3rd Annual Mathlympics - 2010 Prelim round

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3rd Annual Mathlympics - 2010 Prelim round

Postby Vanilla Cake » Fri Aug 27, 2010 5:49 pm

Hi Uncle Tianzhu & Uncle Dharma + other helpful souls,

My younger sister (P5) took the 3rd Annual Mathlympics - 2010 Prelim round, today.Question papers are not allowed to take back(not sure about other schools but her school does not allow), so the following questions are not in exact words. She managed to recall 9 out of 28 questions. Hope that you don't mind and pls help to provide their respective solutions although this post is not supposed to be in PSLE Maths thread.Thanks in advance and pls don't get angry with my post.BTW, I cannot understand how my younger sister had so much energy and time to remember and solve these questions at the same time during stressful examination conditions?

2-mark question
P^2 = pxp
Find (½+1/½)^2

2-mark question
Diagram shows a triangle ABC. On the left side, A,D,E,B. Base is BC.On the right hand side, A,F,G,C.From point D, a line is drawn down to the base.Another line from D is joined to G and from point G, a line is drawn to join the base.This forms a 4-side shaded area.
Hope that you are able to visualise.

D, E, F and G splits each line into 3 equal portions. Find the fraction of the shaded area to the area of the triangle ABC.

2-mark question
I am thinking of a fraction.The sum of the numerator and the denominator is 43. When I add 13 to the denominator, the fraction is 3/5. Find the fraction I am thinking of.

2-mark question
The diagonal of a larger square is 2 times the diagonal of a small square. Find the percentage of the small square to the bigger square.

4-mark question
m^2=(123456^2)+123456+123457
Find the value of m.

4-mark question
A pest inspector killed 15 spiders and cockroaches. The number of the spiders' legs is 36 more than the number of cockroaches' legs. Find the number of cockroaches killed.

5-mark question
This is question 21.
I think of a number. When I add 1 to the number, the new number is divisible by 2,3,4,5,6 and 7. Find the largest possible number I am think of.

5-mark question
This is question 26.
X is a multiple of 11. When 1 is added to X, it is the square of y.
(a) Write an algebraic equation.
(b) Find the smallest possible values of x and y.

5-mark question
This is question 28 (Last question).
Downhill: 72 km/h
Ground level: 63 km/h
Uphill: 56 km/h

Car travels from Town A to Town B in 4 hours. It returns to Town A using the same route in 4 h 40 min. What is the distance between Town A and Town B?

Hi mods,
Opps, I had pressed the wrong button while posting. This is supposed to be under PSLE Maths thread and pls help to merge this post.
Thanks.

Vanilla Cake
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Postby tianzhu » Sat Aug 28, 2010 6:49 am

Hi VC

I am sure members are happy to see you back again as you’ve been away for some time.

I am also happy to see PC doing well in Maths.

Best wishes

tianzhu
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Re: 3rd Annual Mathlympics - 2010 Prelim round

Postby Dharma » Sat Aug 28, 2010 9:42 am

Vanilla Cake wrote:Hi Uncle Tianzhu & Uncle Dharma + other helpful souls,

My younger sister (P5) took the 3rd Annual Mathlympics - 2010 Prelim round, today.Question papers are not allowed to take back(not sure about other schools but her school does not allow), so the following questions are not in exact words. She managed to recall 9 out of 28 questions. Hope that you don't mind and pls help to provide their respective solutions although this post is not supposed to be in PSLE Maths thread.Thanks in advance and pls don't get angry with my post.BTW, I cannot understand how my younger sister had so much energy and time to remember and solve these questions at the same time during stressful examination conditions?

2-mark question
P^2 = pxp
Find (½+1/½)^2

2-mark question
Diagram shows a triangle ABC. On the left side, A,D,E,B. Base is BC.On the right hand side, A,F,G,C.From point D, a line is drawn down to the base.Another line from D is joined to G and from point G, a line is drawn to join the base.This forms a 4-side shaded area.
Hope that you are able to visualise.

D, E, F and G splits each line into 3 equal portions. Find the fraction of the shaded area to the area of the triangle ABC.

2-mark question
I am thinking of a fraction.The sum of the numerator and the denominator is 43. When I add 13 to the denominator, the fraction is 3/5. Find the fraction I am thinking of.

2-mark question
The diagonal of a larger square is 2 times the diagonal of a small square. Find the percentage of the small square to the bigger square.

4-mark question
m^2=(123456^2)+123456+123457
Find the value of m.

4-mark question
A pest inspector killed 15 spiders and cockroaches. The number of the spiders' legs is 36 more than the number of cockroaches' legs. Find the number of cockroaches killed.

5-mark question
This is question 21.
I think of a number. When I add 1 to the number, the new number is divisible by 2,3,4,5,6 and 7. Find the largest possible number I am think of.

5-mark question
This is question 26.
X is a multiple of 11. When 1 is added to X, it is the square of y.
(a) Write an algebraic equation.
(b) Find the smallest possible values of x and y.

5-mark question
This is question 28 (Last question).
Downhill: 72 km/h
Ground level: 63 km/h
Uphill: 56 km/h

Car travels from Town A to Town B in 4 hours. It returns to Town A using the same route in 4 h 40 min. What is the distance between Town A and Town B?

Hi mods,
Opps, I had pressed the wrong button while posting. This is supposed to be under PSLE Maths thread and pls help to merge this post.
Thanks.


Hi Vanilla Cake,

Did it in a rush. Please check.

2-mark question
P^2 = pxp
Find (½+1/½)^2

(1/2 + 1/1/2)^2
=(1/2 + 2) ^2
= (5/2)^2
= 25/4

2-mark question
Diagram shows a triangle ABC. On the left side, A,D,E,B. Base is BC.On the right hand side, A,F,G,C.From point D, a line is drawn down to the base.Another line from D is joined to G and from point G, a line is drawn to join the base.This forms a 4-side shaded area.
Hope that you are able to visualise.

D, E, F and G splits each line into 3 equal portions. Find the fraction of the shaded area to the area of the triangle ABC.

Shaded area = 1 - (2/3 x 1/3) - (1/3 x 1/6) - (2/3 x 1/3) = 1/2
Fraction of shaded area = 1/2


2-mark question
I am thinking of a fraction.The sum of the numerator and the denominator is 43. When I add 13 to the denominator, the fraction is 3/5. Find the fraction I am thinking of.

A/B = ?
A + B = 43
B + 13 => A/ (B + 13) = 3/5
5A = 3B + 39 ---------------( 1)
5A = 215 – 5B --------------(2)

3B + 39 = 215 – 5B
8B = 176
B = 22
A = 43 – 22 = 21
A/B = 21/22


2-mark question
The diagonal of a larger square is 2 times the diagonal of a small square. Find the percentage of the small square to the bigger square.

If diagonal of large square = 4D & diagonal of small square = 2D
Area of large square = 2 x ½ x 4D x 2D = 8D^2
Area of small square = 2 x ½ x 2D x D = 2D^2

% = 1/4

4-mark question
m^2=(123456^2)+123456+123457
Find the value of m.

M^2 = (123456^2) + 123456 + 123456 + 1
M^2 = 123456( 123456 + 1 + 1 ) + 1
M^2 = (123456 x 123458) + 1
M^2 = (123457 – 1)(123457 + 1) + 1
M^2 = (123457^2) – 1 + 1
M = 123457



4-mark question
A pest inspector killed 15 spiders and cockroaches. The number of the spiders' legs is 36 more than the number of cockroaches' legs. Find the number of cockroaches killed.

Spider = 8 legs
Cockroach = 6 legs

S + C = 15 ------------------- (1)
8S – 6C = 36 ----------------( 2)
6S + 6C = 90 ----------------(3) = (1) X 6

(2) + (3)
14S = 126
S = 9
C = 15 – 9 = 6


5-mark question
This is question 21.
I think of a number. When I add 1 to the number, the new number is divisible by 2,3,4,5,6 and 7. Find the largest possible number I am think of.

Is it the largest or smallest?
Smallest = 209 (LCM of nos. + 1 = 210)

5-mark question
This is question 26.
X is a multiple of 11. When 1 is added to X, it is the square of y.
(a) Write an algebraic equation.
(b) Find the smallest possible values of x and y.

a) Y^2 = 11X + 1
b) Y = 10; X = 9


5-mark question
This is question 28 (Last question).
Downhill: 72 km/h
Ground level: 63 km/h
Uphill: 56 km/h

Car travels from Town A to Town B in 4 hours. It returns to Town A using the same route in 4 h 40 min. What is the distance between Town A and Town B?

(A/56 + B/63 + C/72) + (A/72 + B/63 + C/56) = 26/3
2/63 (A + B + C ) = 26/3
A + B + C = 26/3 X 63/2 = 273
Last edited by Dharma on Sat Aug 28, 2010 11:19 am, edited 1 time in total.

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Postby tianzhu » Sat Aug 28, 2010 11:04 am

5-mark question
This is question 26.
X is a multiple of 11. When 1 is added to X, it is the square of y.
(a) Write an algebraic equation.
(b) Find the smallest possible values of x and y.

a) Y^2 = 11X + 1
b) Y = 12; X = 13


Hi Dharma

Good Morning

For part (b)

(11*9) ----99
99+1 --- 100

y=10
x=9

Best wishes

tianzhu
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Postby Dharma » Sat Aug 28, 2010 11:18 am

tianzhu wrote:
5-mark question
This is question 26.
X is a multiple of 11. When 1 is added to X, it is the square of y.
(a) Write an algebraic equation.
(b) Find the smallest possible values of x and y.

a) Y^2 = 11X + 1
b) Y = 12; X = 13


Hi Dharma

Good Morning

For part (b)

(11*9) ----99
99+1 --- 100

y=10
x=9

Best wishes


Good morning Tianzhu,

Thanks for the correction.

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Postby tianzhu » Sat Aug 28, 2010 11:37 am

Hi Dharma

I am clueless about competition Maths.

Judging from the solutions you’ve given, I think those kids taking part in competitions would be specially selected and trained to understand more advanced concepts and algebra.It's not easy for 11/12 yrs old kids, they must have strong interest in Maths.

Best wishes

tianzhu
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Postby Dharma » Sat Aug 28, 2010 3:41 pm

tianzhu wrote:Hi Dharma

I am clueless about competition Maths.

Judging from the solutions you’ve given, I think those kids taking part in competitions would be specially selected and trained to understand more advanced concepts and algebra.It's not easy for 11/12 yrs old kids, they must have strong interest in Maths.

Best wishes


These kids have special training to handle Maths Olympiad kind of questions. Strong interest and passion for Maths is crucial.

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3rd Annual Mathlympics - 2010 Prelim round

Postby Vanilla Cake » Sat Aug 28, 2010 4:32 pm

Dharma wrote:Hi Vanilla Cake,
Did it in a rush. Please check.

Hi Uncle Dharma,
Pls refer to my comments.Thanks.

Vanilla Cake wrote:2-mark question
Diagram shows a triangle ABC. On the left side, A,D,E,B. Base is BC.On the right hand side, A,F,G,C.From point D, a line is drawn down to the base.Another line from D is joined to G and from point G, a line is drawn to join the base.This forms a 4-side shaded area.
Hope that you are able to visualise.
D, E, F and G splits each line into 3 equal portions. Find the fraction of the shaded area to the area of the triangle ABC.

Dharma wrote:Shaded area = 1 - (2/3 x 1/3) - (1/3 x 1/6) - (2/3 x 1/3) = 1/2
Fraction of shaded area = 1/2

My previous description of the diagram is not clear enough.The line that is drawn from point G to the base is a slanted and not straight line. Sorry for the wrong information given in the earlier post. The answer that I work out is 4/9. Pls advise if this is correct?

Vanilla Cake wrote:5-mark question
This is question 21.
I think of a number. When I add 1 to the number, the new number is divisible by 2,3,4,5,6 and 7. Find the largest possible number I am think of.

There is additional information in the question. It should be:"I think of a 4-digit number. When I......................".

Dharma wrote:Is it the largest or smallest?
Smallest = 209 (LCM of nos. + 1 = 210)

It's the largest number. My answer is 9659 and pls confirm if this is correct or not?

Vanilla Cake wrote:5-mark question
This is question 26.
X is a multiple of 11. When 1 is added to X, it is the square of y.
(a) Write an algebraic equation.
(b) Find the smallest possible values of x and y.

Dharma wrote:a) Y^2 = 11X + 1
b) Y = 10; X = 9

Pls check as my answers are :
a) Y^2=X+1
b) Y=10 and X=99

tianzhu wrote:Judging from the solutions you’ve given, I think those kids taking part in competitions would be specially selected and trained to understand more advanced concepts and algebra.It's not easy for 11/12 yrs old kids, they must have strong interest in Maths.

Hi Uncle Tianzhu and Uncle Dharma,
For my younger sister's school, anyone can signup for the Maths competition with or without training.Her training in school was only 10 sessions x 1.5 hours = 15 hours and definitely not enough time to learn such advanced concepts and techniques to tackle such competitions. To be honest, it's not really strong interest in Maths but my younger sister hopes that such competition will help her to handle PSLE 2011 Maths.You know that nowadays ,PSLE Maths is much more difficult than the one that I took in 2008.So, she has to work hard for PSLE 2011 Maths.Thanks for both your helpful replies and feedback.

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Postby tianzhu » Sat Aug 28, 2010 5:03 pm

Hi VC

It's the largest number. My answer is 9659 and pls confirm if this is correct or not?


I think your answer is logical.

LCM of 2, 3, and 4,5,6,7 is 420
Find the highest 4 digit multiple of 420 which is 9660
Therefore 9659 is a logical answer.

Pls check as my answers are :
a) Y^2=X+1
b) Y=10 and X=99

Yes, you are correct.

I believe exposure to competition Maths will definitely helps PC in PSLE Maths.

Best wishes

tianzhu
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Postby Vanilla Cake » Sun Aug 29, 2010 10:34 am

Solutions from Uncle Observer's blog for some questions from 3rd Annual Mathlympics - 2010 Prelim round.

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