Download [PDF] APMOPS (SMOPS) 2012 Round 1 Questions with Answers Mathematical Olympiad

File Information

Filename:	[PDF] APMOPS (SMOPS) 2012 Round 1 Questions with Answers Mathematical Olympiad.pdf
Filesize:	302.45 KB
Uploaded:	24/08/2021 00:23:20
Keywords:	apmops smops 2012 round 1 questions with answers mathematical olympiad pdf
Description:	Download file or read online APMOPS-SMOPS past exam paper 2012 First Round Questions with Answers - The Asia Pacific Mathematical Olympiad for Primary Schools - Singapore Pacific Mathematical Olympiad for Primary Schools.
Downloads:	8

File Preview

Download Urls

Short Page Link

https://www.edufilestorage.com/6f3

Full Page Link

https://www.edufilestorage.com/6f3/PDF_APMOPS_(SMOPS)_2012_Round_1_Questions_with_Answers_Mathematical_Olympiad.pdf

HTML Code

<a href="https://www.edufilestorage.com/6f3/PDF_APMOPS_(SMOPS)_2012_Round_1_Questions_with_Answers_Mathematical_Olympiad.pdf" target="_blank" title="Download from eduFileStorage.com"><img src="https://www.edufilestorage.com/cache/plugins/filepreviewer/3997/pdf/150x190_middle_46f4e7862b1eb5bd4935adbbba5d79e8.jpg"/></a>

Forum Code

[url=https://www.edufilestorage.com/6f3/PDF_APMOPS_(SMOPS)_2012_Round_1_Questions_with_Answers_Mathematical_Olympiad.pdf][img]https://www.edufilestorage.com/cache/plugins/filepreviewer/3997/pdf/150x190_middle_46f4e7862b1eb5bd4935adbbba5d79e8.jpg[/img][/url]

[PDF] APMOPS (SMOPS) 2012 Round 1 Questions with Answers Mathematical Olympiad.pdf | Plain Text

Hwa Chong Institution SMOPS 14 th April 2012 Page 1 Asia Pacific Mathematical Olympiad for Primary Schools 2012 First Round 2 hours (150 marks) 1. Find the value of 29999 + 2999 + 299 + 29 + 9. (SMOPS 2012 Q.1) 2. ABCD is a parallelogram. P, Q, R and S are the midpoints of the 4 sides of the parallelogram. If the area of the shaded region is 20cm 2, find the area of the parallelogram ABCD . (SMOPS 2012 Q.2) 3. Jane added up all the digits of the whole number 3 × 3 × 3 × … 3 ⏟ ������� ������� 2012 ������� 3′� and obtained a new number n1. She then added up all the digits of n 1 and obtained another number n2. She continued doing this until she obtained a single digit number. Find the value of this number. (SMOPS 2012 Q.3) 4. The diagram shows 3 circles. The circumference of the smallest circle passes through the centre of the middle circle and the circumferenc e of the middle circle passes through the centre of the largest circle. Find the ratio of the shaded area to the unshaded area. (SMOPS 2012 Q.4) A Q C D P B R S

Hwa Chong Institution SMOPS 14 th April 2012 Page 2 5. The product of 4 consecutive whole numbers is 5040. Find the value of the smallest number. (SMOPS 2012 Q.5) 6. The diagram shows 3 circles with centres P, Q and R respectively. Each circle has a point of contact with the other circles. If PQ = 35cm, QR = 36cm, and PR = 37cm, find the radius of the circle with centre R. (SMOPS 2012 Q.6) 7. 12! i s equal to (1) 479001600 (2) 479000610 (3) 479000160 (4) 479000061 (5) 479000016 [Note: n! = ( n) × (n−1)× (n−2)× ... × 3 × 2 × 1, for example 5! = 5 × 4 × 3 × 2 × 1.] (SMOPS 2012 Q.7) 8. Only 1 of the 3 boys Abel, Ben and Cain can swim. Abel says, “I can swim.” Ben says, “I cannot swim.” Cain says, “Abel cannot swim.” Only 1 boy is telling the truth. Who can swim? (SMOPS 2012 Q.8) 9. 10 boys received their test papers. The test paper has a maximum score of 10. Each boy added the scores of the other 9 boys. If the 10 totals obtained are 66, 66, 67, 67, 68, 68, 69, 70, 71 and 72, find the lowest score. (SMOPS 2012 Q.9) 10. In the diagram, D and E are the mid -points of AB and AC respectively. BE cuts CD at F. If the area of the 4 -sided figure ADFE is 256cm 2, find the area of the triangle ABE . (SMOPS 2012 Q.10 ) P Q R A B C D E F

Hwa Chong Institution SMOPS 14 th April 2012 Page 3 11. A circle with centre O passes through points A and B as shown. If the circle has a radius of 5 cm and angle AOB is 120° , find the radius of another circle that passes through points O, A and B. (SMOPS 2012 Q.11 ) 12. A line can divide a plane into a maximum of 2 regions. 2 lines can divide a plane into a maximum of 4 regions. Find the number of regions that 5 lines can divide a plane into. (SMOPS 2012 Q.12 ) 13. Find the value of 1 1+1 2+2 2+1 3+2 3+3 3+1 4+2 4+3 4+4 4+⋯ + 1 100 + 2 100 + 3 100 +⋯ + 98 100 + 99 100 +100 100 . (SMOPS 2012 Q.13 ) 14. Trains A and B are travelling towards each other at 48 km/h. In train A, Jane notices that it takes 6 seconds for train B to pass her. Find the length of train B in m etres . (SMOPS 2012 Q.14 ) 15. Find the largest whole number smaller than 1 1 101 + 1 102 +⋯+ 1 109 + 1 110 (SMOPS 2012 Q.15 ) 16. Find the largest whole number k such that 12 × 12 × 12 ⋯ × 12 ⏟ 50 > ������× ������× ������⋯ × ������ ⏟ 75 . (SMOPS 2012 Q.16 ) 17. Jane was given a sum of money for her 10 day trip. At the end of day 1, she spent 1 10 of the money. At the end of day 2, she spent 1 9 of the remaining sum. At the end of day 3, she spent 1 8⋯ . At the end of day 9, she spent 1 2 of the remaining sum and has $99 left. How much money did she have at the beginning? (SMOPS 2012 Q.17 ) A B O

Hwa Chong Institution SMOPS 14 th April 2012 Page 4 18. 4 classes, A, B, C and D each has less than 50 students and the average number of students is 46. Class A and class B differ in number of students by 4, class B and class C by 3, and class C and class D by 2. If class A has the most numbers of students, find the number of student s in A. (SMOPS 2012 Q.18 ) 19. The diagram shows a figure comprising 4 regions. 4 different colours are used at most to colour the figure such that each region is coloured by only 1 colour and regions adjacent to each other cannot have the same colour. Find t he number of different ways to colour the figure. (SMOPS 2012 Q.19 ) 20. The figure consists of 3 squares and a triangle. Find the sum of angles x, y and z in degrees. (SMOPS 2012 Q.20 ) 21. In the diagram, AD = 6 cm, BC = 2cm, angle ABC = angle ADC = 90 ° and angle BCD = 135 °. Find the area of the 4 -sided figure ABCD in cm 2. (SMOPS 2012 Q.21 ) 22. A bus was scheduled to travel from Town A to Town B at a constant speed of x km/h. If the speed of the bus increased by 20%, it could arrive at Town B two hours ahead of schedule. If the bus travelled the first 240 km at x km/h and then the speed decreased to 80%, it could arrive at Town B two hours behind schedule. Find the dista nce, in km, between the 2 towns. (SMOPS 2012 Q.22 ) A B C D

Hwa Chong Institution SMOPS 14 th April 2012 Page 5 23. In how many ways can we shade d exactly 2 of the 9 squares such that the 2 squares have no sides in common? (SMOPS 2012 Q.23 ) 24. Jane has an alarm clock that is slower by 5 minutes for every actual hour. One night, Jane reset the clock correctly at 2100 . If she wanted the alarm clock to ring at 0700 (the actual time) the following morning, what is the time she should set for the clock t o ring? [2100 denotes 9 p.m., 0700 denotes 7 a.m.] (SMOPS 2012 Q.24 ) 25. A particular month has 5 Tuesdays. The first and the last day of the month are not Tuesdays. The last day of the month is a __________. (SMOPS 2012 Q.25 ) 26. Find the value of (1−1 2−1 3−⋯− 1 2011 )×(1 2+1 3+⋯+ 1 2011 + 1 2012 )−(1−1 2−1 3−⋯− 1 2011 − 1 2012 )×(1 2+1 3+⋯+ 1 2011 ) (SMOPS 2012 Q.26 ) 27. A cross shaped figure comprising 5 identical squares is cut into 3 prices A, B and C by 2 straight cuts as indicated by the dotted lines. A, B and C can be rearranged to form a rectangle as shown. If the length of the rectangle is 12 cm, find the width of the rectangle in cm. (SMOPS 2012 Q.27) 28. David wants to go from level 2 to level 1 in a shopping centre. If he walks down 14 steps while taking the escalator, he can move from the top to the bottom of the escalator in 30 seconds. If he walks down 28 steps, he can do the same in 20 seconds. Find the number of steps of the escalator. (SMOPS 2012 Q.28 ) A B C A B C Rectangle

Hwa Chong Institution SMOPS 14 th April 2012 Page 6 29. ABE and BCD are right -angled triangles. D lies on BE such that AE = ED = DC = 1 cm and DB = 2 cm. Find the value of angle ABC in degrees. (SMOPS 2012 Q.29 ) 30. A 6 -digit number ������̅̅̅̅̅̅̅̅̅̅ is such that ������̅̅̅̅̅̅̅̅̅̅ L x H =>?@AB $ $ $ $ $ $ $ $ $ $. Find the 6-digit number ������̅̅̅̅̅̅̅̅̅̅. (SMOPS 2012 Q.30 ) Number of correct answers for Q1 to Q10 : _______ Marks ( ×4 ) : _______ Number of correct answers for Q11 to Q20 : _______ Marks ( ×5 ) : _______ Number of correct answers for Q21 to Q30 : _______ Marks ( ×6 ) : _______ Answers: SMOPS 2012 1 33335 11 5 21 16 2 100 12 16 22 720 3 9 13 2575 23 24 4 13:3 14 160 24 0610 5 7 15 10 25 Wed 6 19 16 5 26 7 (1) 17 990 27 6 8 Ben 18 48 28 56 9 4 19 108 29 45 10 384 20 360 30 142857 A B C D E 1 2012