SEAMO 2018 Paper D © TCIMO 1 1 Find the last 2 digits in the sum 1 + 2 + 3 + 4 +⋯+ 2017 + 2018 (A) 75 (B) 71 (C) 56 (D) 63 (E) None of the above 4 Find the value of g in (A) 9 (B) 5 (C) 7 (D) 4 (E) No[.]
Trang 21 Find the last 2 digits in the sum
1 + 2 + 3 + 4 + ⋯ + 2017 + 2018
(A) 75
(B) 71
(C) 56
(D) 63
(E) None of the above
4 Find the value of g in
(A) 9 (B) 5 (C) 7 (D) 4 (E) None of the above
2 It is now 3:15 PM After how many
minutes will the minute-hand form an
angle of 30° with the hour-hand?
(A) 5 9
11
(B) 5 3
11
(C) 6 9
11
(D) 6 9
12
(E) None of the above
5 It is known that is a prime number
If /+ 2 is also a prime number, find
(A) 2 (B) 3 (C) 5 (D) 7 (E) None of the above
6 Find the number of digits in 4//× 512 (A) 22
(B) 23 (C) 40 (D) 42 (E) None of the above
3 When (45− 4) is divided by 5, where
4 ∈ ℤ:, the remainder is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
QUESTIONS 1 TO 10 ARE WORTH
3 MARKS EACH
Trang 37 There are 7 black, 5 white and
4 orange balls in a bag Four balls are
drawn without replacement Find the
probability that at least 3 balls are
white
(A) 23
362
(B) 1
18
(C) 23
363
(D) 1
19
(E) None of the above
9 Find the positive integral solution of
1
;+
1
<+
1
==
5 6
(A) (2 , 4 , 12) (B) (2 , 6 , 6) (C) (3 , 3 , 6) (D) (3 , 4 , 4) (E) All of the above
10 Today is Saturday What day is it 3100
days later?
(A) Sunday (B) Monday (C) Tuesday (D) Wednesday (E) None of the above
8 Given that the area of ∆BCD is 1 and
EF
GF =GH
HI =JI
IF = K / , what is the area
of ∆LMN?
(A) 7
75
(B) 8
75
(C) 8
27
(D) 1
3
(E) 219
11 If O − P = 3 and O/+ P/ = 5 , then the value of K
Q−K
R is
(A) 1 2 (B) 1
(C) 3 2 (D) 2 (E) None of the above
QUESTIONS 11 TO 20 ARE WORTH
4 MARKS EACH
Trang 412 15 countries took part in The World
Cup Each team played exactly 2
matches The winner scored 3 points
and the loser scored 0 points Each
team got 1 point for a draw How
many more points at most did the
champion score than the runner up?
(A) 48
(B) 51
(C) 53
(D) 56
(E) 59
15 It is known that S is a positive integer such that S × 874 is a 5-digit number ending with 92 Possible value(s) of S is/are
i 48 ii 58 iii 68 iv 108
(A) i only (B) ii only (C) i and iii (D) ii and iv (E) i, ii and iii
16 In the figure below, BCDL is a rectangle E and F are mid-points of
AD and CE, respectively If the area of
∆CLN is 7.5 cm2, find (in cm2) the area of rectangle BCDL
(A) 45 (B) 56 (C) 58 (D) 60 (E) None of the above
13 It is known that S, 4 and are
positive integers, where S < 4 <
If 2U+ 2V+ 2W = 2336, find the value
of S
(A) 4
(B) 5
(C) 6
(D) 7
(E) Unable to determine
14 How many odd digits are there in the
result of 1 111 111 111 × 9 999 999 999?
(A) 10
(B) 11
(C) 8
(D) 9
(E) None of the above
Trang 517 /
X of the journey from Lethbridge to
Medicine Hat is highway, while the
remaining K
X is country road
Connecting the highway to the
country road is the town of St Paul
A van left Lethbridge for Medicine
Hat, travelling at 100 km/h on
highway and 60 km/h on country
road A car left Medicine Hat for
Lethbridge, travelling at 70 km/h on
country road and 110 km/h on
highway The car and the van passed
each other 44 km away from
St Paul Find, in km, the distance
from Lethbridge to Medicine Hat
(A) 248
(B) 339
(C) 441
(D) 453
(E) None of the above
19 The chord AB, common to the circles with centres m and n, has length 2√3
It forms 1 side of an equilateral triangle in circle m and 1 side of a right hexagon in circle n Find the ratio of the areas of both circles
(A) 1 ∶ √3 (B) 3 ∶ 2√3 (C) 1 ∶ 3 (D) √3 ∶ 4 (E) None of the above
18 Let 4 be a positive integer such that
4/+ 154 + 36 is a perfect square Find
the value of 4
(A) 13
(B) 14
(C) 15
(D) 16
(E) None of the above
Trang 620 Starting from any letter ‘M’ below,
the word MADAM can be spelled by
moving up, down, left or right to an
adjacent letter How many ways are
there to spell MADAM?
(A) 90
(B) 120
(C) 144
(D) 169
(E) None of the above
22 It is known that 4 is a 10-digit number of the form 2017;2018<[[[[[[[[[[[[[[[[[ , where ; and < can be any integer 0 to
9 How many such numbers 4 are there that are divisible by 33?
23 It is known that O , P and \ are constants and
when ; = 1,
;X+ O;/+ P; + \ = 1
when ; = 2,
;X+ O;/+ P; + \ = 2
when ; = 8,
;X+ O;/+ P; + \ = ]
when ; = −5,
;X + O;/+ P; + \ = ^
Find (] − ^)
21 It is known that
^V:K= 1
1 +^1 V for 4 = 1, 2, 3, 4, … , 2017, 2018
Evaluate
^K^/ + ^/^X+ ^X^1+ ⋯ + ^/2K`^/2Ka
where ^K = 1
24 Given that (; − 3) is a positive integer and a factor of 3;/− 2; + 9, find the sum of all possible values of ;
QUESTIONS 21 TO 25 ARE WORTH
6 MARKS EACH
Trang 725 It is known that circles with centres
bK and b/ are tangent at point M
AB and CD are external tangents to
both the circles
Given that b/M ⊥ bKB , ∠BbKD = 120°
and b/C = 1 \S, find the area of the
shaded region
Leave your answer in terms of e
End of Paper
Trang 8SEAMO 2018
Paper D – Answers Multiple-Choice Questions
Questions 1 to 10 carry 3 marks each
Questions 11 to 20 carry 4 marks each
Free-Response Questions
Questions 21 to 25 carry 6 marks each
2017
6 +