Olympiad

OlympiadMaths Trainer 6 CONTENTS Week 1 to Week 10 Think Algebra Venn Diagram Whole Numbers Fractions Permutation and Combination Speed I: Catching Up Week 11 to Week 20 Speed II: Encountering Solve By Comparison and Replacement Divisibility Solve Using Table or Drawing Cryptarithm Observation and Induction Week 21 Test 1 Week 22 to Week 31 Age Problems Percentage Ratio Area and Perimeter of Circles Rate Mathematics of Time Week 32 to Week 41 Comparison of Fractions Pigeonhole Principle Number Pattern Logic Number Theory Maxima Week 42 Test 2 Worked Solutions (Week 1 - Week 42) 28 of them like Science. 10 students like both Science and Mathematics. (a) y = 3x 8x – 2y = 8 (b) 4x + 5y = 23 9x – 5y = 3 (c) y = 5x 3x + 2y = 65 (d) 2x + 5y = 23 6x – 5y = 9 2.. 41 like Mathematics and 20 like English. How many students like all the three subjects? 3. 12 students like both Science and English. Each question carries 4 marks. Solve for the values of x and y in each of the following. × 2007 × 2009 Olympiad Maths Trainer 6 ©Terry Chew and SAP Group Pte Ltd WEEK 1 page 1 . 24 of them like both Mathematics and English. given that x and y are whole numbers. 1. Show your working clearly. What is the value of the digit in the ones place of the following? 1 × 3 × 5 × 7 × 9 × 11 × 13 × . Among 64 students.Olympiad Maths Trainer 6 WEEK 1 /24 Name: Class: Date: Marks: Solve these questions.. (a) 4 P3 (b) 5 P4 (c) 8 C2 (d) 12 C3 6. If they start running at the same time but in the same direction. A B If Jonathan and Cindy run towards each other at the same time from Point A and Point B respectively. it will take Jonathan 280 seconds to catch up with Cindy. 1+2+3+4+5+6+7+6+5+4+3+2+1 Evaluate __________________________________________________. Evaluate each of the following. What is the ratio of their speeds? Olympiad Maths Trainer 6 ©Terry Chew and SAP Group Pte Ltd WEEK 1 page 2 . it will take them 40 seconds before they meet. as shown below.4. Jonathan and Cindy run on a circular track where AB is the diameter of the track. 7777777 × 7777777 5. The sum of the digits of a 3-digit number is 18. If the hundreds digit and the ones digits are swapped. 1. The tens digit is 1 more than the ones digit. the difference between the new number and the original number is 396. how many numbers are multiples of 5 or 7? 3. What is the original number? Olympiad Maths Trainer 6 ©Terry Chew and SAP Group Pte Ltd WEEK 2 page 1 . Given that a and b are whole numbers. Between 1 and 2009. Show your working clearly.Olympiad Maths Trainer 6 WEEK 2 /24 Name: Class: Date: Marks: Solve these questions. (a) 2a + 3b = 18 (b) 4a + 6b = 68 (c) 4a + 7b = 73 (d) 3a + 8b = 47 2. solve for a and b in each of the following. Each question carries 4 marks. 1 1 1 1 1 1 1 1 1 1 Evaluate 1 + __ + __ × __ + __ + __ – 1 + __ + __ + __ × __ + __ using a 5 5 7 5 7 5 3 3 3 3 simple method. What was the average speed of the car for the whole journey? Olympiad Maths Trainer 6 ©Terry Chew and SAP Group Pte Ltd WEEK 2 page 2 . ( ) ( ) ( ) ( ) 5. (a) Choose any three letters from a. In how many ways can we arrange the three letters? (b) A teacher wants to choose a captain and vice-captain among 12 volleyball players. In how many ways can he do so? 6. c. b. A car travelled to Town B from Town A at a constant speed of 72 km/h. It then returned from Town B to Town A at a constant speed of 48 km/h. and d.4. ABCD is a rectangle. Each question carries 4 marks. In the figure below. E and F are midpoints of AD and DC respectively. Lucas multiplies his month of birth by 31.Olympiad Maths Trainer 6 WEEK 3 /24 Name: Class: Date: Marks: Solve these questions. A 70 cm2 25 cm2 E G F J 20 cm2 C H 80 cm2 55 cm2 D B 3. Show your working clearly. Find the value of the following. Find the area of the shaded region. 1. 20082009 × 20092008 – 20082008 × 20092009 Olympiad Maths Trainer 6 ©Terry Chew and SAP Group Pte Ltd WEEK 3 page 1 . When is his birthday? 2. The sum of the two products is 213. He then multiplies his day of birth by 12. 00 pm.00 pm? Olympiad Maths Trainer 6 ©Terry Chew and SAP Group Pte Ltd WEEK 3 page 2 .00 pm. A car will travel from Town A to Town B. 3 1 2 1 1 4 Evaluate 29__ × __ + 39__ × __ × 49__ × __. it will arrive at 1. How many 3-digit numbers have the sum of the three digits equals to 4? 6. 5 4 4 2 3 3 5. If it travels at a constant speed of 80 km/h.4. If it travels at a constant speed of 60 km/h. it will arrive at 3. At what speed should it be travelling if the driver aims to arrive at Town B at 2.