tag:blogger.com,1999:blog-67464192069324691182024-03-05T16:55:55.929+08:00Road to PSLEYour FREE resource to better PSLE (Primary School Leaving Examination) scores!Excel Eduservicehttp://www.blogger.com/profile/11691081348489781290noreply@blogger.comBlogger448125tag:blogger.com,1999:blog-6746419206932469118.post-61055065743531523872021-11-29T16:37:00.000+08:002021-11-29T16:37:33.214+08:00Note to visitors to this blog<p>Hi everyone, this post is to notify visitors that we have stopped tuition services since 2014. Past posts are however left the way they are so that they can be used as referral material. Do note that PSLE syllabus do change over time and hence some topics may no longer be relevant eg Solar System, Simple Machines. Also do note that MOE has ceased using the PSLE T-Score and Aggregate Score Method. </p>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-47814042857613113952012-09-12T18:13:00.000+08:002012-09-12T18:13:15.088+08:00Red Swastika Sch 2011 PSLE Math Prelim Paper 2 Q10<span id="internal-source-marker_0.5620069445854882" style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Katelyn
had some green, red and blue ribbons. She had 25% more green ribbons
than red ribbons and 20% less blue ribbons than red ones.</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">a) What is the ratio of red ribbons to green ribbons to blue ribbons?</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">b)
Katelyn exchanges all her blue ribbons for some red and green ribbons.
She now has an equal number of red and green ribbons. How many more
green than red ribbons did she have at first if she has 244 red ribbons
now?</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Solution</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">(a) </span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Red ----- 100%</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Green ----- 25% more than 100% = 125%</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Blue ----- 20% less than 100% = 80%</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Red : Green : Blue</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">100 : 125 : 80</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">20 : 25 : 16</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Answer: 20 : 25 : 16</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">(b)</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Before Katelyn exchanges,</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Red : Green : Blue</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">20 : 25 : 16</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Blue
exchanged for green and red will mean that 16 units of blue will be
given up. Since Katelyn finally has an equal of number red and green, 5
units of the 16 units of blue will be exchanged for red first, with the
remaining 11 units divided equally between red and green. </span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Red will receive ----- 5 units + (11 units divided by 2) = 10.5 units</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Green will receive ----- 11 units divided by 2 = 5.5 units</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Red ribbons now ----- 20 units + 10.5 units = 30.5 units</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">30.5 units ----- 244</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">1 unit ---- 244 divided by 30.5 = 8</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">In the beginning,</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Green - Red</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">25 units - 20 units = 5 units</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">5 units ----- 5 x 8 = 40</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Answer: 40 red ribbons </span><br />
<a href="https://docs.google.com/document/d/1snkzkzNUQiP5xA9HybMw58_nLRje1fjp8NV5zfLQPhs/edit"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13px; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Printer Friendly Version </span></a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-68878127935069282042012-09-11T07:38:00.000+08:002012-09-11T07:38:14.187+08:00 Red Swastika Sch 2011 PSLE Math Prelim Paper 2 Q8<span id="internal-source-marker_0.6324152591258558" style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">The
ratio of the number of apples in Box A to the number of apples in Box B
is 3 : 2. All the apples in Box B are green. The ratio of the number of
green to the number of red apples in Box A is 4 : 5. There are 20 more
green apples in Box B than in Box A. How many red apples are there?</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Solution</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><img height="236px;" src="https://lh3.googleusercontent.com/tJ39pmGvqOnJ7b9g0mCALUk6DcoRbspa4W4_u29hp8NAIQxp8lDMcMUFXSXnKlH0kRSCjEf3x0638ta0Pm41OlFa7OuC3rKMrPPYl_ZYHDoFinfw7Ps" width="266px;" /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">* 4 units of green apples + 5 units of red ---- 9 units in Box A</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">** 3 units in Box A (x 3) ---- 9 units, hence 2 units in Box B (x 3) will give 6 units. </span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Green Apples</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Box B - Box A ----- 20</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">6 units - 4 units ----- 20</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">2 units ----- 20</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">1 unit ----- 20 divided by 2 = 10</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Red Apples</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">5 units ----- 5 x 10 = 50</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Answer: 50 red apples</span><br /><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"></span><br /><a href="https://docs.google.com/document/d/17G3ZKBaMLDy5qHRlB9lTup9-zICViCDmFZGrWIlf2R8/edit#null"><span style="background-color: transparent; color: #1155cc; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline;">Printer Friendly Version</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-4225443271360529512012-05-16T16:56:00.000+08:002012-05-16T16:56:24.020+08:00Maths Q from a readerA reader emailed me this question and I am too busy to solve it for him. Could readers please help him by posting the solution in the comments section. Thank you.<br />
<br />
Mr Lim spent 885 on honey stars and pies. He spent 471 more on pies than on honey stars. The ratio of the number of packets of pies to the number of honey stars is 8:3. Each packet of pie is 0.45 more than honey stars. How many packets of honey stars did he buy?ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com1tag:blogger.com,1999:blog-6746419206932469118.post-17778109890836116912012-02-27T15:49:00.008+08:002012-02-27T15:58:36.740+08:00Rosyth School 2011 CA1 Math Paper 2 Q17Farmer Dan harvested some apples. He sold to Adam 3/4 of the apples and another 105 apples. He sold to Geraldine 3/4 of the remainder but took back 55 apples. Farmer Dan had 890 apples left.<br /><br />a) How many apples did Geraldine have after returning 55 apples to Farmer Dan?<br /><br />b) How many apples did Farmer Dan harvest?<br /><br /><span style="font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); ">Solution </span><br style="font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><br style="font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><div id="h5:." style="margin-top: 0px; margin-bottom: 0px; font-family: Verdana; font-size: 16px; background-color: rgb(255, 255, 255); "><img src="https://docs.google.com/File?id=dfnc2gmv_228369z47gp_b" style="height: 274px; width: 395px; " /></div><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "> </p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span"><span class="Apple-style-span">1/4 of remaining ----- 890 – 55 = 835</span></span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span">3/4 of remaining ----- 3 x 835 = 2505</span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "> </p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span"><br /></span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span">a) Geraldine ----- 2505 - 55 = <u>2450</u></span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span"><br /></span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span">b) 1 unit ----- 4/4 of remaining + 105</span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span">4/4 of remaining ----- 835 x 4 = 3340</span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span">1 unit ----- 3340 + 105 = 3445</span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span">(Total harvested) 4 units ----- 4 x 3445 = <u>13 780</u></span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "> </p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span"><b><br /></b></span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><span class="Apple-style-span"><b>Answer: a) 2450 apples b) 13 780 apples.</b></span></p><br style="font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><div style="margin-top: 0px; margin-bottom: 0px; font-family: Verdana; font-size: 16px; text-align: -webkit-auto; background-color: rgb(255, 255, 255); "><a href="http://docs.google.com/View?id=dfnc2gmv_226crn3n5gt" id="l7xd" title="Printer Friendly Version" style="color: rgb(85, 26, 139); ">Printer Friendly Version</a></div>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-56520593913020896392011-11-21T12:30:00.003+08:002011-11-21T12:32:45.818+08:00PSLE Results to be released on Thursday<a href="http://www.channelnewsasia.com/stories/singaporelocalnews/view/1166682/1/.html">PSLE results out Thursday</a><br />SINGAPORE: The results of the 2011 Primary School Leaving Examination (PSLE) will be released on Thursday.<br /><br />The Ministry of Education (MOE) said pupils may obtain their result slips from their respective schools from 12noon.<br /><br />Eligible pupils will also receive from their respective primary schools, their option forms to select secondary schools.<br /><br />MOE said the results of Secondary 1 postings will be out on 21 December.<br /><br />Nan Chiau High School, which has been designated a Special Assistance Plan school from January next year, will admit only Express course students offering Chinese or Higher Chinese as a Mother Tongue Language.<br /><br />And two more schools - Victoria School and Cedar Girls - will take in their first batch of Secondary 1 students in the six-year integrated programme.<br /><br />- CNA/ckExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-80885676521948758052011-09-20T09:52:00.006+08:002011-09-20T09:59:07.477+08:00Catholic High School 2010 PSLE Math Prelim Paper 2 Q17<b>Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?<br /><br />Solution<br /><br />At first</b><br />Daniel ---- 100% + 40%<br />Brandon ---- 100%<br />Calvin ---- 1 unit<br /><br /><b>After Daniel and Brandon each gave 20% of their stickers to Calvin…</b><br />Daniel ---- 100% + 40% - (28%)*<br />Brandon ---- 100% - (20%)**<br />Calvin ---- 1 unit + (28% + 20% of Dan and Bran --> 80% of 1 unit)#<br />Hence Calvin --- 1 unit + (48% of Dan and Bran --> 80% of 1 unit)<br /><br />* 20% of 140% = 28%<br />** 20% of 100% = 20%<br /># Cal received 28% + 20% = 48% of (Dan + Bran), which is equal to 80% of Cal's original amount of 1 unit.<br /><br />80% of 1 unit ---- 48% of total of Dan and Bran<br />0.8 unit ---- 48%<br />1 unit ---- 48% divided by 0.8 = 60%<br /><br />In the end Calvin<br />1 unit + (48% from Dan and Bran)<br />= 60% + 48%<br />= 108%<br /><br />(Daniel) more than (Calvin) in the end<br />(140% - 28%)## - (108%)<br />= 112% - 108% <br />= 4%<br />## Danile had 140% at first but gave 28% to Calvin<br /><br />Daniel had 20 more stickers than Calvin in the end<br />4% ---- 20<br />1% ---- 20 divided by 4 = 5<br /><br />Brandon at first<br />100% ---- 100 x 5 = 500<br /><br /><b>Answer: 500 stickers</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMjIyZ2g1dHB2Y2Q&hl=en_US" id="c:nh" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-2191059238404736382011-09-14T18:58:00.001+08:002011-09-14T18:59:54.500+08:00Catholic High School 2010 PSLE Math Prelim Paper 2 Q18<b>At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.<br />a) Find the ratio of male speakers to male participants at the conference.<br />b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference?<br /><br />Solution</b><br /><br />Male ----- 120%<br />Female ----- 100%<br /><br />Speakers<br />Male : Female<br />8 (parts) : 5 (parts)<br /><br />Participants<br />Male : Female<br />1 (unit) : 1 (unit)<br /><br />Men ----- 8 parts + 1 unit<br />Women ----- 5 parts + 1 unit<br /><br />But since there are 20% more women than men,<br />Women ----- 5 parts x 120% + 1 unit x 120%<br />= 6 parts + 1.2 units<br /><br />Men ----- Women<br />8 parts + 1 unit ----- 6 parts + 1.2 units<br />8 parts - 6 parts ----- 1.2 units - 1 unit<br />2 parts ----- 0.2 unit<br />1 part ----- 0.1 unit<br />10 parts ----- 1 unit<br />or<br />1 unit ----- 10 parts<br /><br /><br /><b>(a)</b><br />Male Speakers ----- 8 parts<br />Male Participants ----- 1 unit or 10 parts<br /><br />Male Speakers : Male Participants<br />8 : 10<br />4 : 5<br /><br /><b>Answer: 4 : 5</b><br /><br /><b>(b)</b><br />Speakers<br />Male : Female<br />8 (parts) : 5 (parts) -- (altogether 13 parts)<br /><br />Participants<br />Male : Female<br />1 (unit) : 1 (unit)<br />10 (parts) : 10 (parts) -- (before)<br />- 40 : + 60 -- (40 males left; 60 females joined)<br />3 (units) : 4 (units) -- (3/4 as many male as females in the end)<br /><br />(Male) 3 units ----- 10 parts - 40<br />(Female) 4 units ----- 10 parts + 60<br /><br />(Female) - (Male)<br />4 units - 3 units ----- 10 parts + 60 - 10 parts - (-40)<br />1 unit ----- 60 + 40<br />1 unit ----- 100<br /><br />(Male after) <br />3 units ---- 3 x 100 = 300<br /><br />(Male before)<br />10 parts ---- 300 + 40 (need to add the 40 who left)<br />10 parts ----- 340<br />1 part ---- 34<br /><br />All speakers<br />13 parts ---- 13 x 34 = 442<br /><b><br />Answer: 442 speakers</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMjIxYzNuNnJkZHA&hl=en_US" id="w6za" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-6957925863984096832011-09-07T21:40:00.004+08:002011-09-07T21:44:23.150+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q18<b>The figure below shows 2 completely-filled tanks being emptied of the water from 2 different taps.</b><br /><br /><div id="s7m6" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_219hq67g7hn_b" style="height:211.864px;width:400px" /></div><br /><b>The taps at Tank A and Tank B were turned on at 7 am and 8.30 am respectively, until both tanks were completely empty. At 11 am, the water level in both the tanks was the same. At 12.30 pm, Tank B was completely empty and Tank A was only completely empty at 1 pm. If the rate of the flow of water from each tap was constant throughout, what was the height of Tank A?<br /><br />Solution</b><br /><br /><div id="b-pn" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_213chn6w8gx_b" style="height:400px;width:439px" /></div><br /><br />** At 11 am, water level in both Tanks were the same.<br /><br />Note that 3/8 of B's height is the same as 2/6 or 1/3 of A's height.<br /><br />(3/8) of B ----- (2/6) or (1/3) of A<br /><br />(1/8) of B ----- (1/3) of A divided 3 = (1/9) of A<br /><br />(8/8) of B (B's height) ----- 8 x (1/9) = (8/9) of A<br /><br />* Remaining (1/9) of A ----- 5 cm<br />(This is the difference in height between Tank A and B)<br /><br /><br />(9/9) of A (A's height) ----- 9 x 5cm = 45 cm<br /><br /><b>Answer: 45 cm</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMjA5ZmNjcDIyZmQ&hl=en_US" id="eebg" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com3tag:blogger.com,1999:blog-6746419206932469118.post-66336335043017680162011-09-07T21:12:00.001+08:002011-09-07T21:13:34.396+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q17<b>The average length of 6 ropes was 80 cm. The average length of 4 ropes of the ropes A, B, C and D was 15 cm more than the average length of the remaining 2 ropes E and F.<br />a) Find the average length of ropes E and F. Give your answer in metres.<br />b) If Rope E had been 18 cm shorter and Rope F had been 12 cm longer, they would have been of the same length. Find the actual length of Rope E.<br /><br />Solution</b><br /><br />Total of 6 ropes ----- 6 x 80cm = 480 cm<br /><br />Average of A, B, C, D (4 ropes) is more than Average of E and F (2 ropes) by 15 cm.<br />This means each of the 4 ropes (A, B, C, D) has an average length that is 15 cm longer than the average of E and F.<br /><br />Therefore, total length of A, B, C, D is longer than total length of E and F by<br /> ----- 4 x 15cm = 60 cm<br /><br /><div id="h26y" style="text-align:left"><div id="ykyx" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_216g38d9gc2_b" style="height:115px;width:409px" /></div></div><br /><b>a) </b><br />3 units ----- 480cm - 60cm = 420 cm<br />1 unit (E + F) ----- 420cm divided by 3 = 140 cm<br /><br />Average ----- 140cm divided by 2 = 70 cm or 0.7 m<br /><br /><b>Answer: 0.7 m</b><br /><br /><br /><b>b)</b><br /><div id="xrvr" style="text-align:left"><div id="prcb" style="text-align:left"><div id="gu35" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_218qmcx4tch_b" style="height:245px;width:361px" /></div></div></div><br />2 parts ----- 140 - 12 - 28 = 110<br />1 part ----- 110 divided by 2 = 55<br /><br />E ----- 55 + 12 + 18 = 85<br /><br /><b>Answer: 85 cm</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMjA4ZnE0NnBmZms&hl=en_US" id="a2wh" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-19699289908222567282011-09-07T20:51:00.001+08:002011-09-07T20:52:33.916+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q16<b>Yanling had 60% more stamps than Lena. Tricia had 75% fewer stamps than Yanling. Yanling and Lena gave Tricia some stamps in the ratio 4:1. As a result, Tricia had 2 and 1/2 times as many stamps as before and Yanling had 300 stamps more than Lena in the end. How many sttamps did Lena give to Tricia?<br /><br />Solution</b><br /><br /><div id="xu6:" style="text-align:left"><div id="la5c" style="text-align:left"><div id="efz_" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_215hrvjf3hd_b" style="height:165px;width:400px" /></div></div></div><br />*** Tricia had 75% fewer stamps than Yanling<br />----- 25% of 160% is 40%.<br /><br /># Tricia finally had 2 and half times as many stamps as before<br />----- 40% x 2.5 = 100%<br /><br /><br />Tricia's number of stamps increased by<br />---- 100% - 40% = 60%<br /><br />Ratio given by Yanling and Lena was 4:1 -----<br />Y : L<br />4 : 1<br />(Total 5 units) ----- 60%<br /><br />**(Lena gave) 1 unit ----- 60% divided by 5 = 12%<br />*(Yanling gave) 4 units ---- 4 x 12% = 48%<br /><br />In the end, Yanling had more than Lena ----- 300<br />112% - 88% ----- 300<br />24% ---- 300<br />1% ---- 300 divided by 24 = 12.5<br /><br />Lena gave Tricia 12% -----<br />12 x 12.5 = 150<br /><br /><b>Answer: 150 stamps</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMjA2Zm1oaDc4anI&hl=en_US" id="mb.6" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-48528296420663939422011-09-07T20:29:00.001+08:002011-09-07T20:30:31.265+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q15<b>A car and a van started travelling from Town X to Town Y at the same time. The distance between the two towns was 225 km. Both vehicles did not change their speed. The car arrived at Town Y 3/4 h earlier than the van. When the car reached Town Y, the van was still 45 km away from Town Y. What was the speed which the car was travelling?<br /><br />Solution</b><br /><br /><div id="lsg1" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_205dww9gnfz_b" style="height:209px;width:302px" /></div>* When the car reached Town Y, the van was still 45 km away. The car arrived at Town Y 3/4 h earlier than the van.<br /><br />(Van) speed -----<br />45 km divided by (3/4) h<br />= 60 km/h<br /><br />(Van) time for the whole journey -----<br />225 km divided by 60 km/h = 3 and 3/4 hours<br /><br />Therefore, the car travelled in 3 h.<br /><br />Speed of car -----<br />225 km divided by 3 h = 75 km/h<br /><br /><b>Answer: 75 km/h</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMjA0YzY3YndrdDY&hl=en_US" id="rmfx" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-49832212550418863962011-09-07T20:24:00.001+08:002011-09-07T20:31:40.010+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q13<b>The figure below shows 2 quarter circles and a rectangle. The radius of the big quarter circle is 8 cm. The radius of the small quarter circle is 4 cm. Find the difference in area between the two shaded parts of X and Y. Use the calculator value of pi and give your answer correct to 1 decimal place. </b><br /><br /><div id="matv" style="text-align:left"><div id="ns0v" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_203c2mr9mhb_b" style="height:281px;width:316px" /></div><br /></div><b>Solution</b><br /><br />Area of rectangle ----- 8 cm x 4 cm = 32 square cm<br /><br />Area of large quadrant -----<br />(1/4) x pi x 8cm x 8 cm<br />= 16(pi) square cm<br /><br />Area of small quadrant ------<br />(1/4) x (pi) x 4cm x 4cm<br />= 4(pi) square cm<br /><br />Area of Large quadrant - Area of small quadrant -----<br />16(pi) square cm - 4(pi) square cm<br />= 12(pi) square cm<br /><br />Difference between the two shaded parts X and Y -----<br />(12 x pi) square cm - 32 square cm<br />approximately ----- 5.7 square cm<br /><b><br />Answer: 5.7 square cm</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMjAxZndtdnpjYzY&hl=en_US" id="jgmf" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-13177708124026033672011-09-07T20:15:00.003+08:002011-09-07T20:32:05.800+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q9<b>The number of pens in Box X and Box Y are in the ration of 3:2. All the pens in Box Y are green. The ratio of green pens to blue pens in Box X is 4:5. There are 12 more green pens in Box Y than in Box X. How many blue pens are there?</b><br /><br /><b>Solution </b><br /><br /><div id="y87i" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_200fxkgn8cg_b" style="height:283px;width:202px" /></div><br />Green in Box X<br />(4/9) x (3/5) = 4/15<br /><br />There are 12 more blue pens in Box X than in Box Y<br />(2/5) - (4/15) ----- 12<br />(6/15) - (4/15) ----- 12<br />2/15 ----- 12<br />1/15 ----- 12 divided by 2 = 6<br /><br />Blue Pens<br />(5/9) x (3/5)<br />= 1/3<br />= 5/15<br /><br />5/15 ----- 5 x 6 = 30<br /><br /><b>Answer: 30 blue pens</b><br /><br /><a title="Printer Friendly Version" href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTk5ZjlzYnJ0Z3g&hl=en_US" id="xcxw">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-31841730747403491982011-09-07T20:09:00.002+08:002011-09-07T20:32:27.185+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q6<b>Randy brought along a certain amount of money to buy files. If he bought the files at $1.50 each, he would have $17.50 left. If he bought the same number of files at $2.70 each, he would have $9.10 left. How much money did he bring along?<br /><br />Solution</b><br /><br /><div id="gbap" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_198d7jgzpkq_b" style="height:265px;width:463px" /></div><br />1 unit x $1.50 + $17.50 ----- 1 unit x $2.70 + $9.10<br />($2.70 x 1 unit) - ($1.50 x 1 unit) ----- $17.50 - $9.10<br />($1.20 x 1 unit) ----- $8.40<br />1 unit ----- $8.40 divided by $1.20 = 7<br /><br />He brought along -----<br />(7 x $2.70) + $9.10<br />= $18.90 + $9.10<br />= $28<br /><br /><b>Answer: $28</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTk3Y3ZycWNjNGg&hl=en_US" id="q-qc" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-17801832039520389292011-09-07T20:02:00.004+08:002011-09-07T20:32:54.572+08:00Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q5<b>At a bakery, muffins are sold at $1 each. When a customer buys 5 muffins, she can buy one more at half the price. What is the greatest number of muffins that a customer can buy with $20?<br /><br />Solution<br /></b><br />6 muffins ----- $5.50 (Five at $1; One at $0.50)<br /><br />3 groups of $5.50 ----- 6 muffins x 3 = 18 muffins<br /><br />(3 x $5.50 = $16.50) ----- 18 muffins<br /><br />$20 - $16.50 = $3.50 (remaining)<br /><br />With the remaining $3.50, the customer can buy another three muffins at $1 each.<br /><br />Total muffins ----- 18 + 3 = 21<br /><br /><b>Answer: 21 muffins</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTk2MnhmbTVqZHI&hl=en_US" id="wosm" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-89566151277393760462011-06-09T10:17:00.004+08:002011-06-09T10:20:16.748+08:00A time to relax a littleNow that school holidays are around, it is time to relax a little. Just a little, not too much, or you will have problems re-adjusting back to school life when the next semester starts. <br /><br /><iframe width="425" height="349" src="http://www.youtube.com/embed/astISOttCQ0" frameborder="0" allowfullscreen></iframe>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-67402916290835827482011-05-03T08:01:00.002+08:002011-09-04T18:01:00.093+08:00ACS Primary 2010 SA1 Math Paper 2 Q18<b>Keane bought some marbles and gave half of them to Leon. Leon then bought some stamps and gave half of the to Keane. Keane used 5 stamps and Leon gave away 11 marbles. The ratio of the number of stamps to the number of marbles Keane had left then became 1:7 and the ratio of the number of stamps to the number of marbles Leon had left became 1:5. How many stamps did Leon buy?
<br />
<br />Solution</b>
<br />
<br />M ----- Marbles
<br />S ----- Stamps
<br />
<br />Step 1
<br />Keane bought marbles and gave half to Leon,
<br />Keane ----- M
<br />Leon ----- M
<br />Both have same number of marbles.
<br />
<br />Step 2
<br />Leon bought stamps and gave half to Keane,
<br />Keane ----- M , S
<br />Leon ----- M , S
<br />Now both have same number of marbles and stamps
<br />
<br />Step 3
<br />Keane used 5 stamps, Leon gave away 11 marbles,
<br />Keane ----- M , [S - 5]
<br />Leon ----- [M - 11] , S
<br />Now Keane has 5 stamps less, and Leon 11 marbles less
<br />
<br />Step 4
<br />Keane's no. of stamps to no. of marbles now is 1:7,
<br />M ----- (7 units)
<br />[S - 5] ----- (1 unit)
<br />Now Keane has 7 times as many marbles as stamps.
<br />
<br />Step 5
<br />Leon's no. of stamps to no. of marbles now is 1:5,
<br />[M - 11] ----- (5 parts)
<br />S ----- (1 part)
<br />Now Leon has 5 times as many stamps as marbles.
<br />
<br />Step 6
<br />1 unit of Keane's stamps + 5 ----- 1 part of Leon's stamps
<br />1 unit + 5 ----- 1 part
<br />Keane gave away 5 stamps, so to have an equal no. of stamps as Leon now, we add back the 5 stamps Keane gave away.
<br />
<br />Step 7
<br />7 units of Keane's marbles ----- 5 parts of Leon's marbles + 11
<br />7 units ----- 5 parts + 11
<br />Leon gave away 11 marbles, so to have an equal no. of marbles as Keane, we add back the 11 marbles Leon gave away.
<br />
<br />Step 8
<br />Comparing marbles with stamps
<br />(Stamps) 1 unit + 5 ----- 1 part (refer to Step 6)
<br />(Marbles) 7 units ----- 5 parts + 11 (refer to Step 7)
<br />
<br />Step 9
<br />Multiply stamps by 5
<br />(Stamps) 5 units + 25 ----- 5 parts
<br />(Marbles) 7 units --> 5 parts + 11
<br />
<br />(Stamps) 5 units ----- 5 parts - 25
<br />(Marbles) 7 units ----- 5 parts + 11
<br />
<br />Step 10
<br />(marbles) - (stamps)
<br />7 units - 5 units --> 5 parts + 11 - 5 parts - (-25)
<br />2 units --> 11 + 25
<br />2 units --> 36
<br />1 unit --> 18
<br />
<br />Step 11
<br />1 unit ----- S - 5 (refer to Step 4)
<br />18 ----- S - 5
<br />S ----- 18 + 5 = 23
<br />This is the no. of stamps Leon had after giving half away.
<br />
<br />Step 12
<br />Leon bought,
<br />2 x 23 = 46
<br />
<br /><b>Answer: 46 stamps </b>
<br />
<br /><div><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTk0ZnFoemZ4ZG0&hl=en" id="h31r" title="Printer Friendly Version">Printer Friendly Version</a></div>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com4tag:blogger.com,1999:blog-6746419206932469118.post-42034606238696156782011-05-03T07:51:00.003+08:002011-05-03T07:54:30.601+08:00ACS Primary 2010 SA1 Math Paper 2 Q17<b>The shaded figure below is formed by semicircles, quarter circles and straight lines of 15 cm each. For each of the following, use the calculator value of <img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" /> to find<br />a) the perimeter of the shaded figure, correct to 2 decimal places.<br />b) the area of the shaded figure, correct to 2 decimal places.<br /><br /></b><div id="mmik" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_193kv8p6qdd_b" style="height:286px;width:311px" /></div><br /><b>Solution</b><br /><br />(a)<br />Circumference of 2 semicircles (1 circle)<br />--> 2<img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" />r<br />= 2<img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" /> x 7.5cm<br />= 47.12 cm<br /><br />Circumference of 2 quarter circles (1 semi circle)<br />-->(<img alt="\frac{1}{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cfrac%7B1%7D%7B2%7D%20" style="vertical-align:middle" />)2<img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" />r<br />= (<img alt="\frac{1}{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cfrac%7B1%7D%7B2%7D%20" style="vertical-align:middle" />)(2)(<img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" />) x 15cm<br />= 47.12 cm<br /><br />Length of vertical line on the left side of figure<br />--> 2 x 15cm = 30cm<br /><br /><br />Perimeter of shaded figure<br />--> 47.12cm + 47.12cm + 30cm<br />= 124.25cm<br /><br /><b>Answer: 124.25 cm</b><br /><br /><br />(b)<br />Area of 2 quarter circles (1 semi circle)<br />-->(<img alt="\frac{1}{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cfrac%7B1%7D%7B2%7D%20" style="vertical-align:middle" />)<img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" /><img alt="r^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=r%5E%7B2%7D%20" style="vertical-align:middle" /><br />= (<img alt="\frac{1}{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cfrac%7B1%7D%7B2%7D%20" style="vertical-align:middle" />)<img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" /> x 15cm x 15cm<br />= 353.43<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /><br /><br /><br />Area of 2 semi circles (1 circle)<br />--> <img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" /><img alt="r^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=r%5E%7B2%7D%20" style="vertical-align:middle" /><br />= <img alt="\pi " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cpi%20" style="vertical-align:middle" /> x 7.5cm x 7.5 cm<br />= 176.71<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /><br /><br />Area of whole figure<br />--> 30cm x 30cm<br />= 900<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /><br /><br />Shaded area<br />--> 900<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /> - 353.43<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /> - 176.71<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /> <br />= 369.86<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /><br /><br /><b>Answer: 369.86<img alt="cm^{2} " class="ee_img tr_noresize" src="https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=cm%5E%7B2%7D%20" style="vertical-align:middle" /></b><br /><br /><div><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTkyanBwbWdiaG0&hl=en" id="dzev" title="Printer Friendly Version">Printer Friendly Version</a></div>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-33002235508934399192011-04-24T18:57:00.003+08:002011-04-24T18:58:56.068+08:00ACS Primary 2010 SA1 Math Paper 2 Q16<b>Mr Wu had some badges and decided to give them to his two sons, Sean and Matthew. Mr Wu gave 1/3 of the badges and 8 more badges to Sean. He then gave 3/4 of the remainder to Matthew but took back 2 badges. Mr Wu was left with 26 badges. How many badges did Mr Wu have at first?<br /><br />Solution</b><br /><br />Assume all badges --> 1 unit<br /><br /><div id="ljmg" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_191c3k7qvf8_b" style="height:244px;width:406px" /></div><br />Mr Wu was left with,<br /><br />----- 1/4 of Remainder + 2<br /><br />----- 1/4 x (2/3 unit - 8) + 2<br /><br />= (1/6 unit - 2) + 2<br /><br />= 1/6 unit - 2 + 2<br /><br />= 1/6 unit<br /><br />1/6 unit --> 26 badges<br /><br />1 unit ----- 26 divided by 1/6<br />= 26 x 6<br />= 156<br /><br /><b>Answer: 156 badges </b><br /><br /><div><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTkwZnAycnoyZ20&hl=en" id="n7gq" title="Printer Friendly Version">Printer Friendly Version</a></div>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-89883506601509726472011-04-24T18:48:00.003+08:002011-10-16T10:32:32.799+08:00ACS Primary 2010 SA1 Math Paper 2 Q15<b>Both Joanne and Joseph had an equal amount of money at first. Every month, Joanne spent $850 and Joseph spent $912. After a few months, Joanne was left with $1550 while Joseph had 4/5 as much as Joanne. How much money did Joseph have at first?<br /><br />Solution</b><br /><br />Every month,<br />Joanne spends $850<br />Joseph spends $912<br />Difference every month<br />--> $912 - $850 = $62<br /><br /><br />After a few months, Joseph had 4/5 as much as Joanne,<br /><div id="vcmq" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_189c2prjdcs_b" style="height:164px;width:275px" /></div><br />5 units ----- $1550<br />1 unit ------ $1550 divided by 5 = $310<br />($310 is the difference between Joanne and Joseph after a certain number of months)<br /><br /><br />Number of months to achieve the $310 difference,<br />$310 divided by $62 = 5 (mths)<br />It also takes 5 months for Joseph to have 4/5 as much as Joanne.<br /><br /><br />Amount Joseph has at first,<br />Joseph ------ 4 units + (5 mths x $912 spent per mth)<br />----- (4 x $310) + (5 x $912)<br />= $1240 + $4560<br />= $5800<br /><br /><b>Answer: $5800</b><br /><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTg4ZmdqNzU1ZmQ&hl=en" id="q73v" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-42906599469438012682011-04-18T22:24:00.002+08:002011-04-18T22:25:54.688+08:00Another Problem Sum from a readerReceived another question from a reader.<br />Can anyone help this reader out<br /><br />Question:<br />Mrs tan bought 4 times as many toys as teddy bears . She spent $1750 altogether . A toy gun cost $10 less than a teddy bear . The total cost of toy guns was $490 more than the total cost of teddy bears . <br />(a) How much did Mrs tan spend on the teddy bears?<br /> <br />(B) How much did one teddy bear cost ?ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com2tag:blogger.com,1999:blog-6746419206932469118.post-87666385706896972472011-04-14T08:55:00.003+08:002011-09-06T22:37:32.144+08:00ACS Primary 2010 SA1 Math Paper 2 Q14Tony and Charles took part in a car race. Tony drove at a speed of 90km/h. Both of them did not change their speed throughout the race. When Charles had covered 1/3 the distance, Tony was 15 km in front of him. Tony reached the finishing line at 9.35 a.m. At what time did Charles recah the finishing line?<br /><br /><b>Solution</b><br /><br /><div id="y7jq" style="text-align:left"><div id="g55_" style="text-align:left"><div id="y-78" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_187gvm4nk6w_b" style="height:159px;width:429px" /></div></div></div><br />* For every 1/3 of the race Charles covered, Tony was 15 km ahead. When Charles completed the whole race, Tony would have been 3 x 15km = 45km ahead of Charles, if we assume Tony continued to travel beyond the finishing line.<br /><br />Time = 45 km divided 90 km/h<br />= 0.5 hour<br /><br />Half hour after 9.35 am ------ 10.05 am<br /><br /><b>Answer: 10.05 am</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTg2aHMyOXJmY3E&hl=en" id="gar4" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-52450244534731926062011-04-13T11:11:00.001+08:002011-04-13T11:13:19.567+08:00ACS Primary 2010 SA1 Math Paper 2 Q12<b>Weiming had 2/3 as many stickers as Shiyang. After Weiming gave 52 stickers to Shiyang, Weiming had 2/5 as many stickers as Shiyang. How many stickers did Weiming have at first?<br /><br />Solution</b><br /><br /><div id="y7jq" style="text-align:left"><div id="g55_" style="text-align:left"><img src="https://docs.google.com/File?id=dfnc2gmv_185d72qchdh_b" style="height:227.992px;width:400px" /></div></div><br />*(x7) and (x5) to give a common total of 35 units for both "At first" and "In the end", since there is no change in the total number of stickers.<br /><br />Weiming gave<br />14 units - 10 units ---- 52<br />4 units ----- 52<br />1 unit ----- 52 divided by 4 = 13<br /><br />Weiming at first<br />14 units x 13 = 182<br /><b><br />Answer: 182 stickers </b><br /><div id="nu7d" style="text-align:left"><br /></div><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTgzZnF4ZmY1ZHE&hl=en" id="b6op" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0tag:blogger.com,1999:blog-6746419206932469118.post-114557505684907552011-04-13T10:58:00.002+08:002011-04-13T11:07:36.313+08:00ACS Primary 2010 SA1 Math Paper 2 Q9<b>The graph below shows the mass of a container when it is empty and when different combinations of objects X, Y and Z are placed in it. </b><br /><br /><div id="nu7d" style="text-align:left"><br /><img src="https://docs.google.com/File?id=dfnc2gmv_182d65fdmd5_b" style="height:288.93px;width:450px" /></div><br /><b>Solution</b><br /><br />Empty container --> 80g<br />Y + Z ----- 140g - 80g = 60g<br />X + Z ----- 300g - 80g = 220g<br />X + Y ----- 340 g - 80g = 260g<br /><br />Total of all objects<br />----- 60g + 220g + 260g = 540g<br /><br />Average ----- 540g divided by 6 = 90g<br /><br /><br /><b>Answer: 90g</b><br /><br /><a href="https://docs.google.com/Doc?docid=0AXITtOgU2cOnZGZuYzJnbXZfMTgxZ3Y1OGg5Zjc&hl=en" id="qy2h" title="Printer Friendly Version">Printer Friendly Version</a>ExcelEduservicehttp://www.blogger.com/profile/17134552650896445122noreply@blogger.com0