Q&A - PSLE Math

[Tang]

Dharma:

Drdj:

Hi there,


Please help me with the following :

NanHua Prelim 2008

Qn 24
15 cats can catch 15 rats in 15 minutes. How long does it take 60 cats to cath 60 rats? [Ans = 15 mins - how do you know which qty to stay constant/change]

Thanks in advance

15 cats - 15 rats - 15 mins
1 cat - 15 rats - 225 mins
1 cat - 60 rats - 900 mins
60 cats - 60 rats - 900/60 = 15 mins
(Only change 1 independent variable at a time)

15 cats 15 rats 15 min
1 cat 1 rat also 15 min
Hence 60 cats 60 rats also 15 min

[Tang]

Tang:

Dharma:

[quote=\"Drdj\"]Hi there,


Please help me with the following :

NanHua Prelim 2008

Qn 24
15 cats can catch 15 rats in 15 minutes. How long does it take 60 cats to cath 60 rats? [Ans = 15 mins - how do you know which qty to stay constant/change]

Thanks in advance

15 cats - 15 rats - 15 mins
1 cat - 15 rats - 225 mins
1 cat - 60 rats - 900 mins
60 cats - 60 rats - 900/60 = 15 mins
(Only change 1 independent variable at a time)

15 cats 15 rats 15 min
1 cat 1 rat also 15 min
Hence 60 cats 60 rats also 15 min[/quote]15 cats 15 min

60 cats, the number of min will be less (Multiply by 15/60 - Original number of cats / New number of cats).
60 rats, the number of min will be more, since more rats to catch (Multiply by 60/15 - New number of rats / Original number of rats)

So 60 cats to catch 60 rats will require 15 x 15/60 x 60/15 = 15 min.

[Dharma]

Drdj:

Hi there,


Please help me with the following :

Misc
David paints once every 2 days. Larry paints once every 3 days.
If the 2 men met on 28th May, what is the earliest date David has to start work? [Answer = 24th May]

Thanks in advance

The underlying assumption is both David and Larry met for the 1st time on 28 May.

If the assumption is not true, they would have met 6 days before i.e. on 22 May (LCM of 2 and 3)

Since the assumption holds, then the earliest David starts work is on 24 May (2 days after 22 May)

[Andaiz]

Drdj:

Hi there,


Please help me with the following :

Misc
David paints once every 2 days. Larry paints once every 3 days.
If the 2 men met on 28th May, what is the earliest date David has to start work? [Answer = 24th May]

Thanks in advance

I would have assumed too that they've met for the first time on 28th May.
Larry would have worked on 28-3 i.e. 25th; and 25-3 i.e., 22nd.

With David painting every 2 days, he'd have worked 28th, 26th, or 24th or 22nd.

If they have never met previously, David's earliest date he could have started work is 24th.

We used to do the LCM way but now its modelling eh? I'd try with the number line


David 22_________ 24 _______26___________28
Larry 22_______________25_______________ 28

[enoawng]

tianzhu:

Thank you for your help.


RGPS SA2 2008 Q43.


http://www.postimage.org/

3 plane of waters
1st plane has 1 cube
2nd plane has 3 cubes
3rd plane has 6 cubes and 352cm3

2xtimes third plane = 768cm3 + 4 cubes
12cubes + 2x352cm3 is the same as 768cm3 + 4 cubes

8 cubes = 64cm3
1 cube = 2x2x2cm = 8 cm3

Hence height of cube = 2cm ; height of tray = 6cm

[Tang]

[Moderator's note: Topics merged.]


Can't recall if I have posted Uncle Observer's Blog on P6 Maths Questions here previously.

http://prischoolmaths.blogspot.com/


Anyway the answers have been released and you may want to check.


http://prischoolmaths.blogspot.com/2009/07/maths-volume_18.html

http://prischoolmaths.blogspot.com/2009/07/maths-percentage_2485.html

http://prischoolmaths.blogspot.com/2009/07/maths-percentage_4168.html

http://prischoolmaths.blogspot.com/2009/07/maths-percentage_17.html

http://prischoolmaths.blogspot.com/2009/07/maths-whole-number_16.html

http://prischoolmaths.blogspot.com/2009/07/maths-whole-number_18.html

http://prischoolmaths.blogspot.com/2009/07/maths-fraction_19.html

http://prischoolmaths.blogspot.com/2009/07/maths-fraction.html

http://prischoolmaths.blogspot.com/2009/07/maths-rates.html

http://prischoolmaths.blogspot.com/2009/07/maths-speed_22.html

http://prischoolmaths.blogspot.com/2009/07/maths-speed_18.html

http://prischoolmaths.blogspot.com/2009/07/maths-average.html

http://prischoolmaths.blogspot.com/2009/07/maths-circles.html

http://prischoolmaths.blogspot.com/2008/11/maths-challenging_01.html

[N3SKiasu]

Hi I have one Maths question but the answer kit used Algebra to solve, hence wld like to kw if anyone cld help with using Models.


Mr Tan had some apples and oranges in his shop. 30% of the fruits were oranges. He sold 70 apples and bought another 170 oranges. Then 65% of the fruits were oranges. How many apples did he have at first?

Thks in advance!

[Tang]

N3SKiasu:

Hi I have one Maths question but the answer kit used Algebra to solve, hence wld like to kw if anyone cld help with using Models.


Mr Tan had some apples and oranges in his shop. 30% of the fruits were oranges. He sold 70 apples and bought another 170 oranges. Then 65% of the fruits were oranges. How many apples did he have at first?

Thks in advance!

After
-----
Oranges New -- 3 units + 170 (= 65% -- 13 small units)
Apples New -- 7 units - 70 (=35% -- 7 small units

Before
--------
Orange -- Draw 3 units
Apples -- Draw 7 units

Apples -- Shade out 10 in each of the 7 units (to represent 70 apples sold)
Orange -- Shade out 10 in each of the 3 units, then add 170 oranges. You get 3 small units + 3 x 10 + 170 = 13 small units

10 small units --> 3 x 10 + 170 = 200

1 small unit --> 200 / 10 = 20

Apples --> 20 x 7 + 70 = 210 apples.

[faith2u]

1). The average score of a mathematics test in a class is 5.2. One

student, who scored 7 in the test, transferred to another school. As a
result, the average score of the remaining students was 5. How many
students were there at first? (Ans : 10)
*(Note : pls do not use algebra method)

2). Alan, Bob & Carl ran at a speed of 5km/h, 6km/h & 7km/h
respectively. They ran along the same route and started at 6am,
630am & 7am respectively. When Bob passed Alan, he gave Alan a
message to pass to Carl. What time will Carl receive the message?
(Ans : 0.30am)

3). Mona has 60% more stamps than HuiLing. Katherine has 15% less
stamps than Mona. If the difference in the number of stamps that
Katherine & HuiLing is 216, how many stamps does Mona have?
(Ans : 600 but I get 960)

4). There were some 50-cent coins and one-dollar coins in a coin box. 12
50-cent coins were taken out and exchanged for one-dollar coins and
the money was put back into the coin box. The ratio of the number of
50-cent coins to one-dollar coins became 4:3. If all the coins in the
coin box added up to $75, what was the ratio of the number of
50-cent coins to one-dollar coins at first? (Ans 24:13)

[James Ang]

N3SKiasu:

Hi I have one Maths question but the answer kit used Algebra to solve, hence wld like to kw if anyone cld help with using Models.


Mr Tan had some apples and oranges in his shop. 30% of the fruits were oranges. He sold 70 apples and bought another 170 oranges. Then 65% of the fruits were oranges. How many apples did he have at first?

Thks in advance!

Let's attempt this question using the shortest and best equalisation method.

A:O
7:3
-70 +170
7:13

equalising both sides

7x13:13x7

7ux13-70x13 = 3ux7+170x7
91u - 910 = 21u +1190
91u = 21u +2100
70u= 2100
1u = 30
7u = 210

There are 210 apples.

This equalisation method is found in school teachers' guide Unit 7.


ISBN : 9789810195649
Title : Challenging Maths Problems Made Easy (Upper Primary)
Author : Ammiel Wan Chee Hong
Specifications : 210mm x 296mm, 178pp, Perfect

Synopsis :
Recognising the frustrations that teachers, parents and pupils face in applying the heuristic approach to solving Maths problems, Ammiel Wan, an experienced Maths teacher, developed eleven concepts to help teachers, parents and pupils manage the wide range of challenging problems. Challenging maths Problems Made Easy contains concepts that have been tried by pupils who found them easy to understand and to apply, even with very challenging problems. Each of the eleven concepts is presented in a step-by-step manner. The comprehensive explanations and examples allow teachers and parents to guide their children and for pupils to pick up the concepts on their own.