Q&A - PSLE Math

[tianzhu]

mvmir26:

Please help on below. Thanks


John takes 40 min and Peter takes 30min to travel from Point X to Point Y.
A) What is the ratio of John's average speed to Peter's average speed?
B) If John starts traveling 5 min earlier than Peter, how long will Peter take to catch up with John.

Hi

For students who are less familiar with inverse proportion ,one way to do it is by using common multiple..

Use a common distance of 1200m (30*40)

John’s speed ------ 1200/40 -------30m/min
Peter’s speed ------1200/30 -------40m/min

John’s speed: Peter’s speed --------- 3:4

In 5 minutes John travelled 5*30 --------150m

Peter is faster by 10m/min

Time to catch up -------150/10 ------15 mins


For students who are familiar with inverse proportion.

Time
John:Peter ------40:30 -----4:3

Speed
John:Peter ------3:4 (inverse the time ratio)

In 1 min, John travelled 4 units and Peter travelled 3 units.

In 5 min, John travelled 3*5 or 15 units

Difference in speed ------- 1 unit

15/1 ----- 15mins.

Best wishes

[Alchemist]

tianzhu:

vidhyalog:

Hi - Could someone h http://i56.tinypic.com/9tcx1t.jpg\"> elp me with the sum below.

Hi

Draw a bigger square such that the circle is inscribed in it.

This bigger square is twice the area of the smaller square (8)

Area of big square ------ 8*2 -----16
Length of 1 side of big square -------4

Radius of circle ------- 2cm

Best wishes

Thanks Tianzhu. Could I find out though - why is it that the bigger square would have an area that is 2X the area of the smaller square? Pardon my ignorance ..... would like to work it out myself, but in the interest of time - taking short cut of asking you.

Thanks in advance

[kavisuresh]

Pls help to solve:

The fig below is made up of a circle, a triangle and two identical semicircles. The diametre of the circle is 8cm and the diametre of the semicircle is 4cm. Find the area of the shaded regions.

http://i54.tinypic.com/11vnyv8.jpg\">
thanks.

[Daddy]

Thanks vidhyalog


A group of boys tool their pets to a park. Each boy either has a dog or cat. Between the boys and theirs pets, there were a total of 204 leags.
a) How many boys were there?
b) If there were 15 cats, how many more dogs than cats were there?

Every group of Boy + Cat/Dog will have 6 legs.
So total no of such groups - 204/6 = 34.

Therefore a) 34 boys

b) If there were 15 cats - there are 19 dogs. So 4 more dogs than cats.

Am I missing something here?

Daddy:

Hi,

Need help!! Thanks

A group of boys tool their pets to a park. Each boy either has a dog or cat. Between the boys and theirs pets, there were a total of 204 leags.
a) How many boys were there?
b) If there were 15 cats, how many more dogs than cats were there?

Thanks all the masters

Every group of Boy + Cat/Dog will have 6 legs.
So total no of such groups - 204/6 = 34.

Therefore a) 34 boys

b) If there were 15 cats - there are 19 dogs. So 4 more dogs than cats.

How did you do it? :?
Thanks

[MathIzzzFun]

kavisuresh:

Pls help to solve:

The fig below is made up of a circle, a triangle and two identical semicircles. The diametre of the circle is 8cm and the diametre of the semicircle is 4cm. Find the area of the shaded regions.

http://i54.tinypic.com/11vnyv8.jpg\">
thanks.

Hi

Shaded area
= area of big circle - area of triangle + area of small circle

cheers.

[MathIzzzFun]

vidhyalog:

Hi - Could someone h http://i56.tinypic.com/9tcx1t.jpg\"> elp me with the sum below.

Hi

from another perspective...

http://i52.tinypic.com/35kuzrd.jpg\">

area of square = 2 r^2 = 8 cm^2
r^2 = 4, r = 2cm

cheers.

[tianzhu]

mvmir26:

Another question please


Car A left the east village for the west village at the same time when Car B left the west village for the east village. 9 hours later, the two cars passed each other. Another 7 hours later, car A reached the west village but Car B was still 130km away from the east village. Find the distance between the two villages.

Hi

One way to solve it.

For a fixed distance.

Time\t
Car A: Car B ------ 7:9

Speed
Car A: Car B ------ 9:7

Distance
Car A: Car B ------ 9:7

Distance travelled by car A -----9 units.
Distance travelled by Car B ------7 units

2 units -------130
1 unit -------65

Distance between two villages -------9*65 --------585

Best wishes

[tianzhu]

vidhyalog:

Thanks Tianzhu. Could I find out though - why is it that the bigger square would have an area that is 2X the area of the smaller square? Pardon my ignorance ..... would like to work it out myself, but in the interest of time - taking short cut of asking you.
Thanks in advance

Hi vidhyalog

I'll prepare the slide and post it tomorrow.

Best wishes

[Vanilla Cake]

Hi,

As per request from some KSP members, these are some of the questions from this paper. Answers given have not been checked and pls share your way of solving them. TIA.

Q15
A rectangular tank measuring 3 m by 3 m by 1.5 m was 1/3 filled with water. A tap was turned on to fill up with water at a rate of 18 l/min. Every 2 minutes after the tap was turned on, 6 l of water was poured from a pail into the tank. How long did it take for the rectangular tank to be completely filled with water? Leave your answer as a mixed number in its simplest form. [ 4 marks]
Answer given: 428 2/3 min

Q16
In a confectionery, 3/10 of the cupcakes baked were strawberry cupcakes, 1/2 of them were chocolate cupcakes and the rest were grape cupcakes. 2/7 of the strawberry cupcakes were sold. This was 1/2 of the number of chocolate cupcakes sold. The number of grape cupcakes sold was 1/4 the total number sold in the other two flavours. Given that there were 190 cupcakes left, how many cupcakes were there at first? [5 marks]
Answer given: 280

Q17
Packet A, Packet B and Packet C each contained some salt. At first, there were 200 g more salt in Packet A than Packet B. Packet C had 3/4 of the amount of salt in Packet A. After 1/8 of the amount of salt in Packet A was transferred to Packet B, there was 82.15 g of salt in Packet B. How many percent less salt were there in Packet C than Packet A at first? [5 marks]
Answer given: 25%

Q18
In a cinema, the ratio of the number of girls to the number of boys was 3:2. The ratio of the number of women to the number of boys was 5:4. The ratio of the number of girls to the number of men was 2:5. During the movie, 6 women and 27 men left the cinema. The ratio of the number of women to the number of men then became 1:2.
(a) Express the number of women as a fraction of the number of men at first. Leave your answer in its simplest form.
(b) How many children were there in the cinema?
Answer given: (a) 1/3 and (b) 30

[Vanilla Cake]

Q8 and answer given: 75 cm2

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