Q&A - PSLE Math

[bwpj2000]

1)Sum of first 2 odd numbers = 1+3 = 4

Sum of first 3 odd numbers = 1+3+5 = 9
Therefore sum of the first n odd numbers is n^2
So sum of first 210 odd numbers is 210^2= 44100

Not too sure about Q2. :?

[Dharma]

bwpj2000:

1)Sum of first 2 odd numbers = 1+3 = 4

Sum of first 3 odd numbers = 1+3+5 = 9
Therefore sum of the first n odd numbers is n^2
So sum of first 210 odd numbers is 210^2= 44100

Not too sure about Q2. :?

Q1 Sum of odd nos. from 1 to 210 = (210/2) x (210/2) = 11025

To derive :
Sum of all nos. from 1 to 210 = 105 x 211 = 22155 (210 x 211)/2
Sum of all even nos. from 1 to 210 = 2(1+2+...+104+105) =2(105 x 106)/2 = 11130
So, (1+3 + ...+ 209) = 22155 - 11130 = 11025

[bwpj2000]

Oops. :oops:

Sorry, my bad.

[kitty2]

[

To derive :
Sum of all nos. from 1 to 210 = 105 x 211 = 22155 (210 x 211)/2
Sum of all even nos. from 1 to 210 = 2(1+2+...+104+105) =2(105 x 106)/2 = 11130
So, (1+3 + ...+ 209) = 22155 - 11130 = 11025[/quote]

Thanks for the answer,where do you get the 105 from? :?:

[john.09525316]

bwpj2000:

1)Sum of first 2 odd numbers = 1+3 = 4

Sum of first 3 odd numbers = 1+3+5 = 9
Therefore sum of the first n odd numbers is n^2
So sum of first 210 odd numbers is 210^2= 44100

Not too sure about Q2. :?

In fact your approach is good, except the last part should be
n= 210/2 = 105

Therefore, the answer is 105*105 = 11025

[corneyAmber]

john.316:

bwpj2000:

1)Sum of first 2 odd numbers = 1+3 = 4

Sum of first 3 odd numbers = 1+3+5 = 9
Therefore sum of the first n odd numbers is n^2
So sum of first 210 odd numbers is 210^2= 44100

Not too sure about Q2. :?

In fact your approach is good, except the last part should be
n= 210/2 = 105

Therefore, the answer is 105*105 = 11025

Typo error: 105^2 = 11025

[joconde]

kitty2:

Please help to solve these 2 problems,thanks


1)Find the sum of all the odd numbers from 1 to 210


2)The ratio of the number of horses to the number of cows is 3:8.The number of sheep is twice the number of horses.After 30 cows were sold,1/4 of the remaining animals were cows.What was the total number of sheep and horses?

I think this is the ans to Q2 :

http://www.postimage.org/

http://www.postimage.org/image.php?v=Pq14sLxS

[Vanilla Cake]

Hi faith2u,


Q1
In a Primary school of 1960 students, ¼ of the boys and 1/5 of the
girls make up 400 children. How many girls are there?

A1
1/4B + 1/5G = 400
Multiply both sides by 4
B + 4/5G = 1600
B + 5/5G = 1960 (Given)

1/5G = 360
5/5G = 360 x 5 = 1800

Number of girls in the Primary school is 1800

Q2
A carp cost $12. A goldfish cost 75% less than a carp. Ramli bought
some carps and goldfish for $198. 60% of the fish he bought were
goldfish.
(a). how many carps did he buy?
(b). how many goldfish did he buy?
(c). how much more money did he spend on the carps than goldfish?

A2
Cost of a goldfish = 25/100 x $12 = $3

Ratio of the number of fishes bought
C stands for Carps and G stands for Goldfish
C : G
40 : 60
Divide both sides by 20
2 : 3

Cost of 1 'set' of Carps and Goldfish
(2x12) + (3x3)
= 24 + 9
= $ 33

Number of sets to make up total cost of $ 198
= $ 198 / $ 33
= 6

(a) Number of Carps bought = 6 sets x 2 = 12

(b) Number of Goldfish bought = 6 sets x 3 = 18

(c) Difference in the money spent on the carps than goldfish
= (12 x 12) - (18 x 3)
= 144 - 54
= $ 90

Q3
Mr Huang knocked 160 nails along the perimeter of the ceiling of a
function room measuring 20m long by 12m wide. The distance
between each nail was equal. He hung 3 balloons on each nail.
(a). how many nails were knocked along the width of the ceiling?
(b). how many balloons did he buy in all if he has 20 left?

A3
Perimeter of the ceiling of a function room = (20+20+12+12)m = 64 m
Distance between each nail = 64/160 = 0.4 m
Number of 'spaces' in between these nails knocked along the width of the ceiling = 12/0.4 = 30.
(a) Number of nails knocked along the width = 30 + 1 = 31

(b) Number of balloons bought by Mr Huang = (160x3) + 20 = 500

[Vanilla Cake]

Hi faith2u,


Q1
Uncle Seng bought some fruits. 1/3 of the fruits were apples, 1/9 of
them were mangoes and the rest were oranges. The prices of the
fruits are as shown :
Apples – 20 cents each
Mangoes – 70 cents each
Oranges – 30 cents each
Uncle Seng spent $15.60 on the apples and mangoes. How much did
he spend on the oranges?

A1
Ratio of the number of fruits bought
A : M
1/3 : 1/9
(Multiply both sides by 9)
3 : 1
Since total units for all three fruits was 9, units for orange = 5 ( from 9-3-1)

Cost of 1 'set' of apples and mangoes
= [(3 x 20) + (1 x 70)] cents
= (60 + 70) cents
= 130 cents

Number of 'sets' = 1560/130 = 12
Amount of money spent on oranges = 12 x 5 x 30 cents = 1800 cents = $18.00

Q2
Meili has a total of 20 mangoes and oranges. If she exchanges every
mango for 3 oranges, she will have 32 oranges. How many oranges
does she have?

A2
Assume that number of mangoes be M.
Number of oranges = (20-M)

1 mango can be exchanged for 3 oranges
M mangoes can be exchanged for 3M oranges

(20-M)+3M = 32
20 + 2M = 32
2M = 12
M = 6
Oranges = 20-6 = 14

Meili has 14 oranges

Q3
Tank A and tank B had 48 litres and 8 litres of water respectively at
first. Then an equal amount of water was added into each tank. As a
result, the ratio of the amount of water in tank A to that of tank B
became 3:1. How much water was added into each tank?

A3
Key note - Difference remain constant

(3-1)units = ( 48-8 ) litres
2 units = 40 litres
1 unit = 20 litres

20-8 = 12 litres
Amount of water added into each tank was 12 litres

[kiasiparent]

My predictions for this year PSLE maths.

I think it will be slightly more difficult than last years’.

1) Units and parts are required to solve certain tough questions. Or use cross multiply. Or use algebra. Or use guess and check lol and more.

2) Questions on Volume which generally requires calculator to solve as the numbers are very big and hard to divide.

3) Questions on guess and check (or suppose method) which generally requires calculator to solve as the numbers will be quite big.

4) Speed question which requires ratio to solve.

5) Difference of area between circle and another figure.