Q&A - PSLE Math

[lantian]

Cost for 4 hours = $(3*4 +5) = $17


Hi Chiefkiasu, I think this question if from CHS P6 Prelm 2006

At first glance, the answer is $17.But it's a trick to lead you down a slippery slope.At P6 level, it's difficult to find questions requiring only simple substitution.

If the question is phrased as The cost for renting a bicycle is given by C=(3d+5) where d is the number of hours, then your answer is spot on.

For d hours, the cost is C = $(3d+5)
For 1 hour, the cost is C = $(3d+5)/d
Therefore for 4 hours, the cost C = $4(3d+5)/d

[lantian]

ChiefKiasu:

lantian:

Hi, Hope this helps...

Ahhh... cunning!

Hi, Chiefkiasu, cunning is not a good word.

I am just a simple minded man who believe that kids should be kids.They should have time to explore their early lives and enjoy their childhoods.They should be no forced feeding to add more misery to their carefree days.My fondest memory of my my childhood days was playing marbles, flying kites and catching spiders.

Best Wishes

[ChiefKiasu]

lantian:

...At first glance, the answer is $17.But it's a trick to lead you down a slippery slope.At P6 level, it's difficult to find questions requiring only simple substitution...

Now that's some trick ! Then again, I still maintain that the question is ambiguous.

Is my answer to the 2nd question correct?

[ChiefKiasu]

lantian:

... Hi, Chiefkiasu, cunning is not a good word...

That depends on how it is used. In this case, it is out of respect for the cleverness of whoever thought of that answer. No malice intended.

[lantian]

ChiefKiasu:

lantian:

...At first glance, the answer is $17.But it's a trick to lead you down a slippery slope.At P6 level, it's difficult to find questions requiring only simple substitution...

Now that's some trick ! Then again, I still maintain that the question is ambiguous.

Is my answer to the 2nd question correct?

Hi Chiefkiasu

I shall try to explain as follows

If it's 3 hours, then the rental is (3*3+5)
For 1 hour, the cost is (3*3+5)/3
For 4 hours, the cost is 4(3*3+5)/3

If it's 5 hours , then the rental is (3*5+5)
For 1 hour, the cost is (3*5+5)/5
For 4 hours, the cost is 4(3*5+5)/5

Working on Q2, not so fast, oldman already.


Best Wishes

[lantian]

ChiefKiasu:

lantian:

... Hi, Chiefkiasu, cunning is not a good word...

That depends on how it is used. In this case, it is out of respect for the cleverness of whoever thought of that answer. No malice intended.

Hi Chiefkiasu

Why bother about little things in life?Tomorrow may never come.

[Priskhipo]

Hi KiasuChief,


Refering to Suiyuan's Question on 4 squares and a rectangle within them.
Really have to applaud those members for coming up with creative solution for this question and it is correct in a way because it will not put to test the relative of the sides of smaller square to the biggier square.

But it is not possible for the area of 4 squares to be 80 cm2 if the perimeter of the rectangle is 20 cm.

If someone happen to use strategy of Guess and Check or quadratic equation, he would not be able to find any solution.

See Below:
Solution 1: (Guess and Check)

1 length and 1 breadth = 20 ÷ 2 = 10

L + B = 10 cm\t

http://www.postimage.org/image.php?v=Pq1rPQVr

The most squarish rectangle ABCD is 5cm by 5 cm
Area of 4 such squares = 4 x 25 = 100 cm2 (minimum possible total area)

The thinnest rectangle ABCD is 9.9999... cm (round off to 10cm).. x 0.000...001(round off to zero)
= the area of 2 smaller squares is almost 0 cm2
The area of the 2 bigger squares
= 2 x 10 x10 = 200 cm2 (maximum possible total area)

Solution 2: (Using Quadratic Equation to find x)
Breadth = x and Length = (10 – x)
Quadratic Equation = 2xx + 2(10 –x)(10 - x) = 80 (No possible solution)

Sorry, can't superscript. So x multiple by x = xx and so on .
[/list]

[lizawa]

[quote] However, are children in P6 taught how to do an expansion of (x+y)^2 ? Without that step, it is impossible to solve the equation.[/quote]
Yes, first topic in P6 Maths text, algebra.

But I think that the solution provided by lantian is must better.

[ChiefKiasu]

Priskhipo:

...But it is not possible for the area of 4 squares to be 80 cm2 if the perimeter of the rectangle is 20 cm...

Yes, we will not be able to find the answer if we attempt to first find the values of x and y, the sides of the original rectangle, ie.
x + y = 10
x^2 + y^2 = 40
=> x^2 + (10 - x)^2 = 40
=> x^2 + (100 - 20x + x^2) = 40
=> 2x^2 - 20x + 60 = 0
=> x^2 - 10x + 30 = 0

We cannot solve for x because x is not an integer.

lizawa's method solves this problem because x * y is an integer.

But lantian's method is the best.

[Priskhipo]

ChiefKiasu:

Priskhipo:

...But it is not possible for the area of 4 squares to be 80 cm2 if the perimeter of the rectangle is 20 cm...

Yes, we will not be able to find the answer if we attempt to first find the values of x and y, the sides of the original rectangle, ie.
x + y = 10
x^2 + y^2 = 40
=> x^2 + (10 - x)^2 = 40
=> x^2 + (100 - 20x + x^2) = 40
=> 2x^2 - 20x + 60 = 0
=> x^2 - 10x + 30 = 0

We cannot solve for x because x is not an integer.

lizawa's method solves this problem because x * y is an integer.

But lantian's method is the best.

Hi,

I agree lantian's method is best in this case. It illustrates the logic clearly.
(It does not have to check x^2 + y^2 = 40 cm^2 is correct or not.)

I'm only worry that should a student chooses to solve it with Guess and Check strategy, he would not be able to yield an answer because of the error in this question.

A question should yield the same answer no matter which method a student uses.

Below images illustrate why (x^2 + y^2) should not be less than 50 cm^2


http://www.postimage.org/image.php?v=aV1uDemr


http://www.postimage.org/image.php?v=gx1ihypA

The quadratic equation gives a constraint (10 cm) to the relationship of the x and y, therefore it finds x, a sq root of a negative integer (not a real number) if given the total area x^2 & y^2 is 40 cm^2. Hence an impossible case.