Sách đánh thức tài năng toán học 3 gồm hai phần: Hướng dẫn tư duy và luyện tập Nội dung kiến thức có chiều sâu,được sắp xếp xuyên suốt với mức độ luyện tập tăng dần giúp trẻ dễ học tập và rèn luyện. Gồm nhiều dạng toán rèn luyện tư duy logic và khả năng phân tích, tổng hợp 60% kiến thức bộ sách tương đồng chương trình giáo dục của Việt Nam. 30% là các dạng toán tư duy logic, thực tế… rèn luyện trí thông minh, khả năng tư duy sáng tạo, phân tích tổng hợp. 10% còn lại là nội dung kiến thức đặc trưng Singapore.
Trang 1MATHS OLYMPIAD- UNLEASH THE MATHS OLYMPIAN IN YOU! (INTERMEDIATE)
Fir s t E dition 2015
© Singapore Asia Publishers Pte Ltd
Publi s h e d and Distributed by:
Singapot·e Asia Publishers Pte Ltd
ALL RIGHTS RESERVED
All rights reserved No part of this publication may be reproduced, stored in a retrieval s y stem , or transmitted
in any form or by any means, electronic , mechanical, photocopying , recording or otherwise, without the
prior permission of the publishers
ISBN-13 978-9 8 1-4672-14-6
ISBN-I 0 981-4672 -14 -9
Print e d in Singapore
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A Word by the Author
Russian mathematicians ha ve suggested that mathematics is the gymnasium of the brains Likewise,
in China, Mathematics Olympiad is ferociously practised by the large student population, all for a coveted place in one of the elite high schools
Children who exhibit certain traits and penchant for numbers at the age of 5 or 6 ye _ ars old, or even earlier, have great potential to be the mathematical olympians among their peers - provided they are groomed via a systematic, rigorous and routinized training
Singapore was ranked 3'd in Mathematics in a recent TIMSS survey, after Hong Kong and Taiwan Notably, China was not among the list of countries surveyed
The most prestigious competition locally is RIPMWC (Raffles Institution Primary Mathematics World Competition) Meant for primary 6 students or younger, the top 50 to 60 or so participants are selected from Round 1 to compete in Round 2 Thereafter, 6 top participants emerge to take part in the world competition for primary school mathematics in Hong Kong Another popular competition, also meant for primary 6 students, is APMOPS (Asia Pacific Mathematical Olympiad for Primary Schools), which is organized by Hwa Chong Institution since 1989 The following awards are being given at the end of two rounds of competition: Platinum, Gold, Silver and Bronze
At primary 5level, the yearly NMOS (National Mathematical Olympiad of Singapore) competition has also captured the attention of parents since 2006, who eye NUS High as their most preferred high schooL
The first series of books Maths Olympiad: Unleash the Maths Olympian in You! published in 2007 and 2008, has served as an ideal companion to students looking to establish a strong foundation in
Mathematics- be it for PSLE preparation or in hope that they might one day take part in the var ious
local and international competitions The books are, therefore, also first-choice materials for parents
of primary 3 students looking for quality content in gifted programme training
In this new edition yo u will find the following additions:
Fraction
• Ratio Percentage Angles and Triangles Enhancements have also been made to the following:
Write Simple Equations Problems from Page Numbers Pigeonhole Principle
Square Numbers and Value of Ones Digits
The objective is to cater to increasingly smarter children who have been exposed to a wide variety of topics Some of these topics, which overlap the local mathematics syllabus, have also been adopted
by schools here for students to practice on
I feel extremely privileged and honoured to be able to continue serving students in this field My latest series Wicked Mathematics! is currently out on shelves
For related courses and workshops, please visit www.terrychew.org
Terry Chew (2015)
Trang 42 Compute the following
Trang 55 Compute the following (g) 64 X 25 X 125 X 16 (h) 16 000 -7-25
Trang 68 Use a simple method to compute the following 9 Use a simple method to compute the following
(a) 89 X 11 + 11 X 11 (b) 29 X 8 + 42 X 4 (a) 35 X 128-28 X 35 (b) 46 X 234-134 X 46
(C) 58 X 8 + 84 X 4 (d) 58 X 30 + 84 X 15 (C) 287 X 12- 187 X 12 (d) 897 X 30-297 X 30
(e) 63 X 6 + 74 X 3 (f) 74 X 6 + 152 X 3 (e) 69 X 36-38 X 18 (f) 74 X 54-48 X 27
(g) 44 X 4 + 78 X 8 (h) 56 X 16 + 72 X 32 (g) 132 X 36- 196 X 12 (h) 156 X 48- 124 X 12
Trang 710 Use a simple method to compute the following
Problems introduced in this chapter are most commonly solved using tables, which can
be tedious at times Instead, we attempt to solve problems of this nature by asking, "If all wefe "
1 A farmer has 36 chickens and rabbits There are 96 legs altogether How many chickens does the farmer have?
Solution:
M ethod 1: Solve by Assuming
If all are chickens, there will be 36 x 2 = 72 legs
96-72 = 24 All the rabbits have been counted as if they are chickens
4-2=2 The difference in the number oflegs between a chicken and a rabbit is 2
24 + 2 = 12 rabbits 36- 12 = 24 chickens
Method 2: Solve by Assuming
If all are rabbits, there will be 36 x 4 = 144legs
144-96 = 48 There will be an extra 48 legs
4-2=2 The difference in the number oflegs between a rabbit and a chicken is 2
48 + 2 = 24 chickens 36-24 = 12 rabbits
The farmer has 24 chickens and 12 rabbits
Trang 8A cashier collected $312 from the sale of 50 tickets An adult ticket cost $8 A child
ticket cost $4 How many tickets of each type did the cashier sell?
Solution:
Method 1: Solve by Assuming
$400-$312 = $88 There would be an extra $88
$8-$4 = $4 The price difference between an adult ticket and a child ticket was $4
50 - 22 = 28 adult tickets
Method 2: Solve by Assuming
$312-$200 = $112 There would be a shortfall of $112
correct answer and 2 marks are deducted for each incorrect answer If Colin scores 122
marks for the mathematics competition, how many incorrect answers does he give?
Solution:
150 -.122 = 28 There is an extra 28 marks
5+2=7 The difference in marks between a correct answer and an incorrect answer
is 7 marks
He gives 4 incorrect answers
more than a volleyball What is the price of a basketball?
$275 -7- 11 = $25
$25 + $10 = $35 The price of a basketball is $35
Mr Brannon has 58 pieces of two-dollar, five-dollar and ten-dollar notes altogether
ten-dollar notes is the same How many notes of different denominations does he have?
Solution:
$348 - $322 = $26 The difference in the total value of all the notes is $26
$6-$5 = $1 The difference in value between a six-dollar note and a five-dollar note
is $1
Trang 9Method 2: Solve by Assuming
If all are five-dollar notes, the total value will be 58 x $5 = $290
$322- $290 = $32
The difference in the total value of all the notes is $32
$6-$5 = $1
$32 + $1 = 32 pieces of two-dollar and ten-dollar notes
32 + 2 = 16 pieces for each two-dollar and ten-dollar notes
58- 32 = 26 pieces of five-dollar notes
He has 16 two-dollar notes, 26 five-dollar notes and 16 ten-dollar notes
1 A farmer has 45 chickens and rabbits There are 140 legs altogether How many chickens does the farmer have? How many rabbits does the farmer have?
2 A spider has 8 legs A dragonfly has 6 legs 28 spiders and dragonflies have 200 legs altogether How many spiders are there? How many dragonflies are there?
3 Andy spent $55 in all to purchase 20 pieces of two-dollar and five-dollar stamps How many two-dollar stamps did he buy? How many five-dollar stamps did he buy?
Trang 104
5
6
There are 40 cars and motorcycles in a park There are 116 wheels altogether How
many cars are there? How many motorcycles are there?
An adult ticket to a concert cost $35 and a concession ticket cost $18 Mr Walter
paid $598 in all for 20 such tickets How many adult tickets did he buy? How many
concession tickets did he buy?
Jeff has 20 pieces of five-dollar and ten-dollar notes in his wallet The total value
of these notes is $125 How many notes of each denomination does he have?
7
8
answer and 1 mark is deducted for every wrong answer Kelly scores 21 marks for the science quiz How many questions does she answer correctly?
There are 30 questions in a mathematics competition 5 marks are awarded for each question answered correctly and 3 marks are deducted for each wrong answer Rena scores 126 marks for the mathematics competition How many questions does she get wrong?
A mathematics quiz consists of30 questions The first 20 questions are worth 4 marks each The last 10 questions are worth 7 marks each No marks will be deducted for each wrong answer Justin scores 124 marks for the mathematics quiz How many
of the first 20 questions and how many of the last 1 0 questions does he answer
wrongly?
Trang 1110 Mr George spent $375 in all for 5 similar tables and 6 similar chairs Each table
cost $20 more than each chair What was the price of a table? What was the price
of a chair?
11 Mr Gretzky spent $390 on 5 similar basketballs and 4 similar volleyballs Each
basketball cost $15 more than each volleyball
What was the price of a basketball and the price qf a volleyball?
12 Wayne has 20 pieces of notes The types of denominations are $2, $5 and $10
The number of $2 notes and $10 notes is the same The total value of these notes
is $110 How many pieces of each denomination does he have?
PRACTICE
~
1 Complete the number patterns
(a) 1, 2, 4, 8, 16, ( ), ( ), (b) 3, 4, 5, 8, 7, 16, 9, 32, ( ), ( ), (c) 0, 3, 8, 15, 24, ( ), ( ), 63, (d) 6, 1, 8, 3, 10, 5, 12, 7, ( ), ( ), (e) 2, 3, 5, ( ), ( ), 17, ( ),
Trang 123 Find the missing numbers
Trang 139 What are the numbers in the eighth group in the pattern below?
Trang 1415 In the number pattern below, the third number is the sum of the first two numbers
The fourth number is the sum of the previous two consecutive numbers and so on
What is the second number?
as me now, I will be 54 years old," replied his mother How old is Tim's mother?
Solution:
8 years old Tim's present age
Mother's present age
54 years old Mother ' s future age
The difference in age between two people remains the same
54-8 = 46 46-7 2 = 23
23 + 8 = 31
Tim's mother is 31 years old
The sum of the ages of three children is 30 The oldest child is twice as old as the second oldest one The youngest child is 10 years younger than the oldest one What is the age of the oldest child?
Solution:
Method 1: Making a Table
Trang 15Method 2: Using Drawings
?
oldest f - - - : _ _ - - - 1 second oldest f - - - 1
3 In 3 years' time, the sum of the ages of John ann Joseph will be 27 Joseph's age
is the difference between his own and John's ages How old is Joseph?
Solution:
27-2x3=21 21-7-3=7 Joseph is 7 years old
4 Bobbie's present age is a multiple of9 Last year, Bobbie's age was a multiple of
7 If Bobbie is between 15 and 45 years old, how old is he?
Solution:
This year: 18, 27,@ 45, Last year: 21, 28,@ 42, Bobbie is 36 years old
5 The sum ofJaclyn's and Melissa's ages is 19 The sum ofJaclyn's andNikita's ages
is 22 The sum of Melissa's and Nikita's ages is 25 What is the age of the oldest girl?
Solution:
Method 1: Solve by Reasoning
22-19 = 3 Melissa is younger than Nikita by 3 years
25-3 = 22
22 -7-2 = 11 Melissa is 11 years old
11 + 3 = 14 Nikita is 14 years old
19-11=8 Jaclyn is 8 years old
Method 2: Solve by Equations
J + M = 19 J+N=22
2M + 2N + 2J = 66 M+N+J=33 33- 19 = 14 years (Nikita's age)
3 3 - 22 = 11 years (Melissa's age) 33-25 = 8 years (Jaclyn's age) The age of the oldest girl is 14 years
I i
Trang 161 Annabelle is 10 years old One day, she asked about the age of her teacher "I will
be 58 years old by the time you are as old as me now," replied her teacher How
old is her teacher?
2 Cindy is 12 years old One day, she asked about her auntie's age "I will be 62 years
old by the time you reach my present age," repliecl her auntie How old is Cindy's
auntie?
3 Alison is 26 years younger than her father Her father's age will be 3 times her age
in 4 years' time How old is Alison?
4 The sum of the ages of a football coach and his two team members is 100 His age will be the sum of the ages of the two team members in 12 years' time How old is the football coach?
5 "When I was your age, you were only 4 years old I will be 79 years old by the time
you reach my present age," a father says to his daughter How old are the father and his daughter?
l Nelson says to his sister, "When I reach your age, you will be 35 years old." His
ister says to Nelson, "When I was your age, you were only 2 years old." How old
t r e Nelson and his sister?
Trang 177 This year, Mr Lasseter's age is a multiple of7 Next year, his age will be a multiple of
5 If his age is between 20 and 80, how old will Mr Lasseter be in 8 years' time?
8 This year, Karen's age is a multiple of5 Next year, her age will be a multiple of3
Her age is more than 20 but less than 50
How old will Karen be six years from now?
9 The age of a man is the same as his son's when the digits of his age are reversed
The sum of their ages is 77 The man is 27 years older than his son How old is his
son?
10 The su~ ofthe ages ofShaun and Matthew is 29 The sum of the ages ofShaun and Billy is 26 The sum of the ages of Billy and Matthew is 31 Who is the youngest among the three boys? How old is the youngest boy?
11 The product of Vincent's age and Daniel's age is 192 The sum of their ages is 28 How old is each boy if Daniel is the older one?
their ages is 31 How old is Bryan?
Trang 181 Four good friends want to take a group photo sitting in a row In how many ways
can they arrange their sitting positions?
They can arrange their sitting positions in 24 ways
handshakes are exchanged among 11 people?
Solution:
I ~ I : I ~ I ~ I : I : I ~ 1 : 1 ~ I J I ~ I
=55
55 handshakes are exchanged among 11 people
+
S olution:
1+4+2=7
Find the perimeter of the unshaded region
Solution:
We are looking for 2 'square numbers' with a difference of24
1 X 1 = 1 2x2=4 3X3=9
Trang 191
PRACTICE
In how many ways can the digits, 1, 2, 3 and 4, be arranged into a 4-digit number
without repeating the digits?
2 Nadia has 2 fifty-cent stamps and 2 eighty-cent stamps How many different postages
can she make up by using one, two, three or all the stamps?
3 40 pup~ _ ls queued in a line The first pupil of the queue was asked to leave, the second pupil stayed, the third pupil left the queue, the fourth one stayed, This process was
repeated until the last pupil remained in the queue What was the original position
of the last remaining pupil in the queue?
There are one yellow flag, one green flag and one blue flag Different signals can be made using at least one flag How many different signals can these flags make?
Trang 205 Darrell had 10 pieces of $1 notes, 5 pieces of $2 notes and 2 pieces of $5 notes
He needed $10 to purchase a storybook In how many ways could he make up $10
using the dollar notes that he had?
6 How many triangles are there in the figure below?
\ a
~~\
7 Alide, Ben and Charles are going to enrol for the following clubs
Mathematics Creative Writing Arts and Crafts Concert Band
If each of them is allowed to enrol for only one club, how many different combinations are there?
H The figure below is made of 2 squares of different sides Find the perimeter of the figure if its area is 85 cm2
•
Trang 219 A die of 6 faces is numbered 1, 2, 3, 4, 5 and 6 In how many ways will the sum be
an even number if the die is thrown twice?
··~
10 In the figure below, 5 balloons are hung in a shooting game It requires the player to
shoot down the last balloon of each string each time In how many different ways
can the player shoot down the balloons?
11 30 students, numbered from.l to ~0, are asked to queue in a line The first student
in the queue is asked to leave, the second student remains, th~ third student is asked
to leave the queue, the fourth student remains, This process is repeated until the
· last student is left in the queue What is the original number of that last student?
l2 In how many ways can a bee move from cell 1 to cell 5 in the beehive shown below?
3 5
Trang 2213 James' father brings him out to a restaurant for dinner The menu for kids is shown· 15 How' m~ny numbers betw~een ·10· and ~0 ~.~re multiples of 4?
Beverage Chocolate · Tea
Fruit Juice James is to choose one item from each category for his order In how many ways
can he place his order?
14 Jodie wants to exchange a piece of one hundred-dollar note for loose change The
cashier at the supermarket has the following denominations
In how many ways can she exchange the piece of one hundred-dollar note?
1ft The product of two numbers is 144 The sum of the two numbers is 30 Find the
two numbers
Trang 2317 In how many ways can you choose any two numbers from 1 to 40 whose s~m is·
greater than 40?
18 How many numbers smaller than 501 have the sum of their digits equal to 5?
Parentheses are important in complex number sentences as they show the order of
\
perations Below shows the law of parentheses in the order of operations
Ordinary brackets ( Square brackets [
) : First priority ] : Second priority } : Third priority
Find the missing number
Trang 241 Find the missing number
·value of this number?
6 A number is added to 6 The sum is then multiplied by 3 The product is divided
by 8 8 is then subtracted from the quotient
The answer is 1 Find the number
my age to 42 and divide the sum by 3 You then subtract 36 from the quotient Lastly,
you multiply the difference by 25 and the result will be 100." Please help David to
Trang 258 ABC Megamart sold 4 sacks more than half the number of sacks of rice on the first
day of a week It sold 3 sacks fewer than half of the remaining number of sacks
of rice on the second day ABC Megamart ordered another 30 sacks of rice on the
third day It had a total stock of 50 sacks then How many sacks of rice did ABC
Megamart have at first?
9 An army of ants was migrating The soldier ants moved 120 g less than half of
the amount of food on their first trip On their second trip, they managed to move
1 OQ g more than half of the remaining amount.,of food They moved 480 g of food
on their third trip 280 g of food was still unmoved How much food did the army
of ants have at first?
10 ABC Telco sold 20 more than half the number of mobile phones in January It sold
15 more than half the remaining number of mobile phones in February It had 75
mobile phones left in March before any purchase was made How many mobile
phones did ABC Telco carry at first?
11 Sul;?trahend is the number being subtracted in the subtr,action Robert misread the
digit 1 in the ones place of the subtrahend as 7 and the digit 7 in the tens place of the subtrahend as 1 The difference in the subtraction then becam~ 222 What would
be the actual difference if he had read the numbers correctly?
12 There were some marbles in a bag Jeff took half of the number of marbles out of' the bag He then put 1 marble back into the bag He repeated this process five times There were 3 marbles left in the bag at the end How many marbles were there in the bag at first?
I\ Alison, Beatrice and Chloe each had some books Alison gave Beatrice and Chloe
s me books that doubled the number of books they had at first Beatrice then gave
s me books to Alison and Chloe that doubled the number of books they had Lastly,
\t ·first?
Trang 2614 A number of commuters were on a bus when it started its journey from the bus
stop, ~ of the remaining commuters alighted, At the sixth bus stop, half the
number of commuters alighted and the bus was left with only 4 commuters How
many commuters boarded the bus at the bus interchange?
15 Sean was playing Bubble Gun in a park His Bubble Gun could eject 100 bubbles ~~ oiiil.iiiiilliiijj
number of the bubbles would survive for 2 minutes Only 2% of the original number
ofbubbles would make it to the end of3 minutes All the bubbles would burst at the
41
h minute?
When I divide one such group into 4 equal groups again, the remainder will still b
1 When I split one of such groups into 4 equal groups again, the remainder is still
1 What is the minimum number of beads I have?
A teacher has a bag of sweets for her students If each student is given 3 sweets, the
number of sweets is 4 How many students are there? How many sweets does the teacher have?
Solution:
In the first scenario, the excess is 30 sweets
In the second scenario, the excess is 4 sweets
(30- 4) ;- 1 = 26 ;- 1 = 26 There are 26 students
S olution:
Excess = 34 students Shortage = 4 students
34 + 4 = 38 Difference in number of students in a room= 14- 12 = 2 38 ;- 2 = 19
There are 1 9 rooms in the hostel
Trang 273 Michelle walks to school every morning If she walks at a speed of 60 metres per 5
minute, she will be late for 5 minutes If she speeds up to 7 5 metres per minute, she
will reach the school 2 minutes before the bell rings How far away is the school
from her house?
At the speed of 60 rn!min, she is 60 x 5 = 3 00 m away when the bell rings
At the speed of75 rnlmin, she can continue to walk for 75 x 2 =150m before the bell rings
300 + 150 = 450 m 75- 60 = 15 rn!min
;)
450 : 15 = 30 min
30 x 60 + 300 = 2100 m or 30 x 75- 150 = 2100 m
The school is 2100 m away from her house
4 Subtract 104 from 6 times of number A, the difference will be 64 more than 4 time
the value of number A Find the value of number A
Solution:
Excess= 64 Shortage = 1 04
64 + 104 = 168 6-4=2 168 : 2 = 84
Method 2: Writing Equations
A x 6 - 1 04 = difference - equation (1) Difference = 64 + A x 4 - equation (2) 6A- 104 = 64 + 4A
6A- 4A = 64 + 104 2A = 168 A= 168 : 2 = 84
The value of number A is 84
A group of workers is paving a new road It will take them 6 more days to pave the
road if they pave 120 metres per day If they can pave 160 metres per day, they are able to complete the work 4 days in advance
How many days are scheduled for the work?
How long is the road?
Solution:
Shortage = 120 x 6 = 720 m Excess= 160 x 4 = 640 m
720 + 640 = 1360 m 160- 120 = 40 1360 : 40 = 34
34 days are scheduled for the work
Trang 28PRACTICE
1 A basket of apples is to be given out If everyone gets 3 apples, there is an excess
of 16 apples If everyone gets 5 apples, the giver will be short of 4 apples How
many people are sharing the basket of apples? How many apples are there in the
basket?
2 The students from Ridgewood Primary School are going for a field trip If each
bus takes 35 students, 15 students will not get to board the bus If each bus takes 5
more students, there will be one empty bus How many buses does the school need
to charter? How many students are going for the field trip?
3 A teacher has a bag of sweets to be distributed among her students If each student
gets 10 sweets, there is no sweet left If each student gets 16 sweets, the teacher
needs another 48 sweets How many students are there? How many sweets does the teacher have?
If 5 students stay in a room of a youth hostel, 14 students will not have a room If
7 students stay in a room, there will be 4 vacant beds How many rooms does the
youth hostel have? How many students are staying in the youth hostel?
Trang 295 A car is travelling from Town A to Town B If it travels at a speed of 45 km/h, it
will be late by an hour If it travels at a speed of 55 km/h, it will arrive one hour
before the scheduled time How far away is Town B from Town A?
6 The students from Greensville Primary School are going on a field trip If each bus
takes 45 students, 10 students will not get to board the bus If each bus takes 50
students, there will be an extra bus How many buses is the school chartering? How
many students are going on the field trip?
7 A teacher stays back in school to mark test papers If she marks 10 questions every
5 minutes, she will be going home 20 minutes later If she marks 14 questions every
5 minutes, she "will be able to go home 10 minutes earlier How many questions
does she have to mark?
H ubtract 76 from 8 times of a number B, the difference is 68 more than 6 times the
value of the number B Find the value of the number B
Trang 309 David walks to a shopping mall to meet his friend If he walks at a speed of 30
metres per minute, he will be late for 4 minutes If he speeds up to 40 metres per I
minute instead, he will reach the shopping mall 3 minutes before the appointment
11 A group of construction workers is paving a new road If they pave 200 metres per day, they will be able to finish 6 days ahead of schedule If they pave 160 metres
per day, the work will be delayed by 4 days How long is the new road?
time How far away is the shopping mall from his place?
10 If each gift box in a store is sold at $80, the owner will make a profit of $2700 H
each gift box is sold at $40 instead, he will incur a loss of $900 How many gift
boxes are there? What is the cost price of each gift box?
Trang 31In a number sequence where the difference between every two terms is the same, we
can use the formulae shown below
nth term= first term+ (number of terms- 1) x d
where d is the common difference
number of terms in a number sequence= (last term- first term)+ d + 1
where d is the common difference
sum of a sequence= (last term+ first term) x number of terms+ 2
1 Given the number sequence, 1, 4, 7, 10, 13,
Find the 15th term of the number sequence Which term is number 55?
Solution:
d = 4- 1 = 7-4 = 10-7 = 13- 10 = 3 15th term= first term+ (15- 1) x d
n =57+ 3 = 19 The 1Sth term of the number sequence is 43 Number 55 is the 19th terlll
2 Find the 20th term of the number sequence, 1, 6, 11, 16, 21, Which term is number
136/?
-· Solution:
d = 6- 1 = 11-6 = 16- 11 = 21- 16 = 5 20th term = 1 + (20 - 1) x 5 = 1 + 19 x 5 = 96
To find the term of number 136,
Find the 32nct term of the number sequence, 3, 7, 11, 15, 19, Which term is number
'l'h 4th term of a number sequence with a common difference is 16 The 8th term is
Trang 32The 1st term of a number sequence with a common difference is 3 The 51st term is
203 Find the 1 OOth term
Trang 334 Compute 1 + 2 + 3 + + 99 + 100 + 99 + 98 + + 3 + 2 + 1
5 Compute 1 + 2 + 3 + + 1997 + 1998 + 1999
6 In the number sequence, 4, 7, 10, , 295, 298, which term is number 298?
7 Find the value of7 + 15 + 23 + + 767 + 775 + 783
8 Each book on mysteries in a series of 7 such books was published once every 3 years The fourth book was published in 1996 List the years that the rest of the books in that series were published
List the 8 numbers between 4 and 40 in a sequence of 10 numbers with a common difference
Trang 3410 The sum of the sixth and seventh terms in a sequence of 12 numbers with a common
difference is 15 What is the sum of the number sequence?
difference
was to play exactly 1 match with another team How many matches were played
altogether?
13 There ar~ 30 rows of seats in the North Wing of a stadium Each row has 2 seats more than the row in front The last row has 132 seats How many seats does the first row have? How many seats-are there altogether in the North Wing of the stadium?
14 Find the sum of all odd numbers from 1 to 100 that are not divisible by 11
Trang 35A prime number is a number that is only divisible by itself and the number 1 The common
prime numbers are 2, 3, 5, 7,
The product of the two prime numbers is 46
3 The product of two prime numbers is 51 What is the sum of the two prime numbers?
What is the difference of the two prime numbers?
The difference of the two prime numbers is 14
4 · Prime factorisation is the process whereby a number is expressed as the product of two or more prime numbers Perform the prime factorisation of the following
The possible values of the length and breadth of the rectangle are 1 and
165, 3 and 55, 5 and 33, and 11 and 15
Trang 361 Circle all the prime numbers between 30 and 60 from the numbers below
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
2 The sum of two prime numbers is 39 Find the product of the two prime numbers
3 List all the 1-digit, 2-digit and 3-digit numbers using the numbers 1, 2 and 3 Each
digit is to be used only once in each number Which are the prime numbers in thi
Trang 377 A is a prime number A+ 6, A+ 8, A+ 12, A+ 14 are also prime numbers What is A?
8 The sum of two prime numbers is 50 Find the biggest possible product of the two
prime numbers
value of the product of the 3 prime numbers?
Trang 3811 Prime factorisation is the process whereby a number is written as the product of
two or more numbers
18=2 x 3 x 3 Perform the prime factorisation of the following numbers
12 To test if a number is a prime number, we must
(a) find a number, k, such that k2 >the number we are testing;
(b) divide the number by all the prime numbers smaller than k
Example: To test if a number, 529, is a prime number, we must find a number, k,
such that its square is greater than 529
24 X 24 = 576 (> 529) Divide 529 by all the prime numbers smaller than 24
Prime numbers smaller than 24 = 2, 3, 5, 7, 11, 17, 19, 23
529 -:- 23 = 23
529 is not a prime number since it can be divided by numbers other
than 1 and itself
Are the following numbers prime numbers?
Trang 3913 Perform the prime factorisation of 2006 What is the sum of all its prime factors? 15 The length, width and height of a cuboid shown below are prime numbers Given
that A+ B = 220 cm2 find the volume of the cuboid (Note that the cuboid below
is not drawn to scale.)
14 Perform the prime factorisation of 1992 What is the sum of all its prime factors? lc, The product of 1540 and m is a square number
Find the smallest possible value of m
Trang 4017 A number and another number that reads the same when reversed are a palindrome
pair A good example is 243 and 342 Given the product of a palindrome pair is 101
088 Find the sum of the palindrome pair
18 How many rectangles of different sizes can be formed from 3 6 identical
rectangles?
19 In 780 x a = 1716 x b, find the smallest values of a and b
20 Different whole numbers are written on each face of a cube The sum of two whole numbers on the opposite faces equals to each of the·2 other sums of the whole numbers on opposite faces The face opposite 18 is a prime number, a The face opposite 14 is another prime number, b Lastly, the prime number, c, is opposite a whole number, 35
What is the value of a + b + c?
I In how many ways is 37 a sum of3 or more prime numbers?