Tutor MathsGuru: Ask me for your burning Maths questions!
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firebird:
Hi Firebird,Dear Mathsguru
Good morning.
Please help me on the P6 maths:
1) What is the value of 18- 6 + 2 x 5?
My working is 2 x 5 equal 10
6 + 10 equal 16
18 - 16 equal 4
However, the given answer was 22.
My understanding was to follow this sequence:
division, multipilication, addtion and substraction. Please correct me.
2) Given 21 boxes. The 1st has 3 marbles, 2nd box has 6 marbles, 3rd box has 9 marbles and so on in this pattern. What is the total number marbles in all the 21 boxes?
By adding one by one I can get answer 693
My request is: any short cut as this is a 1 mark question?
Many thanks
firebird
1) The order of operations should be BODMAS --> Brackets, Orders, Division AND Multiplication, Addition AND Subtraction.
Note that I highlighted the word \"AND\" for Division/Multiplication and Addition/Subtraction, because Division & Multiplication are of the same \"rank\" and Addition & Subtraction are of the least priority but same rank.
Hence, for this question: 18- 6 + 2 x 5, we should do multiplication 1st since there are no brackets and there is only 1 multiplication. We'll obtain 18- 6 + 10. Next, because Addition & Subtraction are of the same rank, we do from left to right: 12 + 10 = 22.
With more practice, your child should be able to get a hang of the order of operations. It is very very important, so must try to master this asap!
2) For this question, the number pattern is 3, 6, 9, 12, etc --> multiples of 3. Although there's an arithmetic progression formula for this, I will try to explain in a more simplified manner.
As a rule of thumb, for a number pattern that involves a constant difference, the average of the pattern can be obtained by taking the average of the first and last terms.
Last term (21st box) = 3 x 21 = 63.
Average of the 21 boxes = (3 + 63) / 2 = 33.
Using the concept of average, total sum of marbles = average x total number of boxes.
Therefore, total no. of marbles = 33 x 21 = 693.
Though there are several methods out there, I would encourage your child to learn and use this method because it works on all types of number pattern as long as the difference between every 2 consecutive numbers are the same.
For instance, sum of all no.s from 1 to 99:
Average = (1 + 99) / 2 = 50.
No. of numbers = 99.
Total sum = 50 x 99 = 4950.
Best regards,
MathsGuru -
YLH88:
Hi YLH88,Hi Mathsguru,
I'm definitely sure your answer is correct
But need you to help explain some queries :
For Qn 1 on the books, why do we need to break the 1 big unit into 4 units ? I thought 3 : 1 is referring to the original units where Mrs Yee has 6 units (160%) and Mdm Ling has 5 units (100%) ?
For Qn 2 on the diagram, 160 - shaded area = 3 x (64 - shaded area), multiple by 3 is it because of the unshaded triangle is 300% of the unshaded rectangle ?
Thank you very much !
Pls see below for my explanations. Hope they are clear enough...
1) To answer your question, we need to go back to how we derive the total number of units Tang has in the end. She has 1.5 times her original 6 units. This means that she will have an additional 3 units.
These 3 units has to be split into 3:1 between Yee & Ling, because of the 3rd sentence in the question --- Yee & Ling gave some books to Tang in the ratio of 3:1. To split 3 units into 4 equally, it will be easier to understand by splitting 3 units into the 12 (i.e. LCM of 3 & 4). Therefore, each unit has to be split into 4.
2) Yes! 300% means 3 times as much.
Cheers,
MathsGuru -
Hi Mathsguru,
Oic ... Thank you for the explanation. Now i understand liao
Regards -
Dear mathsguru
Good morning
I am totally lost in the following first 2 maths. However, for the 3rd question, I managed to do on guess and check basis. Nevertheless, would be greatful if you could share a systematic method in solving the 3rd question:
1) Miss Wong had just read a novel with 1008 pages. How many digits were used to number the pages from 1 to 1008 in the novel?
2) Mr. Lee left Town M and travelled towards Town N at an average speed of 80 km/h. An hour later Mr. Ong left Town M and travelled towards Town N at an average speed of 100 km/h. Mr. Ong passed Town Q which was halfway between town M and town N 30 minutes earlier than Mr. Lee. If Mr. Ong reached Town N at 10pm, at what time did Mr. Lee leave town M for town N?
3) 100 people were having a health check up. Their average mass was 63kg. Given that the average mass of the women was 60kg and the average weight of the men was 70kg. How many men were there?
Many thanks
firebird -
firebird:
For question 1 you are lost because there is no \"straightforward\" approach. You must do systematic listing.Dear mathsguru
Good morning
I am totally lost in the following first 2 maths. However, for the 3rd question, I managed to do on guess and check basis. Nevertheless, would be greatful if you could share a systematic method in solving the 3rd question:
1) Miss Wong had just read a novel with 1008 pages. How many digits were used to number the pages from 1 to 1008 in the novel?
2) Mr. Lee left Town M and travelled towards Town N at an average speed of 80 km/h. An hour later Mr. Ong left Town M and travelled towards Town N at an average speed of 100 km/h. Mr. Ong passed Town Q which was halfway between town M and town N 30 minutes earlier than Mr. Lee. If Mr. Ong reached Town N at 10pm, at what time did Mr. Lee leave town M for town N?
3) 100 people were having a health check up. Their average mass was 63kg. Given that the average mass of the women was 60kg and the average weight of the men was 70kg. How many men were there?
Many thanks
firebird
For Page 1-9 , 1*9 digits are used
10-99 2*90 digits are used
...
...
2)For such speed questions, the most efficient method is to use algebra.
By expressing the distance between town M and Q, you can \"capture\" the given information by siolving
(d/80) - (d/100) = 1.5hr
3) this is a typical chicken-duck-leg scenario.
Use the heuristic of making a supposition.
Assume 100 women, total weight 6000 instead of 6300.
Obvious the difference resulted from the loss of extra weight from men.
so number of men = (6300-6000)/10 = 30.
Judging by the nature of the 1st 2 qns, are these taken from some math olympiad training? -
Dear coffeecat
Thanks for the help.
All 3 question were from SA2, year 2009, Rulang Primary School, paper 2.
Regards
firebird -
firebird:
Hi Firebird,Dear mathsguru
Good morning
I am totally lost in the following first 2 maths. However, for the 3rd question, I managed to do on guess and check basis. Nevertheless, would be greatful if you could share a systematic method in solving the 3rd question:
1) Miss Wong had just read a novel with 1008 pages. How many digits were used to number the pages from 1 to 1008 in the novel?
2) Mr. Lee left Town M and travelled towards Town N at an average speed of 80 km/h. An hour later Mr. Ong left Town M and travelled towards Town N at an average speed of 100 km/h. Mr. Ong passed Town Q which was halfway between town M and town N 30 minutes earlier than Mr. Lee. If Mr. Ong reached Town N at 10pm, at what time did Mr. Lee leave town M for town N?
3) 100 people were having a health check up. Their average mass was 63kg. Given that the average mass of the women was 60kg and the average weight of the men was 70kg. How many men were there?
Many thanks
firebird
Here are my solutions. Hope they help!
MathsGuru
http://www.postimage.org/image.php?v=Ts7N7x0
http://www.postimage.org/image.php?v=gx8EfI0
http://www.postimage.org/image.php?v=gx8EkHi -
Hi Mathsguru,
Need your help with the below question.
Yusof had a total of 560 local and foreign stamps.After giving away 80% of the local stamps and 50% of the foreign stamp, he had 172 stamps left.
a) how many local stamps did he have at first ?
b) How many foreign stamps did he give away ?
Thank you very much!! -
YLH88:
This is a typical \"simultaneous equation\" question. The only technique tested in psle is the elimination method.Hi Mathsguru,
Need your help with the below question.
Yusof had a total of 560 local and foreign stamps.After giving away 80% of the local stamps and 50% of the foreign stamp, he had 172 stamps left.
a) how many local stamps did he have at first ?
b) How many foreign stamps did he give away ?
Thank you very much!!
you know
20 % of local stamp + 50% of foreign stamp = 172
therefore
40% of local stamp + 100% of foreign stamp = 344
100% of local stamp + 100% of foreign stamp = 560
60% of local stamp = 560 -344 = 216
etc etc.
Alternatively you can use model to represent but the manipulation is the same. -
YLH88:
Hi YLH88,Hi Mathsguru,
Need your help with the below question.
Yusof had a total of 560 local and foreign stamps.After giving away 80% of the local stamps and 50% of the foreign stamp, he had 172 stamps left.
a) how many local stamps did he have at first ?
b) How many foreign stamps did he give away ?
Thank you very much!!
Here's my solution. Hope it helps!
MathsGuru
http://www.postimage.org/image.php?v=aVCeouJ
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