Solution guide to Math GRE Form GR9367
Ian Coley
August 15, 2016
Solution 1. (D) We have f (g(x) = g(x) + 3 = 5 for all x, so g(x) = 2 for all x R.
Solution 2. (C) We have that
sin x
tan x
sin x
= cos x =
.
cos x
cos x
cos2 x
Put this way, we know limx0 c

September 17, 2015
Charlie Marshak
Problem Set #1
1. A. The key is to notice that the integrand can be rewritten as:
1
3
q
2
1 ( x3
3
Then, we have that the antiderivative of arcsin(u) where u = (x 3)/3.
2. E. Recall a0 = f (c). Hence, we must find the ro

GR1268 Solutions
Hello mathematicians!
What follows are my solutions to the questions from the 2015 GRE Mathematics Test Practice Book
(found at https:/www.ets.org/s/gre/pdf/practice_book_math.pdf). The solutions presented here generally
represent the mos

August 2, 2012
Charlie Marshak
Problem Set #1
1. A. The key is to notice that the integrand can be rewritten as:
1
3
q
2
1 ( x3
3
Then, we have that the antiderivative of arcsin(u) where u = (x 3)/3.
2. E. Recall a0 = f (c). Hence, we must find the roots

MATHEMATICS TEST
SAMPLE QUESTIONS
The following questions illustrate the range of the test in terms of the abilities measured, the disciplines covered, and
the difficulty of the questions posed. They should not, however, be considered representative of th

10 In order to send an undetected message to an agent in the held, each letter in the message is replaced by the
number of its position in the alphabet and that number is entered in a matrix M. Thus, for example. DEAD
becomes the matrix M = (4 D) In order

Solution guide to Math GRE Form GR1268
Ian Coley
August 9, 2016
The questions for this solution guide can be found here: https:/www.math.ucla.edu/
iacoley/gre/Practice
1.pdf.
~
Solution 1. (E) Two applications of LHopitals rule:
lim
x0
cos(3x) 1
3 sin(3x)

Solutions to Math GRE Form GR0568
Ian Coley
August 26, 2016
Solution 1. (B) The equation for parametrised arc length is
Z bq
s=
fx2 + fy2 dt.
a
Here, fx = sin t and fy = cos t, so that fx2 + fy2 = 1. This makes the integral
Z
1 dt = .
0
Solution 2. (E) V

Solution guide to Math GRE Form GR8767
Ian Coley
August 18, 2016
Solution 1. (B) Any three (non-colinear) points uniquely determines a plane. Since the
xz-plane contains these points, thats the answer.
Solution 2. (C) I is certainly true if a and b are bo

GRE Mathematics Subject
Test GR0568 Solutions
2nd edition
Charles Rambo
Preface
Thank you for checking out my solutions to the GRE mathematics subject test 0568. This is primarily
intended as a reference, though some theorems were stated only once and the

Solution guide to Math GRE Form 9768
Ian Coley
August 19, 2016
Solution 1. (C) Fundamental theorem of calculus:
Z x
d
log t dt = log x.
dx e
Solution 2. (D) There is an easy way to get a closed formula for this series.
F (2) = 2 + 1/2,
f (3) = 2 + 1/2 + 1

FORM GR1268
68
GRADUATE RECORD EXAMINATIONS
MATHEMATICS TEST
Copyright 2012, 2007 by Educational Testing Service. All rights reserved.
GRE, GRADUATE RECORD EXAMINATIONS, ETS, EDUCATIONAL TESTING
SERVICE and the ETS logos are registered trademarks of Educa

The following sample questions are for:
FPSC Mathematics Lecturer test
Armed Forces Mathematics Lecturer test
Mphill Mathematics, admission test
GAT Mathematics & GRE Mathematics
Sample Questions (21-30) Mathematics
21. sec xdx ?
(A) sec x tan x
(B) c

The following sample questions are for:
FPSC Mathematics Lecturer test
Armed Forces Mathematics Lecturer test
Mphill Mathematics, admission test
GAT Mathematics & GRE Mathematics
Sample Questions (41-50) Mathematics
x2 2
41. For what value of A the f

MU LT N Am ABLE CALLU Lug
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I x
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min . .
(A) n (m 5'; (C) % (D) I (E) 3
5 All limelinns I dened on tile .\',i'-p|:1uc such mm
Fig. . :21".
OrvEA +1.1ndojl-u1 f-Il
are given by /(.\._I') =
(A) x: + xy + y- + C

PIER 6 REVIEW QUESTBONS
Complete the following review questions using the techniques outlined in this chapter.
Chapter 8 for answers and explanations
1. There is only one integer, at, between 100 and 200 such that integer pair (x, y) satises the 39
42x +

4
. For x g 0. i I
d): cfw_XL V 53) z
(A) scener
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exl J
6 Which of the cfw_Oilowing couid be the graph of cfw_he derivative of the
Function whose graph is shown in the gure a

CHAPTER I REVIEW QUESTIONS
Complete the following review questions using the techniques outlined in this chapter Then, see Chapter
8 for answers and explanations.
1. Find the sum of the roots of the equation \/x l + \l2x 1 = x.
(A). 1 . (B) 2 (C) 4 (D) 5

Last Name:
Sample Test
1. Define linear operator S and T on the xy-plane R2 as follows: S rotates each vector
by 90 degrees counterclockwise, and T reflects each vector through the y-axis. If ST
and T S denote the compositions S T and T S, respectively, a

CHAPTER 7 REVIEW QUESTIONS
Complete the following review questions using the techniques outlined in this chapter. Then, see
Chapter 8 for answers and explanations.
1. For which of the following intervals does P(x) = 4x3 4x2 ~ 337: + 45 have a zero?
(A) [-

Federal Public Service Commission (FPSC)
Recruitment for the post of Mathematics Lecturer test BS-17
Sample Questions Mathematics
1. (1 i)10 ?
(A) 2 i
(B) 16 i
(C) 32 i
(D) 4+2 i -32
(E) 4+2 i +32
2. Find the number whose 70% is 70?
(A) 1
(B) 10
(C) 70
(D

CHAPTER 3 REVIEW QUESTIONS
Complete the following review questions using the techniques outlined in this chapter. Then, see
Chapter 8 for answers and explanations.
1. Find the angle between the diagonals of the back and left faces of the cube shown below:

The following sample questions are for:
FPSC Mathematics Lecturer test
Armed Forces Mathematics Lecturer test
Mphill Mathematics, admission test
GAT Mathematics & GRE Mathematics
Sample Questions (31-40) Mathematics
x2
31. If F ( x) e t dt for all pos

CHAPTER 5 REVIEW QUESTIONS
Complete the following review questions using the techniques outlined in this chapter.'Then
Chapter 8 for answers and explanations.
1. Two distinct solutions, x1 and x2, can be found to the linear system Ax = b. Which of the toi

CHAPTER 2 REVIEW GUES'i'IONS
Complete the following review questions using the techniques outlined in this chapter. Then, see Chapter 8
for answers and explanations.
1. Consider the sequence (x) whose terms are given by the formula
x = (cos nrc)(sin2 n)
f

CHAPTER 4 REVIEW QUESTIONS-
Complete the following review questions using the techniques outlined in this chapter. Then see Chapte
for answers and explanations.
1. Lett y- f (x) be the solution of the equation
y: _ x
dx x2 + 1
such that y = 0 when x = 0.

6,. For what vaiue of b is the value of I; (x2 + .x) dx a minimum?
(A) 0 (B) 3 (C) 2 (D) 3 (E) ~4
WWWWWW
7 In how many of the eight standard octants of xyzmspace does the graph of z = ex+y appear?
(A) One (B) Two (C) Three (D) Four (E) Eight
8" Suppose