Q&A - PSLE Math

[leesf]

atutor2001:

Vanilla Cake:

[quote=\"leesf\"]Q3) A street-lamp is erected at an interval of 8m on one side of the street. On the other side of the street, an angsana tree is planted at every 6m. There are 12 more angsana trees than street-lamps.

a) Ho long is the street if there is one street-lamp and one angsana tree on both ends of the street.
b) How many street-lamps and angsana trees are there?

atutor2001:

Q3 The 1st common multiple of 6 & 8 is 24 (i.e. 3 gaps between 2 lamp and 4 gaps between 2 trees)
4 - 3 = 1
Therefore, for there to be 12 more trees than lamp we need to repeat this interval 12 times i.e. the 12 common multiples of 6 & 8

(a) Street length = 12 x 24 = 288m
(b) No. of trees = 5 + 11 x 4 = 49 No. of lamps = 4 + 11 x 3 = 37

(after the first group, the no. of trees & lamps is reduced by 1 because there is already a \"reference tree/lamp\" from the end of the last group\"

e.g.
x x x x)x x x)x x x) - x represents lamps
|--24-|--24-|--24-|[/u]

Lowest common multiple of 6 and 8 is 24.
24÷6=4
4+1=5
So, there are 5 angsana trees for the first 24m.

24÷8=3
3+1=4
So, there are 4 street-lamps for the first 24m.

From the above workings, you can see that there is 1 additional angsana tree for every 24m.
Since there are 12 more angsana trees than street-lamps (given in the question itself), length of the street -> 24÷1x12=288m
(a) If there is one street-lamp and one angsana tree on both ends of the street, length of street = 288m

288÷8=36
36+1=37 street-lamps.
Number of angsana trees -> 37+12=49.
(b) Numbers of street-lamps and angsana trees are 37 and 49 respectively.

Hi Vanilla Cake

Thank you for correcting my mistake. Got confused between trees and distances. Your method for finding the number of trees and lamps is so much better.

I have amended my working in red so as not to cause further confusion. Apology to anyone who got confused by me.[/quote]Thanks to Vanilla cake for clarification.

[tianzhu]

Hi


An interesting question on circle from onsponge.
You may wish to have a go at it.

http://www.onsponge.com/forum/35-thinkingmathonsponge/5482-p6-maths-question-.html

Best wishes

[octopusmum]

Hi Vanilla cake


thks once again for helping! i am sure your sis will do v well cause she has a v helpful and smart sister to guide her

Hi Kancheongmum
thks to you too...actually i have managed to figure out the answer just now but killed many of my brain cells on the way! i don't remember maths was this tough during my time!

actually, there is another question which also stumped my son and I, and surprise surprise, my son's maths teacher as well...it is from the Rosyth School 2010 prelim, question 15. i am not able to reproduce the question cause it is under geometry. there is a square with 2 lines cris crossing each other in it. suppose to find a shaded area in the square.

not sure if u can help again?! thks v much!

regards

[kancheongmum]

octopusmum:

Hi Vanilla cake


thks once again for helping! i am sure your sis will do v well cause she has a v helpful and smart sister to guide her

Hi Kancheongmum
thks to you too...actually i have managed to figure out the answer just now but killed many of my brain cells on the way! i don't remember maths was this tough during my time!

actually, there is another question which also stumped my son and I, and surprise surprise, my son's maths teacher as well...it is from the Rosyth School 2010 prelim, question 15. i am not able to reproduce the question cause it is under geometry. there is a square with 2 lines cris crossing each other in it. suppose to find a shaded area in the square.

not sure if u can help again?! thks v much!

regards

Hi Octopusmum,

You are most welcome. Yes this question Rosyth 2010 Q15, there are a few solutions posted here pg 194, 195 and Observer. Some of the solutions I personally feel that is not for pri level except for the one posted by Dharma. You may want to have a look. I took quite sometime to find a simple and logical way the explain to my DS.

get a midpoint of line AB and name it Z. Draw a line from point F to Z
AZ = ZB = AE = ED = 12/2= 6cm (because is a square)
tri AZF = tri ZBF (both triangles have equal base and height)

Diagonal AC is the line of symmetry

So tri AEF = tri AZF (AE=AZ, EF=FZ)
area of tri AEB = area of (tri AEF + tri AZF + tri ZBF) = 1/2x12x6=36cm2
tri AEF = 36/3 = 12 cm2
tri ADC = 1/2 x 12 x 12 = 72 cm2

shaded area = 72 - 12 = 60 cm2

Hope this help and let me know if you need further explanation.

[tianzhu]

Hi


I think this question is likely to floor many students during exams. To begin with, it’s not an easy one.

Students with knowledge about symmetry will find it easier to crack it. I think symmetry is covered in P4 Maths.

Kancheongmum has earlier introduced the idea of solving this problem with symmetry in one of the earlier posts in this thread.You may want to show your child by folding a piece of square paper.

I shall put it in visual form, hope this helps.

Best wishes

http://farm5.static.flickr.com/4105/5037820184_49243da940_b.jpg\">

http://farm5.static.flickr.com/4103/5037820252_8aa41e056c_b.jpg\">

[abc_parent]

Hi all

Please help if you can.

Q15) Study the number pattern below.
5 to power 2 = 5 x 5 =25
5 to power 3 = 5 x 5 x 5 = 125
5 to power 4 = 5 x 5 x 5 x 5 =625
5 to power 5 = 5 x 5 x 5 x 5 x 5 =3125
(a) In 5 to power 6 , what is the sum of the digits in the ones and tens place?
(b) What is the sum of the last 3 digits in 5 to power 15?
What is the sum of the last 4 digits in 5 to power 210?


Ans: 7,8,18

Q16) Country A and Country B took part in a Youth Game. From Country A, the ratio of the number of male supporters to the number of female supporters is 5: 6. From Country B, the ratio of the number of male supporters to the number of female supporters was 1:3. The total number of supporters from Country A is 1/4 of the total number of supporters from Country B.
(a) What is the ratio of the number of female supporters from Country A to the number of female supporters from Country B? Express your answer in the simplest forml
(b) After 4985 male supporters from both countries left, the percentage of all the female supporters became 78%. How many more male supporters from country B than country A were there at first?

Ans: 2:11, 5982

[abc_parent]

Hi all,


Q15) Mr Tan had 130 durians and mangosteens. After he sold 2/3 of the durians and 2/5 of the mangosteens, he had 36 more mangosteens than durians left. How many fruits had he left in all?

Ans: 66

Q16) [Please help if you have the diagram] The figure below is made up of a circle, a triangle and two identical semicircles. The diameter of the circle is 8cm and the diameter of the semi circle is 4cm. Find the area of the shaded regions. (Take pi = 3.14)

Ans: 30.8 cm square

Q17) Ahmad and Halim together took 5 days to paint their house. If Ahmad and Halim took together for 2 days, followed by Ahamd working alone for 8 days, Halim will take 1 more day to complete the remaining work. How long will Ahmad take to paint the house all by himself?

Ans: 17.5

Q18) Tracy counted the number of 10cents coins, 20cents coins and 50cents coins in her piggy bank. The number of 10 cents coins was 24 more than the number of 50 cents coins. After spending 3/5 of the 10cents coins, 1/4 of the 20 cents coins and 18 50 cents coins, she had an equal number of 10 cents and 20 cents coins. The number of 50 cent coins now formed 40% of the remaining number of coins.
(a) How many 10 cents coins did Tracy have at first?
(b) How much did she spend in all?

Ans: 90, $16.80

[abc_parent]

Hi, please help if you can?


Water from 3 taps was used to fill an empty water tank. Tap X, Tap Y, Tap Z could fill the tank completely in 3 hours, 4 hours, 5 hours respectively.
(a) What fraction of the tank was filled with water after half an hour when all taps were turned on at the same time? Give your answer in the simplest form.

Now, only Tap X and Tap Y were both turned on to fill another empty water tank. Immediately after 20 minutes, Tap Z was also turned on. Both Tap X and Tap Y were turned off at the same time after turning on for an hour and only Tap Z was left to fill the tank completely.
(b) How much longer would Tap Z take to fill the tank completely with water after both Tap X and Tap Y were turned off?
Express your answer in terms of hours in its simplest form.

(a) 47/120
(b) 1 & 5/12 h

[Brenda10]

[quote=\"abc_parent\"]Hi all,


Q17) Ahmad and Halim together took 5 days to paint their house. If Ahmad and Halim took together for 2 days, followed by Ahamd working alone for 8 days, Halim will take 1 more day to complete the remaining work. How long will Ahmad take to paint the house all by himself?

Ans: 17.5

Hi, for this question, please refer the following link:

http://www.onsponge.com/images/fbfiles/images/forum_2010_06_07_rate_1.png

[kancheongmum]

Hi Tianzhu


Thank you for the beautiful illustration of the answer to the Rosyth Q15. You have certainly put my solution into better visual effects and benefit everyone who was stumped on this question. BTW have you crack the circle question you mentioned earlier from the onsponge forum. Care to share with us. I am still trying to find the key to unlock.
Best regards