Q&A - PSLE Math

[tianzhu]

adanial:

Hi Tianzhu, Ksi,
Ive checked the paper again... the numbers are correct. I'm puzzled how did the teacher solve this one.. lol
thank for the help.

Hi adanial

Based on the original question, you can still arrive at a solution, however it defies logic.

Consider a group of 3 TV, 2 fans and 4 WM.

The cost per group is (3*1350) + (2*102) + (4*640) or 4050+204+2560.
This adds up to $6814 per group.

34070/6814 --- 5
Hence, you’ve 5 groups.
This means the shop sold 15 TV, 10 fans and 20 WM.

3 units ----- 45
4 units ----- 60

The shop had 60 items in the beginning.
3 parts or 36 are for TV, leaving a remainder of 24 for fans and WM.
1/8 of this remainder are for fans, this means 3 fans and the remaining 21 are for WM.

Here we’ve an awkward situation where the number of fans sold (10) is more than the number of fan in the store (3).

If you change 3/5 to 1/3 and 12.5% to 25%, the question will be more logical.

Best wishes

[Concerndad]

2/5 x 100% = 40% (% of TV)

100% -40% = 60% (%of remainder)
12.5% x 60% = 7.5% (% of fans)
60% - 7.5% = 52.5% (% of washing machines wm)

3 x 1350 = 4050 (3units of tv)
2 x 102 = 204 (2units of fans)
4 x 640 = 2560 (4units of wm)
4050 +204 + 2560 = 6814

34070/ 6814 = 5 (5sets)

3units+2units+4units =9units
9x5=45 (total no. of items sold off during sales)

3units - 45
1 units - 15
4units - 60 (total items in the stores)

52.5% of 60 = 31.5 ?? (Hmm…paiseh…is there something wrong in the question?)



Question 2

1st day - 20%
2nd day - 60
total for 1st and 2nd days - 20% + 60

2units -> 20% + 60 (if can draw model to show will be clearer)
1 unit -> 10% + 30
7units -> 70% + 210

therefore 30% -> 210
10% -> 210/3 = 70
100% -> 70 x 10 = 700

the jigsaw puzzle consist of 700pcs.

[adanial]

ksi:

adanial:

Hi Tianzhu, Ksi,
Ive checked the paper again... the numbers are correct. I'm puzzled how did the teacher solve this one.. lol
thank for the help.

Hi adaniel, do you know the answer for this question?

Hi Tianzhu, the answer is 21

[linden2000]

Alternative solution to Q2


1st day
Completed - 2units
Uncompleted - 8units
Total 10 units

2nd day
Completed - 2 units
Uncompleted - 5 units
Total 7 units

Since the total number of pieces is unchanged, equate total units on both days to a common number (lowest common multiple).

So
1st day
Completed 2x7=14
uncompleted 8x7=56
total 70

2nd day
Completed 2x10=20
uncompleted 5x10=50
total 70

Change in number completed =20-14=6
so 6 units = 60
1 unit = 10
Total number of pieces = 70 units = 70x10= 700

[blitz]

Can some kind soul please help with the following?


http://img.photobucket.com/albums/v257/tbctbc/mathq.jpg\">
Sorry, I omitted the Y when drawing. It is above T.

THe above figure shows a rectangle PQRS. PYR is a straight line and XYZ is parallel to SRT. Given that PX=10cm, TR=9cm and ZR =4cm, find the shaded area of rectangle XYTS.

[CJ-2011]

Any kind soul can explain the rationale behind the solution for question PSP102, pg 368 of "Problem Solving Processes in Maths (New Syllabus)" by Fabian Ng ?


The problem is listed below :-

At 0800, Noel left town A for town B while Jane left town B for town A. At 1600 their cars passed each other. 5 hour later Jane reached town A but Noel was 240km away from town B,
a) How long after they start before they passed each other
b)Find the distance between the two towns

Solution :
a) 1600 - 0800 = 0800
Each driver had driven for 8 hr when they passed each other.

b) 240 / (8-5) = 80
The total speed of the two drivers was 80 km/h

80 x 8 = 640
The two towns was 640 km apart
----------------------------------------------------------------
I cannot comprehend and explain the part (b) on total speed. Is this some form of relative speed ? Is the concept of total speed taught in school ?

Thanks

[dovetail]

blitz:

Can some kind soul please help with the following?


http://img.photobucket.com/albums/v257/tbctbc/mathq.jpg\">
Sorry, I omitted the Y when drawing. It is above T.

THe above figure shows a rectangle PQRS. PYR is a straight line and XYZ is parallel to SRT. Given that PX=10cm, TR=9cm and ZR =4cm, find the shaded area of rectangle XYTS.

first you need to identify that triangle PYX is similar to triangle YRT.
Reason: observe that the angles in the 2 triangles are all the same size.

Now, use ratio

PX/YT = XY/TR
10/4 = XY/9
XY = 90/4

Area of XYST = XY * 4
= 90/4 * 4
= 90

Ans. 90 cm square.

[adanial]

linden2000:

Alternative solution to Q2


1st day
Completed - 2units
Uncompleted - 8units
Total 10 units

2nd day
Completed - 2 units
Uncompleted - 5 units
Total 7 units

Since the total number of pieces is unchanged, equate total units on both days to a common number (lowest common multiple).

So
1st day
Completed 2x7=14
uncompleted 8x7=56
total 70

2nd day
Completed 2x10=20
uncompleted 5x10=50
total 70

Change in number completed =20-14=6
so 6 units = 60
1 unit = 10
Total number of pieces = 70 units = 70x10= 700

Hi,

thank you so much !

[blitz]

dovetail:

blitz:

Can some kind soul please help with the following?


http://img.photobucket.com/albums/v257/tbctbc/mathq.jpg\">
Sorry, I omitted the Y when drawing. It is above T.

THe above figure shows a rectangle PQRS. PYR is a straight line and XYZ is parallel to SRT. Given that PX=10cm, TR=9cm and ZR =4cm, find the shaded area of rectangle XYTS.

first you need to identify that triangle PYX is similar to triangle YRT.
Reason: observe that the angles in the 2 triangles are all the same size.

Now, use ratio

PX/YT = XY/TR
10/4 = XY/9
XY = 90/4

Area of XYST = XY * 4
= 90/4 * 4
= 90

Ans. 90 cm square.

Wow, Dovetail. :rahrah: Thanks so much! I never thought of using ratio to find area. Do they really give such difficult questions for PSLE?

[corneyAmber]

Blitz, this question is not the ultimate tough, it is just using the similar triangles concept and get ratio to find the sides, hence area. The more difficult ones are those you need to bend and twist the pictures to fit into a certain form to get the answers which needs some lateral thinking.....