Q&A - PSLE Math

[mathnoobs]

tianzhu:

jewelbox:

Thanks Tianzhu, you are fast. I will slowly digest your solutions. Meanwhile i have prob solving this qn. Thanks. http://i42.tinypic.com/zbp0o.jpg\">

Hi

Good Morning.

Imagine you are seeing a reflection of the picture or image. Flip the image so that you can see a square formed by the two isoceles triangles.

Find the area of (Area of quadrant – Area of isosceles triangle) and divide it by 2.

Area of quadrant ------ 38.5

Area of isosceles triangle ------ 24.5

38.5 – 24.5 ------14

Difference in shaded area ----- 14 /2 ------ 7

Best wishes

Hi Tianzhu
I'm afraid I'm a bit weak in geometry. Hard to visualize things.
I can see the area of a quadrant, which is 1/4 of area of circle, radius 7cm. I can also see the area of isosceles triangle, which is 1/2 area of square.
But I don't see how (area of quadrant - area of triangle)/2 leads to difference in the 2 shaded regions.

[tianzhu]

mathnoobs:

Hi Tianzhu

I'm afraid I'm a bit weak in geometry. Hard to visualize things.
I can see the area of a quadrant, which is 1/4 of area of circle, radius 7cm. I can also see the area of isosceles triangle, which is 1/2 area of square.
But I don't see how (area of quadrant - area of triangle)/2 leads to difference in the 2 shaded regions.

Hi

You're on the right track as you can see the quadrant and isosceles triangle.

I'll prepare the sketch to show you how (area of quadrant - area of triangle)/2 leads to difference in the 2 shaded regions.

Watch your PM.Please give me some time.

Best wishes

[Zack7]

ADoc:

peggy:

Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

Hi! Other than algebra, which some primary students may not be too comfortable with, we explain to them that before we can compare ratio or fraction units of the SAME qty, we must change them to the same number of units. This is an important concept in order to score those ratio qs, that I'm sure parents and students here are already very familiar with.

(2/3) x 3 = 6/9 } ali
(3/5) x 2 = 6/10 } raju

We see that Ali has 1 unit less than raju ---> 100 books
therefore Ali has 9 x 100 = 900 books.

Another variation of this sort of 2-mark qs is to ask for the fraction or ratio of say, Ali's to raju's.

cheers
eugene

your method is quite unorthodox i must say...

firstly, (2/3) x 3 = 2, not 6/9. same with 3/5

secondly, 6/9 is not 1 unit less than 6/10... in fact, 6/9 > 6/10. it might work as a shortcut in this question, but i don't think it is clear to the kids or even the right concept.

a clearer way would be

2/3 ali = 3/5 raja (as per the question)
ali = 9/10 raja (cross multiply)

now here comes the crucial step namely, how to interpret the above equation.
the equation tells you ali has only 9/10 as many books as raja.
always ask yourself when you are forming your conclusion, who has more books who has less. does it agree with the question? in this case, ali has less.

the equation might look like raja has fewer since there is a 9/10 factor, but this is not true because of the equal sign. it is important to note the equality sign.

so in this case, one should interpret it as : the WHOLE of ali is only EQUAL to 9/10 of raja. that means everything that ali has is not even equal to the whole of raja, but rather only equal to 9/10 of raja's books.

so this means 1/10 of raja's books is the amount that is more than ali. so ali has 100 books less than raja, which means raja has 100 more than ali.

9/10 of raja, which is = ali, is then 100x9 = 900.

[Michaelia0816]

Ok now I need help! Pls help!

Question:
A) Mr Chan had a total of 160 pieces of $2 notes and $5 notes. He gave 50% of the $2 notes and 25% of the $5 notes to Susan and had 92 notes left.
a) Find the percentage of the number of $2 notes at first.
b) How much money did Mr Chan have at first?
B) A shopkeeper had some apples and oranges. If 34 apples were sold, the ratio of the number of apples to the number of oranges would be 3:1. If 85 oranges were sold, the ratio would be 29:4. How many apples did he have? :thankyou:

[Zack7]

Michaelia0816:

Ok now I need help! Pls help!

Question:
Mr Chan had a total of 160 pieces of $2 notes and $5 notes. He gave 50% of the $2 notes and 25% of the $5 notes to Susan and had 92 notes left.
a) Find the percentage of the number of $2 notes at first.
b) How much money did Mr Chan have at first?

let x be no. of $2 notes, y be $5

x+y = 160
0.5 x + 0.25 y = 68

2 equations 2 unknowns, you can solve it.

answer should be 70% and $464

part b)

x be apples, y be oranges

x - 34 = 3y
4x = 29( y- 85)

solve

answer should be 493 apples 153 oranges

[Michaelia0816]

O Thank you again you solved all my question and also science one!!!

[Winx5015]

The distance between Town A and Town B is 48km. Tom runs from Town A to Town B at an average speed of 11km/h. At the same time, Mr Tan runs from Town B to Town A at an average speed of 5km/h. How far would each of them have run when they meet on the way?


Thanks

[Michaelia0816]

Hi Zack7,

Would you mind writing down the apple and orange question steps

[MathIzzzFun]

Winx5015:

The distance between Town A and Town B is 48km. Tom runs from Town A to Town B at an average speed of 11km/h. At the same time, Mr Tan runs from Town B to Town A at an average speed of 5km/h. How far would each of them have run when they meet on the way?


Thanks

Hi

this question is similar to the one that you posted earlier -\"The distance between Town A and Town B is 40km. Mr Goh drove from Town B towards Town A at the speed of 85km/h. At the same time, Mr Wong drove from Town A towards Town B at 75km/h. How many hours later would they meet?\"
You may want to try ? Here are some pointers that may help:
- the distance between Tom and Mr Tan was 48 km at first, and when they meet, the distance is zero.
- what is their closing speed ie in hour, what is the total distance that they will run ?

cheers.

[MathIzzzFun]

Zack7:

ADoc:

]Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

Hi! Other than algebra, which some primary students may not be too comfortable with, we explain to them that before we can compare ratio or fraction units of the SAME qty, we must change them to the same number of units. This is an important concept in order to score those ratio qs, that I'm sure parents and students here are already very familiar with.

(2/3) x 3 = 6/9 } ali
(3/5) x 2 = 6/10 } raju

We see that Ali has 1 unit less than raju ---> 100 books
therefore Ali has 9 x 100 = 900 books.

Another variation of this sort of 2-mark qs is to ask for the fraction or ratio of say, Ali's to raju's.

cheers
eugene

your method is quite unorthodox i must say...

firstly, (2/3) x 3 = 2, not 6/9. same with 3/5

secondly, 6/9 is not 1 unit less than 6/10... in fact, 6/9 > 6/10. it might work as a shortcut in this question, but i don't think it is clear to the kids or even the right concept.

a clearer way would be

2/3 ali = 3/5 raja (as per the question)
ali = 9/10 raja (cross multiply)

now here comes the crucial step namely, how to interpret the above equation.
the equation tells you ali has only 9/10 as many books as raja.
always ask yourself when you are forming your conclusion, who has more books who has less. does it agree with the question? in this case, ali has less.

the equation might look like raja has fewer since there is a 9/10 factor, but this is not true because of the equal sign. it is important to note the equality sign.

so in this case, one should interpret it as : the WHOLE of ali is only EQUAL to 9/10 of raja. that means everything that ali has is not even equal to the whole of raja, but rather only equal to 9/10 of raja's books.

so this means 1/10 of raja's books is the amount that is more than ali. so ali has 100 books less than raja, which means raja has 100 more than ali.

9/10 of raja, which is = ali, is then 100x9 = 900.

hi Zack7,

if you were to go through the solution and understand the logic, you should see that it was just a typo omission by ADoc, the method is correct.

2/3 ali = 3/5 raja.. \"equalize\" the numerator ie 2/3 x 3/3, 3/5 x 2/2
we will get 6/9 Ali = 6/10 Raja --> So, Ali --> 9 units & Raja --> 10 units

.. this is a common method taught and it is easy to understand because one can easily draw a model to see that indeed Ali has 9 blocks and Raja has 10 blocks.

there will always be different approaches to solving a problem - no one method is better than the other.. it is a question of preference. One person may prefer the algebra approach, another may like the unit approach, while another will simply stick to model drawing. So, be open to various approaches because for some questions, the algebra approach is not the most efficient one.

cheers.