Tao Nan School P5 SA2 2007 Math Q42

A rectangular fish tank 80 cm long and 60 cm wide is filled with water from a tap which flows at a rate of 3 litres per minute. If the tap is turned off after 40 minutes, what is the height of the water level in the container?

Solution

1 minute ----- 3 litres or 3000 ml
40 minutes ----- 40 x 3000 ml
= 120 000 ml or 120 000 cubic cm

Height of water level -----

Volume = length x base x height
120 000 cubic cm = 80 cm x 60 cm x height
120 000 cubic cm = 4800 square cm x height
Height = 120 000 cubic cm divided by 4800 square cm
Height = 25 cm (Answer)

Tao Nan School P5 SA2 2007 Math Q41

Lily and Kumar had an equal number of marbles. After a game, Lily lost 20 of her marbles. Lily then had 1/3 as many marbles as Kumar. How many marbles did each of them had at first?

Solution



2 units ----- 20
1 unit ----- 20 divided by 2 = 10
3 units ----- 3 x 10 = 30

Answer: They had 30 marbles each at first.

Tao Nan School P5 SA2 2007 Math Q40

WXYZ is a rectangle. Find the area of the shaded part.



Solution

Area of rectangle ---- 12 cm x 6 cm = 72 square cm

Area of unshaded triangle ----
½ x base x height
= ½ x 7 cm x 6 cm = 21 square cm

Area of shaded part -----
(72 – 21) square cm= 51 square cm (Answer)

Common Errors and confusion – Cell Division

Cell division is the process where the cell splits into two new cells. What is the purpose of cell division? That depends on: If the organism is a multi-cellular organism, (for example a cat, a mango tree, a mushroom) the purpose is for growth and replacement of old cells. A kitten needs to grow into a cat. A seedling needs to grow into an adult plant. Hence, cells need to go through the process of cell division so that the organism can grow. 

Cell division also helps replace older cells that die. If the organism is a single-cellular organism, (for example paramecium, bacterium) the purpose is for reproduction. All living things reproduce more of their own kind for the continuity of their species. 

The most common confusion among students is that they erroneously think that the purpose of cell division is for growth, replacement of old cells and reproduction for all organisms. This concept is WRONG. Below, is a table that summarises the right and wrong concepts of the function of cell division.

  

Tao Nan School P5 SA2 2007 Math Q39

There are some pigs, cows and goats in a farm. The ratio of the number of pigs to the number of cows is 3 : 4. The ratio of the number of cows to the number of goats is 2 : 3. What is the ratio of the number of pigs to the total number of animals in the farm?

Solution



Pigs ----- 3 units
Total ----- 13 units

Pigs : Total
3 : 13

Answer: The ratio of number of pigs to the total number of animals is 3:13

Tao Nan School P5 SA2 2007 Math Q38

If Premila withdraws $150 from her savings account, she will have $450 left. What fraction of her savings should she withdraw so that she will have $75 left? Express your answer in the simplest form.

Solution



Fraction that is needed to be withdrawn -----
$525 divided by $600 = 7/8

Answer: The fraction of her savings that she should withdraw is 7/8.

Free Nan Hua P6 CA1 2007 Math Worked Solutions

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Tao Nan School P5 SA2 2007 Math Q37

A book and 3 pens cost $11.25. The book cost twice as much as a pen. Find the cost of 4 books.

Solution

Book ----- 2 units
Pen ----- 1 unit

1 book + 3 pens ----- $11.25
2 units + 3 units ----- $11.25
5 units ----- $11.25
1 unit ----- $11.25 divided by 5 = $2.25

(4 books) 4 x 2 units ---- 8 units
8 units ----- 8 x $2.25 = $18

Answer: The cost of 4 books is $18.

Tao Nan School P5 SA2 2007 Math Q36

A baking machine can bake 20 muffins in 10 minutes. At this rate, how long does this machine take to bake 48 muffins?

Solution

Unit Method
20 muffins ----- 10 min
1 muffin ----- 10 min divided 20 = ½ min
48 muffins ----- ½ min x 48 = 24 minutes


Ratio Method
Muffins : Minutes
20 : 10
2 : 1
48 : 24

Answer: It takes 24 minutes to bake 48 muffins

The Three States of Water

Most PSLE students know that water exists in three states – solid, liquid and gas. Most students also know that the ‘magic numbers’ are ‘0’ and ‘100’ deg Celsius, because that is the temperature at which water changes its state.

Students also know that ice exists at 0 deg C and below, while steam exists at 100 deg C and above.

However, quite a few students get confused, when the temperature is at or between 0 and 100 deg Celsius. Some students get the impression that water exists in liquid form only when the temperature is at or between 0 and 100 deg C. This concept is wrong.

At or between 0 to 100 deg C, water can exist in two forms – liquid (as in lakes, rivers) and gas (water vapour). Below is a diagram to illustrate the states of water, in relation to the temperature.



Simply put,
Solid - At 0 deg C and below.
Liquid – At and between 0 and 100 deg C.
Gas – At 0 deg C and above.


Important and useful point to note –

Because water can exist in 2 forms (liquid and gas) from 0 to 100 deg C, we have evaporation, condensation in this world and hence, the very critical Water Cycle, which is so important to life on earth.

If water exists only as liquid between 0 to 100 deg C, it will not evaporate to form water vapour, then condense to form clouds, and eventually fall back to earth as rain.

This wide range of 0 to 100 deg C, where water exists in 2 forms is unique, unlike many other substances, where at a given temperature, it exists only in one form.

Summary – Water exists in two forms (liquid and gas) from 0 to 100 deg C and NOT in liquid form only.