SEAMO 2018 Paper E © TCIMO 1 1 Arrange the 3 numbers in ascending order 4"#$, 6$#(, 5*#+ (A) 6$#( < 5*#+ < 4"#$ (B) 6$#( < 4"#$ < 5*#+ (C) 5*#+ < 4"#$ < 6$#( (D) 5*#+ < 6$#( < 4"#$ (E) None of the abo[.]
Trang 21 Arrange the 3 numbers in ascending
order
4"#$, 6$#(, 5*#+
(A) 6$#( < 5*#+ < 4"#$
(B) 6$#( < 4"#$ < 5*#+
(C) 5*#+ < 4"#$ < 6$#(
(D) 5*#+ < 6$#( < 4"#$
(E) None of the above
3 Given that -$− 8- + 1 = 0 , find the value of -(+ *
4 5
(A) 6 (B) 8 (C) 3838 (D) 3842 (E) None of the above
4 Find the last 2 digits of
18$8*9 + 18$8*9+ ⋯ + 18$8*9
;<<<<<<<<<=<<<<<<<<<>
9 × *9 @ABC
(A) 76 (B) 68 (C) 32 (D) 24 (E) None of the above
2 The distance from Georgetown to
Greenville is 120 km An SUV and a
sedan left Georgetown for Greenville
at the same time After an hour, the
SUV was 24 km ahead of the sedan If
the sedan arrived at Greenville
25 minutes after the SUV, find the
speed of the sedan
(A) 68 km/h
(B) 72 km/h
(C) 76 km/h
(D) 80 km/h
(E) 84 km/h
QUESTIONS 1 TO 10 ARE WORTH
3 MARKS EACH
Trang 35 Points P and Q are centres of the
circles as shown below Chord AB is
tangent to the circle with centre P
Given that the line PQ is parallel to
chord AB and the length of AB is
24 cm, find the area of the shaded
region
(A) 452 (
I
(B) 454 (
I
(C) 452 "
I
(D) 454 "
I
(E) None of the above
6 Neha added the page numbers of a book from 1, 2, 3, … , K The result was
2018 She then realized one of the numbers was added twice Find the number
(A) 2 (B) 12 (C) 22 (D) 32 (E) None of the above
7 Find 4-digit square number LLMMNNNNNNN where
L ≠ M
(A) 1188 (B) 2299 (C) 5566 (D) 6655 (E) 7744
Trang 48 Goldbach’s Conjecture suggests that
any even number greater than 2 can
be written as the sum of 2 primes
186 can be expressed as the sum of 2
primes What is the greatest possible
product of these 2 primes?
(A) 905
(B) 1153
(C) 8633
(D) 2249
(E) None of the above
10 In trapezium QRST shown below,
QT ∥ RS , QR ⊥ RS , QR = RS and
QW = QT Given that W is a point on QR where ∠RWS = 75°, find ∠TSW
(A) 45°
(B) 50°
(C) 55°
(D) 60°
(E) 65°
9 Evaluate
5
6+
23
24+
59
60+
119
120+
209 210
(A) 4 **
$*
(B) 4 **
$Z
(C) 4 *+
$*
(D) 4 *+
$Z
(E) None of the above
11 Find the remainder when 2$8*9 is divided by 33
(A) 19 (B) 22 (C) 23 (D) 24 (E) 25 QUESTIONS 11 TO 20 ARE WORTH
4 MARKS EACH
Trang 512 Find the value of - in
log1319+ log9591− log57+ log 5 = log -
(A) 5
(B) 6
(C) 7
(D) 8
(E) None of the above
14 A sequence is as shown below:
(1), (2,3), (4, 5, 6), (7, 8, 9, 10), … Find the sum of the numbers in K`a set
(A) K(K$+ 1) (B) b$(K + 1) (C) b$(K$+ 3) (D) b$(K$+ 1) (E) None of the above
13 Q, R, S and T are concyclic QS is the
diameter of the circle and QT = TS
Given that the area of QRST is 20 cm$,
find the length of TW
(A) 2√3
(B) 3√3
(C) 2√5
(D) 3√5
(E) None of the above
15 It is known that L + 2M + e = 4 for
L, M, e ∈ g Find the maximum value of
LM + Me + eL
(A) 2 (B) 4 (C) 6 (D) 8 (E) None of the above
16 In ∆QRS, it is known 9L$ + 9M$ = 19e$ Find ij` k
ij` lmij` n
(A) 1 7 (B) 3 7 (C) 5
Trang 617 There is 11o of alcohol in Barrel Q and
15o of water in Barrel R At first,
some alcohol from Q is poured to R
Then, some mixture from R is poured
back into Q The alcohol content in Q
and R finally becomes 62.5% and
25%, respectively How many litres of
mixture was poured from R to Q?
(A) 6o
(B) 6.2o
(C) 7o
(D) 7.3o
(E) None of the above
19 Two fair dice are thrown The probability that the difference between the numbers obtained is
i 2 is $
#
ii 3 is *
+
iii at least 2 is *
"
iv at most 4 is I
#
Which of the above statements is/are true?
(A) i and ii (B) i and iii (C) ii and iii (D) iii and iv (E) All of the above
18 How many real solutions has the
following system of equations?
- + r = 2
-r − s$ = 1
(A) 2
(B) 3
(C) 4
(D) 5
(E) None of the above
20 If 3-$+ - = 1, find the value of 6-"− -$− 3- + 2018
(A) 2016 (B) 2017 (C) 2018 (D) 2019 (E) None of the above
Trang 7
21 The areas of ranches 1, 2 and 3 are
313 , 10 and 24 acres, respectively,
where grass grows at constant rates
The 1t` ranch can sustain 12 oxen for
4 weeks The 2uv ranch can sustain
21 oxen for 9 weeks For how many
weeks will the 3rd ranch sustain 36
oxen?
24 QRST is a parallelogram where
wx ∥ QT and Wy ∥ QR Given that the area of TWzx is 9 e{$ and the area of Rwzy is 15 e{$, find the area of ∆QzS
22 It is known that
log|(LM) = - What is log}(LM) when expressed in
terms of -?
25 Suppose L, M, e, ~ and are consecutive positive integers and L < M < e < ~ < ,
M + e + ~ is a perfect square and
L + M + e + ~ + is a cubic number Find the smallest value of e
23 It is given
LM
L + M= 2;
Le
L + e= 5;
Me
M + e = 4,
Find the value of L + M + e
QUESTIONS 21 TO 25 ARE WORTH
6 MARKS EACH
Trang 8SEAMO 2018
Paper E – 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
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