenthesis decreasing into the fourth quadrant down
to a trough at open parenthesis six comma three close parenthesis increasing up to the x axis open parenthesis
eight comma zero close parenthesis increasing into the first quadrant then continuing to increase .
 (−∞negative infinity, −negative 9]
 [−negative3, 4]
 [4, ∞infinity)
 [−negative6, 0]
Answer to question 38
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: D. (Objective 0007) The graph of f(x)
has a local minimum at (−6, −5) and a local maximum at (0, 8); thus, the graph of f(x)
is increasing over that interval.
Correct Response: D. (Objective 0007) The graph of f of x has a local minimum at
open parenthesis negative 6 comma negative 5 close parenthesis and a local maximum at open parenthesis
0 comma 8 close parenthesis; thus, the graph of f of x is increasing over that interval.
Question 39
39. A function f(t) represents the distance traveled in meters by a particle over
time (t in seconds). Which of the following quantities could be used to determine the speed
of the particle in meters per second?
 the limit of the function
 the length of the curve
 the first derivative of the function
 the maximum value of the graph
Answer to question 39
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0007) The function f(t)
relates the position of a particle at time t to time t, and the slope at any point
of f(t) describes the speed of the particle. The slope at any point is determined
by the first derivative of the function.
Correct Response: C. (Objective 0007) The function f of t relates the position
of a particle at time t to time t, and the slope at any point of f of t describes
the speed of the particle. The slope at any point is determined by the first derivative of the function.
Question 40
40. At a certain bank, a certificate of deposit account returns 3% interest annually, while a savings
account returns only 1.2% annually. A customer plans to invest $P for a twoyear period. Assuming
no other deposits or withdrawals, which of the following expressions determines the additional amount
the customer would receive after two years having chosen the certificate of deposit over the savings
account?
 P(1.03 − 1.012)^{2}

 P(1.03^{2} − 1.012^{2})

Answer to question 40
 Answer Enter to expand or collapse answer. Answer expanded
 Correct Response: C. (Objective 0007) After 2 years with
no other deposits or withdrawals, the amount of money in the 3% account will be P(1.03)^{2}
and the amount in the 1.2% account will be P(1.012)^{2}. The difference is P(1.03)^{2}
− P(1.012)^{2} = P(1.03^{2} − 1.012^{2}).
Correct Response: C. (Objective 0007) After two years with no other deposits or
withdrawals, the amount of money in the three percent account will be P open parenthesis 1.03 close
parenthesis the quantity squared and the amount in the 1.2 percent account will be P open parenthesis
1.012 close parenthesis the quantity squared. The difference is P open parenthesis 1.03 close parenthesis
the quantity squared minus P open parenthesis 1.012 close parenthesis the quantity squared which equals
P open parenthesis 1.03 squared minus 1.012 squared close parenthesis.