Q&A - PSLE Math

[Vanilla Cake]

kancheongmum:

Hi Tianzhu

Need help in these 2 questions, solutions posted but cannot understand

Sorry for the interruption,have you checked Observer's solutions?

kancheongmum:

2010 prelim papers Maha Bodhi Q12 Meals question

http://psle2010a.blogspot.com/2010/09/decimal-p6-2010-sa2-maha-bodhi-p2-q12.html

kancheongmum:

2010 prelim papers River Valley Q18 vanilla and chocolate sweets

http://psle2010a.blogspot.com/2010/09/rvps-p6-prelim-2010-p2-q18.html

VC's mum

[tianzhu]

kancheongmum:

Hi Tianzhu

Need help in these 2 questions, solutions posted but cannot understand
2010 prelim papers Maha Bodhi Q12 Meals question
2010 prelim papers River Valley Q18 vanilla and chocolate sweets
Thank you

Hi kancheongmum

Please refer to VC's mum's post.

Please let me know if I can be of any help.

Best wishes

[Dharma]

Suz855:

Hi,


Need help on the solution for the following question, thanks

A,B, C and D shared a box of pens. A received 20% of the total number of pens which B, C and D received altogether. B received 50% of the total number of pens which A, C and D received altogether. C received 80% of the total number of pens which A, B and D received altogether. D received 6 pens. How many pens were in the box at first?

Ans : 108
:oops: [/img]

A => 1/6
B => 1/3
C => 4/9
D = 1- 1/6 – 1/3 – 4/9 = 1/18
1/18 => 6 pens
18/18 = 18 x 6 = 108 pens

[tianzhu]

Circle P6 2010 SA2 Nanyang P2 Q18

18. The figure below is created using the curved lines (arcs) of quadrants with radius 1 cm, 2 cm and 3 cm. Find the area of the shaded parts.
(Take pi as 3.14)

Q18 looks intimidating at first glance. It helps if one can rearrange the shaded areas.

What I am sharing here may help students who prefer to work with more familiar shapes. It may not be the shortest way.

Interestingly, the rearranged figure looks like a big eye and a small eye.

PSLE students should be familiar with calculating the areas of shaded area within the 3cm square (big eye) and the small eye within the 1cm square.

The area of the shaded area in Q18 is the 2(area of big eye – area of small eye)

Best wishes

http://farm5.static.flickr.com/4085/4988720284_36afd045ba_b.jpg\">

[tiger262]

Respected Uncle Tianzhu,


I am amzed at your tireless energy in conceiving and posting the above drawing. You are helping so many students to do far better in PSLE Maths than they would have done otherwise.

In my view, you and uncle Dharma have at least added 7 to 10 marks to their PSLE aggregate by your contributions in this forum. Not a small feat. You both deserve a ‘big thank you’ from all the students and their parents.

Best regards and grateful thanks.

[Vanilla Cake]

tiger262:

Respected Uncle Tianzhu,


I am amzed at your tireless energy in conceiving and posting the above drawing. You are helping so many students to do far better in PSLE Maths than they would have done otherwise.

In my view, you and uncle Dharma have at least added 7 to 10 marks to their PSLE aggregate by your contributions in this forum. Not a small feat. You both deserve a 'big thank you' from all the students and their parents.

Best regards and grateful thanks.

Agreed, my DD1 will never be able to achieve stellar grades in PSLE Maths & Science without the help of both gentlemen - Dharma and Tianzhu. I hope that they will continue to contribute to helping all students (+parents) in the upcoming PSLE Maths exams.

Another remarkable gentleman is Observer. His http://prischoolmaths.blogspot.com/ and http://psle2010a.blogspot.com/ are great blogs with excellent and detailed solutions in PSLE Maths.

VC's mum

[snowman.022851697]

Use ratio.


In the question, they are comparing one person to the other 3 people for all the ratios. Therefore, the total will be the same.

So, first we convert the percentage to ratio (remember that decimal, fraction, ratio and percentage are all interchangeable)

20% of b, c and d becomes 1:5
50% of a, c and d becomes 1:2
80% of a, b and d becomes 4:5

---------
Express in ratio:

Set 1A : B + C + D (6units together)1 : 5Set 2B : A + C + D (3units together)1 : 2Set 3C : A + B + D (9units together)4 : 5

LCM (Lowest Common Multiple) of 6, 3, 9 is 18.

Therefore if we were to change the ratio such that the total in each set has the same number of units,
18/6= 3 (x3 for set 1)
18/3= 6 (x6 for set 2)
18/9= 2 (x2 for set 3)

Therefore, we \"multiply\" each ratio by 3

Set 1A : B + C + D3 : 15Set 2B : A + C + D6 : 12Set 3C : A + B + D8 : 10

3+ 15= 18
6+ 12= 18
8+ 10= 18
As you can see, if you add up the no of units in each set the total is 18. Now we can compare as the unit sizes are the same.

Now figuring out the amount of units of pens each guy has is simple: Refer to the working above.

A -> 3uB -> 6uC -> 8u D -> 10u-6u-3u=u  -> u

In the question, D has 6 pens.
Therefore, u = 6.

Total amount of units -> 18u

Therefore, 18 x 6 = 108
Answer: 108

Solved. Any questions, post back

[kancheongmum]

Hi Tianzhu and VC mum tks finally understand the solutions now. But still cannot understand the model solution posted by pecalis on the vanilla and chocolate questions. Is ok my ds is not good with model. Need help in this question Maha BodhiQ6 (Ans $12)

each apple cost 40cts each pear cost 60 cts
Mrs Gopal and Mrs Ari went to the supermarket. Both women decided to spend all their money on either apples or pears and they would not buy the same fruit. If Mrs Gopal bought only pears, she would have 9 more fruits than Mrs Ari. If she bought only apples, she would have 41 more fruits than Mrs Ari. How much more money has Mrs Gopal than Mrs Ari?

Thank you

[Vanilla Cake]

kancheongmum:

Hi Tianzhu and VC mum tks finally understand the solutions now. But still cannot understand the model solution posted by pecalis on the vanilla and chocolate questions. Is ok my ds is not good with model. Need help in this question Maha BodhiQ6 (Ans $12)

each apple cost 40cts each pear cost 60 cts
Mrs Gopal and Mrs Ari went to the supermarket. Both women decided to spend all their money on either apples or pears and they would not buy the same fruit. If Mrs Gopal bought only pears, she would have 9 more fruits than Mrs Ari. If she bought only apples, she would have 41 more fruits than Mrs Ari. How much more money has Mrs Gopal than Mrs Ari?

Hi kancheongmum,

Just browse through VC's workings on the vanilla and chocolate question and noted that she didn't use model solution. So, pls wait for Tianzhu, Pecalis etc to help on this question. As for the MBS P6 Prelim Maths Paper 2 Q6, here's my non-model solution:

Cost of 1 apple = 40 cents each = $0.40
Cost of 1 pear = 60 cents each = $0.60

Case 1
Gopal: u+9 (Pears)
Ari: u (Apples)

Ari: ux$0.40 = $0.4u (amount spent)

Case 2
Gopal: p+41 (Apples)
Ari: p (Pears)

Ari: px$0.60 = $0.6p (amount spent)

Compare Ari in both cases,
$0.4u = $0.6p
u = 1.5p

Case 1
Gopal: u+9 (Pears) -> 1.5p+9 @ $0.60/pear
Ari: u (Apples) -> 1.5p

Case 2
Gopal: p+41 (Apples) -> p+41 @ $0.40/apple
Ari: p (Pears)

Equate the amount spent by Gopal in case 1 and case 2,
0.60(1.5p+9)=0.40(p+41)
0.9p + 5.40 = 0.4p + 16.40
0.5p = 11
p = 22

From above, u=1.5p = 1.5x22= 33

Case 1
Gopal: u+9 (Pears) -> 33+9 = 42 pears
Ari: u (Apples)-> 33 apples

Gopal: 42 pears x $0.60 = $25.20
Ari : 33 apples x $0.40 = $13.20
Difference = $(25.20-13.20) = $12.00

Mrs Gopal has $12.00 more money than Mrs Ari.

This is my own workings as VC is still not back home yet, she only did those 4/5 marks questions for the 2010 P6 Prelim Maths papers to help her younger sister (P5) to practise. Hope others can come up with a better method than mine.
Thanks.

VC's mum

PS: Have you look through http://psle2010a.blogspot.com/2010/09/rvps-p6-prelim-2010-p2-q18.html for the vanilla/Chocolate sweets question? His solution is also not based on models.

[kancheongmum]

Hi VC mum thank you, yes I understand Uncle Observer’s solution on the vanilla and chocolate sweets questions. Wow this apples and pears question has such long working for a 3 mark question. Thank you very detailed and clear. You are certainly there for your dds, and very sure you groom them well. All these months seem like we are sitting for PSLE. This year I am sitting for 3 major exams, PSLE, O Level, A Level. Ha Ha just to destress.