Q&A - PSLE Math

[Maths Monster]

kitty2:

Please kindly help with these questions, :thankyou:


2)Mr Miki had some track shoes in his shop.3/7 of them were Brand x,1/4 of the remainder were brand Y and the rest were brand Z


Types of shoes Amt earn/pair

Brand x $8
Brand Y $6
Brand Z $10

The table shows the amt he earn per pair of shoes.The number of brand X shoes sold to the number of Brand Y shoes sold to the number of brand Z shoes sold was 1:2:4.In total,he sold 1/5 of the shoes and earn $840.How many pairs of Brand Z shoes did he have at first?

Ratio of number of shoes sold
X : Y : Z
1 : 2 : 4

Ratio of amount shoes sold
$X : $Y : $Z
8x1 : 6x2 : 10x4
8 : 12 : 40

8 + 12 + 40 parts => 840
1 parts => 14

Amount of shoes sold
$X : $Y : $Z
$112 : $168 : $560

Number of shoes sold
X : Y : Z
14 : 28 : 56

Total shoes sold = 14 + 28 + 56 = 98
Total shoes at first = 98 x 5 = 490

Ratio of shoes at first:
X : Y + Z
3 : 4

Y : Z
1 : 3

X : Y : Z
3 : 1 : 3

3 + 1 + 3 parts => 490
1 part => 70
3 parts => 210

Therefore, he has 210 Brand Z shoes at first.

Check:
Total shoes = 490
Total shoes sold = 98
X shoes sold = 14 => 14 x $8 = $112
Y shoes sold = 28 => 28 x $6 = $168
Z shoes sold = 56 => 56 x $10 = $560
Total amount = $840

[Maths Monster]

kitty2:

Please kindly help with these questions, :thankyou:


3)A car & a lorry were heading from Town A to Town B.When the car overtook the lorry,they were 375km away from town B.The car arrived 1h15 min earlier than the lorry which was still 75km away from town B.

a) Find the average speed of the lorry
b) Find the average speed of the car

When car reached Town B, Lorry is 75km away and will take 1h15min to reach Town B.

a) Lorry speed = 75 / 1.25 = 60km/h

Time taken by Lorry from where Car overtook Lorry to Town B = D / S
= 375 / 60 = 6.25h

Time taken by car = 6.25 - 1.25 = 5hr

b) Car speed = D / T = 375 / 5 = 75km/h

[Maths Monster]

kitty2:

Please kindly help with these questions, :thankyou:


4)Siti had some red & blue marbles.80% of the marbles were red.After she bought another 63 red marbles & 46 blue marbles,75% of the marbles were red.Find the total number of marbles she had at first.

Let 10u be the total number of marbles

Before:
Red [8u]
Blue [2u]

After:
Red [8u+63]
Blue [2u+46]
If 75% of the marbles were red, we can write,
8u + 63 = 3 x (2u + 46)
8u + 63 = 6u + 138
2u = 75
u = 37.5

Therefore, total number of marbles at first = 10u = 375

Check:
Before:
Red = 0.8 x 375 = 300
Blue = 0.2 x 375 = 75

After:
Red = 300 + 63 = 363
Blue = 75 + 46 = 121
Total = 484
% of Red = 363/484 x 100% = 75%

[tianzhu]

kitty2:

:goodpost: yes i agree,thanks for your effort and time.

Hi kitty2

You’re welcome.

Best wishes

[ksmama]

Ann is driving to a destination. If she travels at 80km/h, she would be 20min late. If she travels at 60km/h, she would be 45 min late. How long will journey take if she travels at 90km/h.


For your help. Thnx!

[tianzhu]

Brenda10:

Hi Tianzhu


Sure. This forum really has a lot of resourceful/helpful members that provide help to solve our headache.

BTW, is question on “speed” very difficult as I can see quite a numbers of question recently posted are related to this topics.

Thank you.

Hi Brenda10

If I remember correctly, your girl is in P5.So the only ‘speed” she should experience now is the exciting rides from roller coasters and water slides.
Questions on Speed in P6 are interesting, and some children may find them challenging. From some of your previous posts, I gathered that your girl is able to solve problems logically. She should be able to handle them.

Best wishes.

[Brenda10]

Hi Tianzhu


Yes. You’re right.

She is spending most of her time on reading or playing those Mystery game since not much work from school. I do wish your judgment is correct.

Thank you and have a nice day. :lol:

[Maths Monster]

ksmama:

Ann is driving to a destination. If she travels at 80km/h, she would be 20min late. If she travels at 60km/h, she would be 45 min late. How long will journey take if she travels at 90km/h.


For your help. Thnx!

Since distance is the same, the ratio of speed is inverse to the ratio of time taken:

Ratio of speed
80km/h : 60km/h
4 : 3

Ratio of time taken
3 : 4

1 part => 45 - 20 = 25 mins

Time taken for speed of 80km/h = 3 x 25 = 75 mins
Time taken for speed of 60km/h = 4 x 25 = 100 mins

Distance = 80 x 75 / 60 = 100km

Therefore, time taken if speed is 90km/h is = 100 / 90 = 1 1/9h

Check:
To be on time, she must reach the destination in 75 - 20 = 55mins
If speed is 60km/h, she will late by 100 - 55 = 45 mins

[tianzhu]

Hi ksmama


From going through with my boy last year, I realised that the formula, Distance = Speed*Time is commonly used to solve questions on Speed in P6.

I’ll share three ways to solve your question. Generally, P6 students should be familiar with the first two methods. The last method uses the concept of inverse proportion.This means that as one quantity becomes smaller, the other becomes larger.This should be covered in secondary Maths. But, I understand, they are taught to selected groups of P6 students in schools.Students who attend enrichment classes may also be exposed to this concept.

It’s good to expose kids to different solutions and let them choose the method they are most comfortable with.

I hope you will find them useful.

Best wishes

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[liketoeat]

tianzhu:

Hi


This question touches on distances moved by the tips of the hour and minute hands. It refers to distance moved along the circumference of a circle (arc).

In half an hour, the minute hand moves 180 degrees.
In half an hour, the hour hand goes through 15 degrees.

Distance moved by tip of hour hand is 15/360 * 2πr, where r is the length of the hour hand. ------ 1/12 πr

Distance moved by tip of minute hand is 180/360 * 2π (3r), where 3r is the length of the minute hand. ------- 3πr

Therefore, the answer is 36:1

(Sorry, pi appears as π when I transferred the text from Words 2007 to this thread)

Best wishes

Thank you, Tianzhu.