Tutor MathsGuru: Ask me for your burning Maths questions!
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YLH88:
Hi YLH88,Hi Mathsguru, Vanilla Cake,
Thanks for the solution!
For the 2nd qn on the distance run, why is the total distance 10u - 3km + 1km and not 10u + 1km since David stopped 1 km before the finishing line ?
You are welcome!
From the question itself, it stated that David stopped 1 km before the finishing line and he ran 3 km less than twice the distance Ben ran.
We know that Ben had run 5 units from Ben ran 5 times as far as Alex before he stopped.
So, David ran 5 units x 2 = 10 units minus 3 km. But he stopped 1 km before the finishing line, therefore the length of the run must be 10 units minus 3 km + 1 km.
From the earlier calculation, 1 unit has been worked out to be 1.5 km.
10 units - 3 km + 1 km
= 10(1.5) km - 3 km + 1 km
= (15-3+1) = 13 km which was the length of the run. -
Hi firebird,
All your questions are from http://www.orlesson.org/orp/09Ma/2009-P6-Math-SA2-SCGS.pdf and some of them have been answered by Uncle Observer. Pls refer to them while waiting for Mathsguru's solutions.firebird:
This is a 2-mark question from Singapore Chinese Girls' School Paper 1 Q15. Four answer options are given for this question. Option (1) 40 min, Option (2) 50 min, Option (3) 60 min and Option (4) 100 min1) Alan completed a race in 1 hour 40 minutes. In the race, he ran at an average speed of 30 m/min from Point A to Point B and then ran back to from Point B to Point A at an average speed of 20 m/min. How long did he take to run back to Point A from Point B.
Fixed Distance or constant distance or common distance
Ratio of speed
Pt A to Pt B : Pt B to Pt A
30 : 20
3 : 2
Ratio of speed is inversely proportional to the ratio of time
Ratio of time
Pt A to Pt B : Pt B to Pt A
2 : 3
Time time taken to complete the race was 1 h 40 min = (60+40) min = 100 min. Total time (ratio) in terms of units = 2+3 = 5.
5 units = 100 min
1 unit = 20 min
From Point B to Point A, it took Alan 3 units = (3 x 20) min = 60 min which is Option (3).firebird:
This is a 3-mark question from paper 2 - Q6 from the same paper.2)The ratio of the amount of money Colin has to the amount of money Daniel has is 4:7. After each of them spends $28, their ratio becomes 3:7.Find the amount of money Colin has now.
Using ratio to solve.
Before
C : D
4 : 7
Multiply both sides by 4
16 : 28
Change
Each of them spends $28.
After
C : D
3 : 7
Multiply both sides by 3
9 : 21
Note that the difference for Colin = (16-9) = 7 units and
the difference for Daniel = (28-21) = 7 units
meaning that both difference are equal as they spend equal amount of money.
7 units = $28
Now, Colin has 9 units means 28/7x9 = $36firebird:
This is a 4-mark question from paper 2 - Q14 from the same paper.3) Mrs Lim bought some forks and spoons in the ratio of 4:3. Each spoon cost 50 cents more than each fork. If she spends $156 altogether and the amount she spent on the fork was $12 more than the amount she spent on spoons. How many forks and spoons did she buy?
Pls refer to http://2.bp.blogspot.com/_NGNaLTzN5_U/SrIXzZccQLI/AAAAAAAADqk/8w0na5ziEss/s1600-h/Maths0609SA2P2SCGSRatioQ14A.JPG.firebird:
This is a 4-mark question from paper 2 - Q15 from the same paper.4) 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?
Pls refer to http://4.bp.blogspot.com/_NGNaLTzN5_U/SrG9JlyKltI/AAAAAAAADps/RwzFeaqu_D8/s1600-h/Maths0609SA2P2SCGSFractionQ15A.JPG.firebird:
This is a 5-mark question from paper 2 - Q17 from the same paper.5) Ahmad and Halim together took 5 days to paint their house. If Ahamad and Halim work together for 2 days, followed by Ahamad working alone for 8 days, Halim will take 1 more day to complete the ramaining work. How long will Ahamad take to paint the house all by himself?
Pls refer to http://1.bp.blogspot.com/_NGNaLTzN5_U/SrG8lTC896I/AAAAAAAADpU/avMk0Drfs9k/s1600-h/Maths0609SA2P2SCGSRatesQ17A.JPG.firebird:
This is a 5-mark question from paper 2 - Q16 from the same paper.6) The figure below is made up of a circle, a triangle and two identical semi-circles. The diameter of the semi-circle is 4 cm. Find the area of the shaded regions.
Pls refer to http://1.bp.blogspot.com/_NGNaLTzN5_U/SrMyBXxSdlI/AAAAAAAADuE/NikqH4qQHjs/s1600-h/Maths0609SA2P2SCGSCircleQ16A.JPG. -
firebird:
Hi firebird,1) Tracy counted the number of 10cents coins, 20 cents coins ans 50 cents coins in her piggy bank. The number of 10cents 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 50cents coins, she had equal number of 10cents coins and 20 cents coins. The number of 50 cents 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?
This is a 5-mark question from Singapore Chinese Girls' School 2009 P6 Prelim Paper 2 Q18.
Pls refer to http://3.bp.blogspot.com/_NGNaLTzN5_U/SrG9I8OgCGI/AAAAAAAADpk/Bhcf1auBZqo/s1600-h/Maths0609SA2P2SCGSFractionQ18A.JPG. -
Dear Vanilla Cake
Good morning.
A lot of thanks. Thank you again.
firebird -
YLH88:
Hi YLH88,Hi Mathsguru, Vanilla Cake,
Thanks for the solution!
For the 2nd qn on the distance run, why is the total distance 10u - 3km + 1km and not 10u + 1km since David stopped 1 km before the finishing line ?
The total distance David ran was 3km short of twice Ben's distance (5units x 2). Hence, 10units - 3km = 12km is what David ran. Since he stopped 1km before the finishing line, the total distance is 12km + 1km = 13km.
Hope this clarifies...
Cheers,
MathsGuru -
Hi Mathsguru, Vanilla Cake,
OIC... Thank you! Now I understand
Sorry, 1 more question below need your expertise advise. :?
This question is from St Nich SA1 Paper 2 Qn 12 :
The figure below is made up of 2 squares and a rectangle. The ratio of the area of A to the area of B to the area of C is 9 : 4 :3.
The ratio of the unshaded part of B to the unshaded part of C is 4 : 1.
If the shaded part is 56 m sq, find the area of A that is not covered by B.
(ans is 105 cm sq)
http://www.postimage.org/image.php?v=aVxniQS
Thank you very much! -
YLH88:
In ratio stuff like constant difference or constant total are crucial.Hi Mathsguru, Vanilla Cake,
OIC... Thank you! Now I understand
Sorry, 1 more question below need your expertise advise. :?
This question is from St Nich SA1 Paper 2 Qn 12 :
The figure below is made up of 2 squares and a rectangle. The ratio of the area of A to the area of B to the area of C is 9 : 4 :3.
The ratio of the unshaded part of B to the unshaded part of C is 4 : 1.
If the shaded part is 56 m sq, find the area of A that is not covered by B.
(ans is 105 cm sq)
http://www.postimage.org/image.php?v=aVxniQS
Thank you very much!
Area of
A:__B : __C : Difference between B & C : unshaded B : unshaded C
9: ___4 : 3 :________________1
___________________________3 : 4 : 1
27: 12 : 9 :_________________3 : 4 : 1
(pardon the underscores they are used for alignment)
from this we know that
the shaded portion of B = 12-4 = 8 units which correspond to 56m^2
therefore difference between A & B is (27-12) * 7 -
firebird:
Hi Firebird,Dear Mathsguru
Good morning.
Kindly help me on the following maths:
1) Alan completed a race in 1 hour 40 minutes. In the race, he ran at an average speed of 30 m/min from Point A to Point B and then ran back to from Point B to Point A at an average speed of 20 m/min. How long did he take to run back to Point A from Point B.
This is a 2 mark question. Given answer 60 minutes. But I really do not know!
2)The ratio of the amount of money Colin has to the amount of money Daniel has is 4:7. After each of them spends $28, their ratio becomes 3:7.
Find the amount of money Colin has now. Given answer $36.
3) Mrs Lim bought some forks and spoons in the ratio of 4:3. Each spoon cost 50 cents more than each fork. If she spends $156 altogether and the amount she spent on the fork was $12 more than the amount she spent on spoons. How many forks and spoons did she buy?
Given answer 42.
4) 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?
Given answer 66.
5) Ahmad and Halim together took 5 days to paint their house. If Ahamad and Halim work together for 2 days, followed by Ahamad working alone for 8 days, Halim will take 1 more day to complete the ramaining work. How long will Ahamad take to paint the house all by himself?
Given answer 17 1/2 days
6) The figure below is made up of a circle, a triangle and two identical semi-circles. The diameter of the semi-circle is 4 cm. Find the area of the shaded regions.
I apologise for not inserting the diagram here. Kindly, help me. The question is from S'pore Girls School Preliminary Exam 2009 Question number 16 paper 2.
Given answer 30.8cm2. I really do not know were to start for this question.
Very sorry for the inconveience casused.
Reagrds
firebird
Here're my solutions. Hope they are clear enough!
MathsGuru
http://www.postimage.org/image.php?v=gx7MMx0
http://www.postimage.org/image.php?v=gx7MP19
http://www.postimage.org/image.php?v=gx7MRwi
http://www.postimage.org/image.php?v=gx7MU0r
http://www.postimage.org/image.php?v=gx7MWvA
http://www.postimage.org/image.php?v=gx7MY_J -
firebird:
Hi Firebird,Dear mathsguru
Please help me on this maths, which i have forgot to post earlier:
1) Tracy counted the number of 10cents coins, 20 cents coins ans 50 cents coins in her piggy bank. The number of 10cents 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 50cents coins, she had equal number of 10cents coins and 20 cents coins. The number of 50 cents coins now formed 40% of the remaining number of coins.
a) How many 10 cents coins did tracy have at first? Given ans 90
b) How much did she spend in all? given ans $16.80
Many thanks
firebird
Here's my solution.
Cheers,
MathsGuru
http://www.postimage.org/image.php?v=gx7NJor -
YLH88:
Hi YLH88,Hi Mathsguru, Vanilla Cake,
OIC... Thank you! Now I understand
Sorry, 1 more question below need your expertise advise. :?
This question is from St Nich SA1 Paper 2 Qn 12 :
The figure below is made up of 2 squares and a rectangle. The ratio of the area of A to the area of B to the area of C is 9 : 4 :3.
The ratio of the unshaded part of B to the unshaded part of C is 4 : 1.
If the shaded part is 56 m sq, find the area of A that is not covered by B.
(ans is 105 cm sq)
http://www.postimage.org/image.php?v=aVxniQS
Thank you very much!
You're most welcome. Glad you understand it!
Here's the solution!
MathsGuru
http://www.postimage.org/image.php?v=PqLImQJ
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