MATHEMATICS ADMISSIONS TEST
For candidates applying for Mathematics, Computer Science or one of their
joint degrees at OXFORD UNIVERSITY and/or IMPERIAL COLLEGE LONDON
and/or UNIVERSITY OF WARWICK
November 2021
Time Allowed: 2½ hours
Please complete the following details in BLOCK CAPITALS. You must use a pen.
Surname
Other names
Candidate Number M
This paper contains 7 questions of which you should attempt 5. There are directions
throughout the paper as to which questions are appropriate for your course.
A: Oxford Applicants: if you are applying to Oxford for the degree course:
• Mathematics or Mathematics & Philosophy or Mathematics & Statistics, you should
attempt Questions 1,2,3,4,5.
• Mathematics & Computer Science, you should attempt Questions 1,2,3,5,6.
• Computer Science or Computer Science & Philosophy, you should attempt 1,2,5,6,7.
Directions under A take priority over any directions in B which are relevant to you.
B: Imperial or Warwick Applicants: if you are applying to the University of Warwick for
Mathematics BSc, Master of Mathematics, or if you are applying to Imperial College for any
of the Mathematics courses: Mathematics, Mathematics (Pure Mathematics), Mathematics
with a Year Abroad, Mathematics with Applied Mathematics/Mathematical Physics,
Mathematics with Mathematical Computation, Mathematics with Statistics, Mathematics with
Statistics for Finance, you should attempt Questions 1,2,3,4,5.
Further credit cannot be obtained by attempting extra questions. Calculators are not
permitted.
Question 1 is a multiple choice question with ten parts. Marks are given solely for correct
answers but any rough working should be shown in the space between parts. Answer
Question 1 on the grid on Page 2. Each part is worth 4 marks.
Answers to questions 2-7 should be written in the space provided, continuing on to the blank
pages at the end of this booklet if necessary. Each of Questions 2-7 is worth 15 marks.
_________________________________________________________________________
FOR OFFICE Q1 Q2 Q3 Q4 Q5 Q6 Q7
USE ONLY
,1. For ALL APPLICANTS.
For each part of the question on pages 3-7 you will be given five possible answers, just
one of which is correct. Indicate for each part A-J which answer (a), (b), (c), (d), or
!
(e) you think is correct with a tick ( ) in the corresponding column in the table below.
Please show any rough working in the space provided between the parts.
(a) (b) (c) (d) (e)
A
B
C
D
E
F
G
H
I
J
2
,A. A regular dodecagon is a 12-sided polygon with all sides the same length and all
internal angles equal. If I construct a regular dodecagon by connecting 12 equally-spaced
points on a circle of radius 1, then the area of this polygon is
√ √ √ √
(a) 6 + 3 3, (b) 2 2, (c) 3 2, (d) 3 3, (e) 3.
B. The positive number a satisfies
a
√
x + x2 dx = 5
0
if
√ 1/3 √
(a) a= 21 − 1 , (b) a = 3, (c) a = 32/3 ,
√ 2/3
(d) a = ( 6 − 1) , (e) a = 52/3 .
Turn over
3
, C. Tangents to y = ex are drawn at (p, ep ) and (q, eq ). These tangents cross the x-axis
at a and b respectively. It follows that, for all p and q,
(a) pa = qb,
(b) p − a < q − b,
(c) p − a = q − b,
(d) p − a > q − b,
(e) p + q = a + b.
D. The area of the region bounded by the curve y = ex , the curve y = 1 − ex , and the
y-axis equals
(a) 0, (b) 1 − ln 2, (c) 12 − 12 ln 2,
(d) ln 2 − 1, (e) 1 − ln 12 .
[Note that ln x is alternative notation for loge x.]
4
For candidates applying for Mathematics, Computer Science or one of their
joint degrees at OXFORD UNIVERSITY and/or IMPERIAL COLLEGE LONDON
and/or UNIVERSITY OF WARWICK
November 2021
Time Allowed: 2½ hours
Please complete the following details in BLOCK CAPITALS. You must use a pen.
Surname
Other names
Candidate Number M
This paper contains 7 questions of which you should attempt 5. There are directions
throughout the paper as to which questions are appropriate for your course.
A: Oxford Applicants: if you are applying to Oxford for the degree course:
• Mathematics or Mathematics & Philosophy or Mathematics & Statistics, you should
attempt Questions 1,2,3,4,5.
• Mathematics & Computer Science, you should attempt Questions 1,2,3,5,6.
• Computer Science or Computer Science & Philosophy, you should attempt 1,2,5,6,7.
Directions under A take priority over any directions in B which are relevant to you.
B: Imperial or Warwick Applicants: if you are applying to the University of Warwick for
Mathematics BSc, Master of Mathematics, or if you are applying to Imperial College for any
of the Mathematics courses: Mathematics, Mathematics (Pure Mathematics), Mathematics
with a Year Abroad, Mathematics with Applied Mathematics/Mathematical Physics,
Mathematics with Mathematical Computation, Mathematics with Statistics, Mathematics with
Statistics for Finance, you should attempt Questions 1,2,3,4,5.
Further credit cannot be obtained by attempting extra questions. Calculators are not
permitted.
Question 1 is a multiple choice question with ten parts. Marks are given solely for correct
answers but any rough working should be shown in the space between parts. Answer
Question 1 on the grid on Page 2. Each part is worth 4 marks.
Answers to questions 2-7 should be written in the space provided, continuing on to the blank
pages at the end of this booklet if necessary. Each of Questions 2-7 is worth 15 marks.
_________________________________________________________________________
FOR OFFICE Q1 Q2 Q3 Q4 Q5 Q6 Q7
USE ONLY
,1. For ALL APPLICANTS.
For each part of the question on pages 3-7 you will be given five possible answers, just
one of which is correct. Indicate for each part A-J which answer (a), (b), (c), (d), or
!
(e) you think is correct with a tick ( ) in the corresponding column in the table below.
Please show any rough working in the space provided between the parts.
(a) (b) (c) (d) (e)
A
B
C
D
E
F
G
H
I
J
2
,A. A regular dodecagon is a 12-sided polygon with all sides the same length and all
internal angles equal. If I construct a regular dodecagon by connecting 12 equally-spaced
points on a circle of radius 1, then the area of this polygon is
√ √ √ √
(a) 6 + 3 3, (b) 2 2, (c) 3 2, (d) 3 3, (e) 3.
B. The positive number a satisfies
a
√
x + x2 dx = 5
0
if
√ 1/3 √
(a) a= 21 − 1 , (b) a = 3, (c) a = 32/3 ,
√ 2/3
(d) a = ( 6 − 1) , (e) a = 52/3 .
Turn over
3
, C. Tangents to y = ex are drawn at (p, ep ) and (q, eq ). These tangents cross the x-axis
at a and b respectively. It follows that, for all p and q,
(a) pa = qb,
(b) p − a < q − b,
(c) p − a = q − b,
(d) p − a > q − b,
(e) p + q = a + b.
D. The area of the region bounded by the curve y = ex , the curve y = 1 − ex , and the
y-axis equals
(a) 0, (b) 1 − ln 2, (c) 12 − 12 ln 2,
(d) ln 2 − 1, (e) 1 − ln 12 .
[Note that ln x is alternative notation for loge x.]
4
