PRAXIS
Listening. Learning. Leading
THE SERIES
The Qfficjaj
Practice Test Pre-Professional Skills Test (PPSP): Mathematics Test Codes: 0730, 5730
‘‘r—
Authentic Full-Length Practice Test and Answer Sheet Test Instructions Answer Key and Score Conversion Tables
[
IiM;b
••
JLL
Copyright © 2007 by Educational Testing Service. PPST, EDUCATIONAL TESTING SERVICE, ETS, and the ETS logo are registered trademarks of Educational Testing Service. THE PRAXIS SERIES is a trademark of Educational Testing Service.
Pre-Professional Skills Tests (PPST®): Mathematics Features of This Booklet The test in this booklet is an authentic paper-based PPST® Mathematics test.’ It was given at actual test administrations before being retired for use as a practice test. Besides the authenticity of a real test, this booklet gives you additional support: •
A table showing the correct answer and content category for each question so you can determine your score and check your strengths and weaknesses in each of the three content areas
•
A score conversion table so you can convert your score to a scaled score and compare your scaled score with your state’s passing score
Using This Practice Test with the Study Guide For most people, this practice test will be most helpful in combination with the Praxis Pre Professional Skills Tests (PPST): Mathematics Study Guide. (The guide can be purchased at www.ets.org/store.html or in your local bookstore.) You can take this test first to gauge what areas you need to focus on with the study guide. Or you can take this test after you have worked through the study guide’s review chapters and practice questions. A third alternative is to take this test before and after you use the study guide, to check for improvement gained from your review work. This practice test booklet contains a paper-based PPST Math test. The paper-based version contains 40 multiple-choice questions. The PPST Math test is also available as a computerbased test. The computer-based test contains 46 questions, and 6 of these questions are “pretest” questions. There are no pretest questions on the paper-based test. The pretest questions on the computer-based test do not count toward your score. ETS includes pretest questions in many of its tests to gauge their statistical characteristics before administering them as “operational” questions, the kind that count toward your official score. The pretest questions are scattered throughout the test and are not detectable. You should not spend any time trying to figure out which questions are pretest questions; you should answer each question as if it counts toward your score.
Taking the Practice Test You will probably find it helpful to simulate actual testing conditions when taking the practice test, giving yourself 1 hour to work on the test. You can cut out the answer sheet provided if you wish.
Please note that, as of November 2007. the score reporting categories for the PPST \lalheniatics Lest will he revised. The new categories are as follows:
Category Category Category Category
I—Number and Operations Il—Algebra Ill—Geometry and Measurement IV—Data Analysis and Probability
Although the suhect matter in the new categories difters slightly from that presented in this practice test, the format of the score reports sent to examinees will remain unchanged. That is, the number of correct anssvers in each category will be reported aloitg with the conesponding nationwide aserages. The overall score on the test will continue to be expressed in the same scaled score metric. svhich ranges from ISO points to 190 points. More detailed information is available online at www.ets.org/praxis in a document entitled “Test at a Glance.” Sample questions ate provided in the Appendix of this practice test.
—1—
When you have finished the practice test, you can score your answers using the charts on pages 15—16. The instructions on the next page are taken directly from the back cover of the PPST Math test. Read these instructions carefully because they contain useful information about such things as guessing and scratchwork. If you take the computer-based PPST Math test, there will be additional instructions related to the software. An introduction to the computer-based test can be found in the Praxis Pre Professional Skills Tests (PPST): Mathematics Study Guide, chapter 2.
-2-
PPST: MATHEMATICS The supervisor will tell you when to begin work on the test and when to stop. if you finish before time is called, go back and check your work on the test. Work as rapidly as you can without sacrificing accuracy. Do not spend too much time puzzling over a question that seems too difficult for you. Answer the easier questions first; then return to the harder ones. Try to answer every question even if you have to guess. Your score will be based on the number of questions you answer correctly. Unanswered questions and incorrect answers are not counted in your score. Where necessary, you may use blank spaces in the test book for scratch paper. Do not use any other paper or the margins or back of the answer sheet to do scratchwork. YOU MUST INDICATE ALL OF YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. No credit will be given for anything written in this test book. After you have decided which of the suggested answers is best, fill in the corresponding lettered space on the answer sheet. BE SURE THAT EACH MARK IS HEAVY AND DARK AND COMPLETELY FILLS THE ANSWER SPACE. Light or partial marks may not be read by the scoring machine. Sample Answer
EXAMPLE: Which of the following is the capital of the United States? (A) New York, NY (B) Washington, DC (C) Chicago, IL (D) Los Angeles, CA (E) Boston, MA
Give only one answer to each question. if you change an answer, be sure that the previous mark is erased completely. Incomplete erasures may be read as intended answers. This test may include one or more questions that do not count toward your score.
Total Time 60 minutes 40 Questions
DO NOT BREAK THE SEAL UNTIL YOU ARE TOLD TO DO SO.
-3-
1. NAME
0
0 0 0 0 0 0 0
000000
@00000 000000 000000 000000 @00000 @00000 000000
0 0
0
0 0 0 0
0
0
®00000 000000
000000
@00000 000000 000000 000000
000000
00000
(UI
0 0 0 0 0 0 0
—
F I
@00000 @00000 @00000 000000 000000 @00000 0000
Last Name (Brat 6 tellers)
Eiiteryaur last name and first initial. Omit spaces, hyphens, apostrophes, etc.
/‘N
Apt. it (If any)
M. I.
0
Feb.
Jan.
TELEPHONE NUMBER:
l0@@@@@@
Q
[o®®®®®®
00’000000 00000000 00000000 00000000 00000000 @0000000 00000000 ®®®®®®®®
5. CANDIDATE ID NUMBER
SIGNATURE:
0
9
S
Home
Country
Center Name
State or Province
Room Number
1
2
3
Copyright © 2006 Educational Testing Service. All rights reserved. Edocatinnal Touting Sesice, ETS, and the ETS Inyn are registered tradenrarks of Edecatisnal Testing Service. The Praxis Series isa tsadenrark at Educational Testisg Service.
City
Center Number
4
1
0 00 000 0000000 0000000 ®®®®®®® @000000 0000000 @000000
0
0
®
® 00 ®®
Day
-
-
000000000 000000000 000000000 @00000000 000000000 @00000000
000000000
000000000
728495
10. TEST NAME
9.TEST FORM
I
PAGE 1
@@@@i@,@@@@
-
IIIf
4. SOCIAL SECURITY NUMBER
Si 23456789T
8. TEST BOOK SERIAL NUMBER
Qeec.
QNov.
Sept.
C Cccl.
QAug.
0
FO7I
6.TEST CENTER / REPORTING LOCATIST
ATE
ness
Zip or Postal Code
July
7 Couvliy
0 June
6
State or Province
April
QMar
Q 0
Month
QMay
dress
Firnt Name (Given)
I II 3. DATE OF BIRTH
Q
iO. Bu or Street
Last Name (Family or Surname)
Answer
5
(Print)
MAILING ADDRESS;
(Print)
YOUR NAME:
2.
S’
PRAXIS A I E
THE S E
4
3
2
0
letter or
Use only a pencil with soft black lead (No. 2 or HB) to complete this answer sheet. Be sure to lilt in completely the oval that corresponds to the proper number. Completely erase any errors or stray martos.
DO NOT USE INK
Ill
0 a)
a) a) a) U, = Cc
a,
=
0 Cc a)
0
a. a)
a) a) U,
a)
•0
-ø C a)
a)
E a) = UC
_0
—
El a)
z 0
.0 0)
>
o a)
C)
.2= -U,
uJ
C 0
H -C.
I-.0
0w
N
N
Co
C LU LU ED LU
I— (I) -J -J
cr
C
U) UJ
C)
UJ
ED
C!)
ED LU
LU
FU) -J -J LL
LU
F-
LU -J
0
0
C) ED
ED U)
C)
U)
w D
I—
z
LU W
>U_ .0 — i—a,
LU
0
U)
UJ.c
1-
C%I CN
.
CN
CO
C1
1-
CO
.-
c)
CN
C) U,
1
U,
1
0 C) r
C) 1
CN C) 7
C) C) T
C) —
Ifl C) 1
U, C) 1
C) —
U, C) 7
C
—
1
Co
CI
1-
1
U,
—
C4
U, C’4
CDN/j0) U,
T
U) U, C’1 C1 (1 1-
U) CO
CHH @@@tH)
CCCCC
U)
U,
F--
Co
0)
01- Cd
—
—
—
C1 —
C)
0 - CN C’) 0 0 0 0
o
)U)U,U,O)0 Cd U) U) U, U) U, U, CD CO CO U,
—
U)
0 1
U, 1
1
—
—
1
—
1
— — —
— —
C’)
1
C’J
1
— —
—
CO
—
F--
1 —
Co
1 1-
0)
1
U)
1
1-
1
1
1
1-
1
1
1-
0 Cd
U, 0) 0 i- C’i C) U) U, CQ 0) 0 U) U) U) U, U) U, U, U, U) U) CD 1
—
U) CO F-- CO 0) 0 0 0 0 0 00— —
CO
CD
CO
CD
(0
F--
—
Cd
C’)
U)
CO
r.-
0) 0 F--Co
®®——®®®®®®
C’)
@®®®®®®€)®®® Cd
—
—
—
—
—
—
—
—
—
Cd
C’.I
Cd
Cd Cd
Cd
Cd
Cd
Cd
Cd
C’)
C’)
C’)
C’)
C’)
C’)
C’)
C’)
C’)
C’)
®®®ee®eeee®®®®®®@® .-
0)
C)
C
I-
0
C
C
CO
C
CC,
C
Co
‘C
C’)
C
‘C
0
0
MATHEMATICS Time—60 minutes 40 Questions Directions: Each of the questions or incomplete statements below is followed by five suggested answers or comple tions. Select the one that is best in each case and then fill in the corresponding lettered space on the answer sheet with a heavy, dark mark so that you cannot see the letter. Remember, try to answer every question. Special Note: Figures that accompany problems in the test are intended to provide information useful in solving the problem. The figures are drawn as accurately as possible except when it is stated in a specific problem that its figure is not drawn to scale. Figures can be assumed to lie in a plane unless otherwise indicated. Position of points can be assumed to be in the order shown, and lines shown as straight can be assumed to be straight. The symbol L denotes a right angle.
1. The Lopez family plan to drive 250 miles on the first day of their vacation and at most 70 miles on each of the next 4 days to allow time for sightseeing. At most, how many miles do they plan to drive during their 5 days of vacation?
3. Donald planted more than 8 bushes and more than 4 trees on his new lot. What is the minimum total number of bushes and trees that Donald planted? (A) (B) (C) (D) (E)
320 530 600 (D) 1,280 (E) 1,600
(A) (B) (C)
10 11 12 13 14
BUDGET DISTRIBUTION 2. Which of the following is equivalent to 2.75? (A) (B) (C) (D)
Department S
Department R 24% Department V-
12
12%
Department U
8
20%
Department T
4. The graph above shows the percent of a corn pany’s yearly budget distributed to each of its five departments. What percent of the company’s yearly budget is distributed to Department U?
11
(E) ifE
(A)
8%
(B) 9% (C) 10% (D) 11% (E) 12%
Unauthorized copying or reuse of anypartofthispageisillegal.
-7-
GO ON TO THE NEXT PAGE.
5. Jackie wants to make bags of candy so that each bag contains 25 pieces of candy. If Jackie has a total of 562 pieces of candy, what is the greatest number of bags of candy that she can make? (A) (B) (C) (D) (E)
9. A map is drawn with a scale of 1 inch representing 6 feet. How many inches on the map would represent 18 feet? (A)2 (B) 3 (C) 6 (D)9 (E) 12
19 20 21 22 25
10. Of the following, which is the closest approximation of 72,059 ÷ 794?
6. Which of the following units of measure is most appropriate for reporting the distance between City A and City Z? (A) (B) (C) (D) (E)
(A) 30 (B) 90 (C) 300 (D) 900 (E) 3,000
Kilometer Centimeter Millimeter Liter Light-year
V
•
School
Number of Classrooms
A B C
18 36 24
30 44.
18
I2 6
7. The table above shows the number of classrooms in each of the three schools in a certain school district. A fourth school is to be built in the district. How many classrooms should be in the fourth school if the average (arithmetic mean) number of classrooms per school is to be 30 ? (A) (B) (C) (D) (E)
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
-x 1
2
5
11. The relationship between which of the following could be represented by the four points in the graph above?
40 41 42 43 44
(A) (B) (C) (D) (E)
Seconds and minutes Minutes and hours Hours and days Days and weeks Weeks and years
8. What digit is in the tenths place of the number 543.712? (A) 2 (B) 3 (C) 4 (D)5 (E) 7
Unauthorized copying or reuse of any part of this page is illegal.
-8-
GO ON TO THE NEXT PAGE.
49, 50, 24, x, 58, 37, 29
NUMBER OF STAMPS
(A) (B) (C) (D) (E)
Jen Phil I
Deb
54 43 38 29 21
I
I
I
1
Male 7 4 3 2
15. Four stamp collectors met to trade stamps. The number of stamps each collector brought to trade is shown in the graph above. At the end of trading, Bob had 105 stamps, Jen had 165, and Phil had 75. How many stamps did Deb have?
More than Ten Years
Ten Years or Less
Internists Cardiologists Surgeons Pediatricians
Female 7 5 3 1
Male 9 5 6 4
(A) (B) (C) (D) (E)
Female 7 6 8 3
100 110 115 120 125
16. Each of the students in two classes applied for a merit award. One of the classes had 30 students, 1 of whom received a merit award. The other class had 33 students, 2 of whom received a merit award. If no student is in both classes, what fraction of the students in the two classes received a merit award?
13. The table above lists the specialties of the 80 doctors in a certain medical group by length of time in the group and by gender. What fraction of the doctors in the group are female surgeons who have been in the group for more than ten years? (A)
(A)
(B)
(B)
(C)
(C)
(D)
(D)
(E)
(E)
(A) (B) (C) (D) (E)
[
I
20 40 60 $() 100 120 J40 60
Specialty
14. If 3x + 5y 2x + 4y =
I
BobLJ.
12. If the range for the data listed above is 34, which of the following CANNOT be the value of x ? (The range is the difference between the greatest and the least numbers in a set of data.)
=
30 and x
+
y
=
5, then
35 25 20 15 10
Unauthorized copying or reuse of any part of this page is illegal.
-9-
GO ON TO THE NEXT PAGE.
17. Claire bought 6 packages of pencils, with 24 pencils in each package. Claire would have had the same number of pencils if she had bought (A) (B) (C) (D) (E)
21. In a high school club, 42 members own a bike and 36 members own in-line skates. Of the club members who own a bike or in-line skates, 24 own both a bike and in-line skates. If there are 56 members in the club, how many members own neither?
9 packages with 16 pencils each 10 packages with 14 pencils each 12 packages with 10 pencils each 16 packages with 8 pencils each 18 packages with 6 pencils each
(A) 0 (B) 2 (C) 4
(D)5 (E) 6
18. In the figure above, if v then w =
=
30 and z
=
NUMBER OF PEOPLE OUT OF 100 WHO REGULARLY PLAY VIDEO GAMES Age 11Wand 26- 41 and 19group 18 Younger 25 40 Older
70,
Number of People
(A) 100 (B) 80 (C) 50 (D) 40 (E) 30
30
20
11
10
2
22. A total of 100 peopLe responded to the survey question “Do you regularly play video games?” The table above shows the number of “yes” responses for various age-groups. What is the probability that a person chosen at random from the 100 people who responded to the survey is age 26 or older and plays video games regularly?
19. Which of the following numbers can be used to show that the square root of a number is NOT always less than or equal to the number? (A) 0 (B) 0.25 (C) 2.25 (D) 4.9 (E) 10
(B) (C) 0.215632156321563
-
(D)
20. In the decimal number above, the first five digits to the right of the decimal point are 2, 1, 5, 6, and 3. These digits repeat indefinitely in that order. What is the 87th digit to the right of the decimal point?
(E)
(A)1 (B) 2 (C) 3 (D)5 (E) 6
JUnauthorized copying or reuse of any part of this page is illegal.
-10-
GO ON TO THE NEXT PAGE.
23. Norbert took ajob selling magazines. The first week he earned x dollars. The second week he earned two dollars less than he earned the first week, and the third week he earned one dollar less than three times what he earned the second week. Which of the following represents the amount of money, in dollars, that Norbert earned the third week? (A) (B) (C) (D)
25. A club has a total of n members. If k of the members play chess, which of the following represents the fraction of the club membership that does NOT play chess? (A) (B)
3(x—l) 3(x 3) 3x—4
(C)
—
(D)
3x—5 (E) 3x—7
(E) Year
Net Income
2000
$80,000
2001
S88,000
n—k k—n n—k n+k
=
£, if x is tripled,
then the value of M will be (A)
as great
(B) 2 times as great (C) 3 times as great (D) 6 times as great
$100,000 $104,000 $106,000 $110,000 $112,000
Unauthorized copying or reuse of any part of this page is illegal.
k—n
26. In the formula M
24. The table above shows the net income of a small company in 2000 and 2001. For each of the next two years, the percent increase of the company’s net income is equal to the percent increase from 2000 to 2001. Which of the following is closest to the company’s net income in 2003 ? (A) (B) (C) (D) (E)
n—k
(E) 9 times as great
—11-
GO ON TO THE NEXT PAGE.
x
s—i
STUDENT CLUB MEMBERSHIP
8
5 2 27. In the table above, the sum of the numbers in each row, column, and diagonal is 15. What number should be in the box directly below the box containing 5? (A)3 (B) 4 (C) 6 (D) 7 (E) 9
French Club
29. Each of the circles in the Venn diagram above represents a club, whose membership is given by the numbers shown. How many students are members of at least two of the three clubs?
Ms. Smith wants to give 5 nickels to each of 5 children. She has 75 cents worth of nickels. How many more nickels does she need?
(A) (B) (C) (D) (E)
28. Which of the following can be used to find the answer to the question above?
30. If p = 0.4997 x 0.5003 x 0.4998, which of the following is true?
I. (5x5)— 0.75
II. (5 x 5)
26 30 35 38 40
(A)
—
III. (0.05 x 0.05) (A) (B) (C) (D) (E)
(B) —
(C)
I only II only I and II only II and III only I, II, and ITT
Unauthorized copying or reuse of any part of this page is illegal.
(D) (E)
-12-
1
1
1
1
1
