Q&A - PSLE Math

[youngmum]

Dharma:

elkniwt:

[quote=\"tianzhu\"]Thank you for your help.


http://farm3.static.flickr.com/2547/3984945203_a6bc525a6c_o.jpg\">

Hi,

Is the answer 19:14?

If yes, this is how I got it, but I'm not sure if you can do the working this way in primary sch.

Unshaded = Area of triangle PRV + Area of triangle VSQ - overlap
= 1/2 x QR x PV + 1/2 x QR x VQ - 75
= 1/2 x 45 x 22 - 75
= 420
Shaded = Area of rect - unshaded
= 45 x 22 - 420
= 570
Hence ratio of shaded to unshaded is 570:420 = 19:14

The unshaded area = Area of 1/2 rect - 75 = 495 - 75 = 420
Shaded area : Unshaded area = (495 + 75) : 420 = 570 : 420 = 19:14[/quote] how the unshaded area = Area of 1/2 rect
i cannot see it

[small]

youngmum:

how the unshaded area = Area of 1/2 rect

i cannot see it

Hi youngmum,

Please invert the diagram and take a look, it will be more clear.

The base of two triangles is 45 cm and the height is 22cm, thus their area:

1/2 x 45 x 22 which will be same as half of rectangle (area of rectangle = 45 x 22 ).

[youngmum]

small:

Please invert the diagram and take a look, it will be more clear.
The base of two triangles is 45 cm and the height is 22cm, thus their area:
1/2 x 45 x 22 which will be same as half of rectangle (area of rectangle = 45 x 22 )

i cannot see it

[small]

Hi youngmum,


From our working, we knew the area for the two triangles is 1/2 x (45x22)

Let the area of big rectangle be 1 unit,which is 1 unit = (45 x 22)

Half rectangle =
= 1/2 x 1 unit
or
= 1/2 of ( 45x22 )

Hope this clear.


Don't worry too much on the method of solution, the most important thing is our child able to solve the question during the exam, it just that correct working will save some of their time which will allow them to have more time for other questions.

[Vanilla Cake]

Praise:

1) There are some black and white marbles in a bag. If 20 black marbles are removed from the bag, the total number of marbles left will be 7 times the number of black marbles left. If 50 white marbles are removed from the bag, the total number of marbles left will be 5 times the number of black marbles left. How many marbles are there in the bag?


2) 65% of the animals on a farm were cows and the rest were goats. When 240 more cows and goats were added to the farm, the percentage of cows increased by 20% and the number of goats doubled. How many goats were there on the farm at first.

3) The ratio of the number of pencils to the number of erasers in a box was 2 : 3. When 42 pencils were added and 15 erasers were removed, the ratio of the number of pencils to erasers became 3:4. How many erasers were there left in the box?

Quick one before I go to school. Wish every P6 student all the best in his/her PSLE 2009.

A1
Assume black be B and white be W.
Case 1
(B-20)/W = 1/6
W=6B-120
W+120=6B
1/3W +40=2B

Case 2
B/(W-50)=1/4
W-50=4B
1/2W-25 = 2B

1/3W+40=1/2W-25
1/2W-1/3W=65
1/6W=65
W=390
B=[1/2(390)-25]/2 = 85

Number of marbles in the bag is 390+85 = 475

A2
Before
Cows-> 65%
Goats->35%

After
Cows->120/100x 65% = 78%
Goats->35x2 = 70%

78-65=13
13+35=48
48%=240
1% = 5
35% = 175
Number of goats on the farm at first was 175

A3
P : E
2:3 (Before)

(2 units+42)/(3 units-15) = 3/4
9 units - 45 = 8 units + 168
1 unit = 213
3 units = 639
639-15=624
Number of erasers left in the box was 624

[James Ang]

James Ang:

Let me relate this \"story\" that I tell all my students. I was previously an AO in an airline company and I was in charge of purchasing/tenders. So this story comes from my own experience.

An airline company does not employ any \"cleaners\" on their payroll but their planes are always spanking, sparkling clean. Obviously the planes are not cleaned by pilots and air crew, so who clean the planes? Are \"cleaners\" important to keep the plane clean for the airline to continue to do a profitable business? (story to be continued after some forumers give their answers)

In reality, the cleaning of aircrafts is outsourced to a cleaning company by way of tender and contracts system. The cleaning work is done by third party (it doesn't matter who cleans it, can be a young or old cleaner, even a monkey if well trained!), but the cleanliness is checked by the airline staff/supervisor. The wisdom lies therein, who is more important, the cleaner or the checker? The right answer is the checker!

In the same way, there are \"two people\" doing every Maths problem all the time. One person who does the sum and the other who checks the sum for correct answer. Normally the person who does the sum is the student and the person who checks the sum is the teacher/parent/tutor. With the scientific calculator being introduced for PSLE Maths, the student can now also be promoted to become a \"checker\" as well as it is very easy and takes less than a minute to check answers with a calculator. Many problem sums can be checked for accuracy and correct answer simply by substitution of answer to check for correctness. That is the real power behind getting perfect scores for Maths sums consistently. Checking the answers! The student is the owner for both doing and checking the Maths sums.

I get all my PSLE students to check their answers using the powerful FX95SGplus Scientific calculator to solve for all Maths (and especially for secondary level Maths as well because of the \"equation\" mode) problems and they consistently score above 90. Many of them will score A* for tomorrow's Maths paper because of the good habit of \"checking answers with calculator\" they have picked up.

[atutor2001]

James Ang:

Many of them will score A* for tomorrow's Maths paper because of the good habit of \"checking answers with calculator\" .....

I think you have tackled only half of the problem. Checking alone cannot ensure correct answer because we will be blinded by silly mistakes; our eyes will fool us.

[myxpozay]

Praise:

1) There are some black and white marbles in a bag. If 20 black marbles are removed from the bag, the total number of marbles left will be 7 times the number of black marbles left. If 50 white marbles are removed from the bag, the total number of marbles left will be 5 times the number of black marbles left. How many marbles are there in the bag?

I saw this question a few weeks back using ratio to solve it

case 1: 20 black removed
b:w
1:6

case 2: 50 white are removed
b:w
1:4

Solve
B:W
1:6
+20 -50
----------
1 : 4

Re-writing using common multiples
B:W
4:6
+80 -50
------------
4 : 4


2u-->130
u-->65
7u-->475


the complete solution was found here

http://www.onsponge.com/forum/35-thinkingmathonsponge/859-ratio.html#871

[Muffins]

Hi myxpozay,


this question was also in ACS Prelim 2009 paper 2 Q48! Answer is correct by the way.

[Tang]

youngmum:

Dharma:

[quote=\"elkniwt\"]
Hi,

Is the answer 19:14?

If yes, this is how I got it, but I'm not sure if you can do the working this way in primary sch.

Unshaded = Area of triangle PRV + Area of triangle VSQ - overlap
= 1/2 x QR x PV + 1/2 x QR x VQ - 75
= 1/2 x 45 x 22 - 75
= 420
Shaded = Area of rect - unshaded
= 45 x 22 - 420
= 570
Hence ratio of shaded to unshaded is 570:420 = 19:14

The unshaded area = Area of 1/2 rect - 75 = 495 - 75 = 420
Shaded area : Unshaded area = (495 + 75) : 420 = 570 : 420 = 19:14

how the unshaded area = Area of 1/2 rect
i cannot see it [/quote]Unshaded Area = Area of 1/2 Rectangle - 75