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Đánh thức tài năng Toán học grade 1,2 là bộ giáo trình Toán của Singapore dành cho trẻ từ 78 tuổi được viết bằng tiếng Anh “Đánh thức Tài năng Toán học” do NXB Singapore Asia Publisher Pte Ltd (SAP) phát hành. SAP được thành lập năm 1977, một trong những đơn vị xuất bản chuyên về sách giáo dục lớn nhất tại Singapore. Tác giả Terry Chew, một thầy giáo đồng thời là người viết sách nổi tiếng ở Singapore. Các đầu sách toán ông đã cho xuất bản:
us on Facebook! 1iad-Maths-Trainer J anicounti"B Committed To Your Learning Complete your learning with these books! & S INGAPORE A SIA P UBLISHERS ~ c~ ~ ~ - - , - - - - - -.- - -~~~~~~~~~~~== ·- -= ··- ·= = = ,. =·=· = -= ·-~ ~ ~ ~ -~ -~-~ ~ ~~ -. -: • CONTENTS Chapter Tell Me the Time! Chapter Problems from Planting Trees- Intervals -10 Chapter Addition 20 Chapter Solve by Comparison and Replacement - 26 Chapter Age Problems 35 Chapter Division 44 Chapter Chicken-and-Rabbit Problems 55 Chapter Looking for a Pattern - 64 Chapter Counting 72 Chapter 10 Logic 80 For each clock, write the correct time on the line provided ~ ~ w pm am pm Solution: (a) 7.10 (b) 10.30 Chapter 11 Make a List, Make a Table - 88 Chapter 12 Using Model . - 97 Chapter 13 In Search of a Series 105 Chapter 14 What Comes Next? 117 Chapter 15 IQ Maths - 124 Chapter 16 Geometry - 132 Chapter 17 Odd and Even Numbers 141 Chapter 18 Queuing Problems 148 Chapter 19 Working Backwards 154 (b) 3.45 Chapter 20 Pigeonhole Principle 161 (c) 10.10 ~lJlSl!JrJrlJl\T~ S1 - S25 (c) 1.30 For each clock, write the correct time on the line provided ~ ~ w pm am Solution: (a) 12.20 Singapore Asia Publishers Pte Ltd Chapter pm A concert started at 8.30 pm and ended at 10.15 pm How long did the concert last? PRACTICE Solution: From 8.30 pm to 9.30 pm ~ hour From 9.30 pm to 10.30 pm ~ hour hour + hour = hours hours - 15 minutes = hour and 45 minutes The concert lasted hour and 45 minutes For each clock, write the correct time on the line provided w Trains arrive at a subway station every minutes How many trains would have arrived at the subway station in 30 minutes? _ _ _ am 10 15 20 25 7'h trains 30 minutes _ _ _ am _ _ _ pm (e) (d) Solution: ~ 00 (f) trains would have arrived at the subway station in 30 minutes The clocks below are images in the mirror Write the correct time on the lines provided _ _ _ pm _ _ _ am _ _ _ pm (b) (a) _ _ _ am Draw the hour and minute hands on the face of each clock to show the correct time Write the correct time on the lines provided (a) 25 minutes later _ _ _ pm Solution: (a) 7.10 (b) 2.30 2pm (b) 40 minutes ago 5.45pm © Singapore Asia Publishers Pte Ltd Chapter Singapore Asia Publishers Pte Ltd A movie started at 2.30 pm and ended at 4.05 pm How long was the movie? Carl attended a birthday party The time that the birthday party started and ended are shown on the two clocks below starting time ending time How long did the birthday party last? The signboard shown on the right is placed outside a shop For how many hours is the shop open daily? Benson played for 10 minutes after reaching home He watched television for another 20 minutes before taking his lunch His lunch, which lasted for 20 minutes, was finished at 2.50 pm At what time did Benson reach home? Business Hours 11 am- 9.30 pm Singapore Asia Publishers Pte Ltd In the pattern below, draw the hour and minute hands on the face of each clock Write down the correct time on the lines provided The clocks below are images in a mirror For each clock, write the correct time on the line provided (a) 7.20 am 8.10 am 8.50 am (b) (c) _ _ _ am (d) _ _ _ am _ _ _ am _ _ _ pm _ _ _ pm Buses arrived at a bus stop every 15 minutes Lincoln needed to board the bus at 8.30 am but he was late for minutes At what time did Lincoln arrive at the bus stop? How long did he have to wait for the next bus? 10 _ _ _ pm Trains leave a station every 40 minutes At what time would the third train leave the station if the first train left at 6.30 am? Singapore Asia Publishers Pte Ltd 11 Trains arrived at the subway station every minutes How many trains would have arrived at the subway station in 60 minutes? 13 A grandfather clock chimed once at o'clock, twice at o'clock, thrice at o'clock How many times would it have chimed by o' clock? 12 The Greyhound coaches leave a station every one and a half hours If the first coach leaves at five o'clock in the morning, at what time does the fourth coach leave the station? 14 The two clocks below show the time Jolene started and ended her birthday party How long was her birthday party? starting time Singapore Asia Publishers Pte Ltd ending time The road in front of my school is planted with trees The trees are m away from each other How far is the sixth tree away from the first one? ~~~~~ ' -y -1 ' -y -1 ' -y -1 ' -y -1 ' -y -1 4m 4m 4m 4m 4m Solution: x m= 20m The sixth tree is 20 m away from the first one matchsticks are placed at an equal distance away from each other How many intervals are there? Solution: ~ ~ ~ ~ The distance between the first and the eighth trees along a stretch of road is 21 m How far are the trees away from each other along that stretch of road if they are placed at regular intervals? ~ ' -y .!' -y )' -y .!' -y ) 1st 2nd 3rd 4111 There are intervals '-y -1 '-y -1 '-y -1 '-y -1 '-y -1 '-y -1 '-y -1 knots are tied on a rope How many intervals are there from the 1st knot to the 6th knot? Each staircase has 12 steps How many steps such staircases have? Solution: X 12 = 36 such staircases have 36 steps 10 Chapter 21m -:-7 =3m The trees are m away from each other along that stretch of road There are intervals © Singapore Asia Publishers Pte Ltd Solution: Solution: Singapore Asia Publishers Pte Ltd 11 Chapter Jimmy ties knots on a piece of rope The knots are 20 em apart from one another How far is the fifth knot from the first one? trees are planted along a stretch of road The distance between every two trees is m How far is the sixth tree from the second one? Stella lines coins up on a table Each coin is 10 em apart from the other How far is the ninth coin from the first one? It takes Peter minutes to saw a plank of wood into two pieces How many minutes will Peter take to saw a plank of the same length into four pieces? 'lngupore Asia Publishers Pte Ltd A grandfather clock takes seconds to chime times at o'clock How many seconds will the grandfather clock take to chime times at o'clock? 11 A subway train takes minutes to reach the next station It stays at a station for minute before moving to the next station How many minutes does the subway train take to travel from the first to the fifth station? 10 Alison stays on the 5th floor of an apartment The staircase leading to every floor has 10 steps How many steps does Alison have to climb before she reaches home? 12 A train has compartments Each compartment is m long The compartments are joined by connectors oflength m How long is the train? Slngnpore Asia Publishers Pte Ltd 10 There are blue balls, orange balls and yellow balls in a bag Sheila will be blindfolded before she takes the balls out, one at a time How many balls must Sheila take out in order to get balls of the same colour? (Note that she has to begin with blue, orange and yellow balls.) 11 If we colour the regions in each circle with either blue or red, then at least regions will have the same colour (SOLUTIONS) ©Singapore Asia Publishers Pte Ltd ALL RIGHTS RESERVED : :::: :: : :: : :::::::::::::::::::::::::::::::::::::::::: ::: ::: · '; · ~ :::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::: :: ::::~·~:~~~~ (b) 2.45 (d) 10.40 (f) 6.15 (a) 7.15 (c) 4.55 (e) 5.50 minutes after 8.30 am is 8.38 am Lincoln arrived at the bus stop at 8.38 am 15 minutes after 8.30 am is 8.45 am 12 (a) 2.50 (b) 8.15 (c) 7.30 (d) 5.45 5.05 2.25 10 40 minutes after 6.30 am > 7.10 am 40 minutes after 7.10 am > 7.50 am The third train would leave at 7.50 am 2.30 pm to 3.30 pm > hour 3.30 pm to 4.00 pm > half an hour or 30 minutes 4.00 pm to 4.05 pm > minutes hour + 30 minutes + minutes = hour 35 minutes The movie was hour and 35 minutes 2"d 3'd 4'" minutes 11.00 am to 12.00 pm > hour 12.00 pm to 9.00 pm > hours 9.00 pm to 9.30 pm > half an hour or 30 minutes hour+ hours + 30 minutes = 10 hours and 30 minutes The shop is open for 10 hours 30 minutes daily 2.30 pm to 5.30 pm > hours 5.30 pm to 5.45 pm > 15 minutes hours + 15 minutes = hours 15 minutes The birthday party lasted hours 15 minutes ©Singapore Asia Publishers Pte Ltd 12 long 9.40 51 Chapter X X X 2"d 3'd 4'" 5'" ITi!iJ ITi!iJ ITi!iJ ITi!iJ ITi!iJ ITi!iJ 13 10 10 10 10 10 10 ? ,.-A ,.-A ,.-A ,.-A ,.-A ,.-A c::J c::J c::J c::J c::J c::J c::J 1" 2"d 3'd 4'" 5'" 6'" 7'" coaches will leave the station in 60 minutes x 10 em = 80 em The ninth coin is 80 em from the first one '' ' ''' ' ' '' '' '' '' l I 14 ~-+ ~~~ ~~-I need to cut the ribbon times 80 em = 10 em Each piece of ribbon is 10 em Peter needs to saw the plank of wood times x = 15 Peter will take 15 minutes to saw a plank of wood of the same length up into four pieces 15 Method + + = 12 Method2 X = 15 15-3=12 Deduct as the comers are counted twice Vanessa uses 12 coins to form the triangle 6s X X X X ' )'y2ndy3'dY4•h 6s73=2s Each interval is seconds X S = 10 S The grandfather clock will take 10 seconds to chime times at o'clock Maths Olympiad- Unleash The Maths Olympian In You! (Junior I) © Singapore Asia Publishers Pte Ltd A X x m=36 m (total length of all compartments) 5x1m=5m (total length of all connectors) 36m+ m=41 m The train is 41 m long x 3m= 12m The sixth tree is 12 m from the second one X 14 starting time > pm ending time > 40 pm Her birthday party was hours and 40 minutes t' 4x2min=8min The subway train takes minutes to travel from the first to the fifth station 3x1min=3min The subway train waits a total of minutes at the station + = 11 The subway train takes 11 minutes to travel from the first to the fifth station = 21 It would have chimed 21 times by o'clock ~~~~ 1" 13 + + + + + ~;~ X There are intervals from the first knot to the fifth one x 20 em = 80 em The fifth knot is 80 em from the first one 7.20 am to 8.10 am > 50 minutes 8.10 am to 8.50 am > 40 minutes 8.50 am to 9.20 am > 30 minutes 9.20 am to 9.40 am ~ 20 minutes Maths Olympiad- Unleash The Maths Olympian In You! (Junior I) 11 12 1'1 coach > 5.00 am 2"ct coach > 6.30 am 3'ct coach > 8.00 am 4th coach > 9.30 am The fourth coach leaves the station at 9.30 am 10 minutes+ 20 minutes+ 20 minutes= 50 minutes 50 minutes before 2.50 pm is pm Benson reached home at pm 9.20 There are intervals along the road X = 14 There are 14 trees along that stretch of road There are intervals from the first lamp post to the fourth one x m =15m The fourth lamp post is 15 m from the first one 60 = 10 10 + = 11 11 trains would have arrived at the subway station in 60 minutes Method2 56 There are intervals along the road 3x3m=9m The fourth tree is m from the first one 5'" 6'" 7'" 8'" 9'" I 0'" 11 '" trains 12 18 24 30 36 42 48 54 60 11 Method I" There are intervals ' v -' ' v -' ' v -' ' v -' ' v -' ' v -' ' v -' From 8.38 am to 8.45 am > minutes He had to wait another minutes for the next bus (b) (a) 10 There are staircases leading from the t'Ollltd fl to the Sth floor X 10 = 40 Alison has to climb 40 steps before she reach home 52 Chapter ' ······································ ::~ ~ ~ ~ ~ ~ ~~~ ~~g~gggggggsssuaiiiiiunggggg~~~~ ~ ~ ~ ~ ~ ~ ~; · ' ~:~/ =20 (c) + + + = 10 + 10 • •••• • ' '- so / = 80 (h) 16+17+18+19 = 10 + + + + 17 + 18 + 19 (e) 13 + 28 + 22 + 17 = 30 +50 ~~~/ = 70 = 100 (a) 18 + 19 + 13 = 18 + 19 + + + 10 ' zo ->