P5/P6 Math: Revisting Before and After Ratio ( Both Parties Change )

This question type is similar to the one posted here.

There are 2 values being compared using ratio and each of them undergo addition or subtraction and the ending ratio is also provided.

Such questions are common in Paper 2 of P6 exams.

Calculator usage is allowed.

Eric and Tyra were given money by their father in the ratio of 7:2. 

After Eric spent $165 and Tyra was given $210 more, 

the ratio of Eric to Tyra's money at the end became 2:7. 

How much did Tyra have at first?

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P5/P6 Math: Repeated Identity (Ratios as Fractions)

The question presents 3 unique items of different quantities and each or 2 of them are compared with the total using "fractions".
2 of such comparison statements are given and the total is also known.

Questions like these requires students to use "ratio" methods to solve a seemingly "fraction" problem sum.

Cocepts such as "total unchanged" and "repeated identity" are required to solve such questions.

These questions will usually appear in Paper 2 of P5 and P6 exam papers.

Calculator usage is allowed.

Patricia has a collection of 135 books, stickers and pens.

²/₃ of these items were not pens.

³/₅ of these items were either books or pens.

a) How many items of Patricia's collection were stickers?

b) What is the ratio of her stickers to pens?

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P5/P6 Math: Fraction of Remaining (Intermediate)

The following question type require students to be able to understand "fraction of remaining".

2 fractions are given to represent 2 items
and 2 numbers are given to represent one of the items and the final amount left.

Such questions appear in P5 and P6 exams and will be in Paper 2.
Calculator usage is allowed.

Joe started reading a novel.

He read ²/₅ of the novel on Monday.
He read another 58 pages of the novel on Tuesday.
After reading ¹/₄ of the remaining novel on Wednesday,
he finished reading the last 96 pages of the novel on Thursday.

How many pages were there in this novel?

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P3/P4 Math: Set Method (Equal Quantity)

The question below deals with "sets" with equal quantities of 2 items.
(each with different value)

Such questions are common for P3 SA2 and P4 SA1/SA2.

Patrick was given the equal number of $2 notes and $5 notes.

The $2 and $5 has a total value of $98.

How many $5 notes was he given?

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P3 Math: Comparisons Between 2 Parties

Questions like the ones below are designed to improve P3 student's proficiency in drawing comparison models and placing the correct values in different parts of the model.

Once students can draw such models and place the values at the correct parts of the model, the comparison model will actually help them to be able to write down the number statements required.

Basic foundation of such model can also be practiced at this link below.

P3 Math: Comparison Model Drawing Exercise (More Than/Less Than)

Alan and Beth have 95 vuvuzelas altogether.

Beth has 35 vuvuzelas.

How many more vuvuzelas does Alan have than Beth?

What is a vuvuzela?

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P5 Math: Assumption (Advance)

This P5 version of "Assumption" method is different because there is a deduction of value.

This question usually appears in paper 1 for P5 mid-year SA1 or SA2.

Calculator usage is not allowed.

Mr Guetta is a delivery rider.
He delivered 15 parcels on Monday.

For each parcel delivered on time, he will earn $5.
For each parcel delivered late, $3 will be deducted.

He received $59 for the parcels delivered on Monday.
How many parcels were delivered late?

How are mail sorted at the post office?

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P4 Math: Assumption

This question type is identical to "Guess and Check" which students have learnt in P3.

But in P4, a mathematical method is preferred to using a Guess/Check table.

The "Assumption" method is a required skill in P4 onwards

Such questions will begin to appear in P4 WA1 or SA1 in Section C.

In a carpark of 30 cars and motorcycles,

these vehicles have a total of 100 wheels.

How many motorcycles are there in this carpark?

What goes on at a car manufacturing plant?

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P6 Math: Average: Before and After (Advance)

The question below deals with the topic of "Average".
Each of the 2 groups' average is known and the average of both groups is also given.

However the exact number of the parties in one of the groups was not provided.

Such questions appears in P6 mid year and prelims.
Calculator usage is allowed.

15 girls spent an average of $30 on stationery.

A group of boys spent an average of $22 on stationery.

Both the boys and girls spent an average of $25 on stationery.

How many children were there altogether?

How pencils are made at the factory?

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P5 Math : Same Capacity to Hold 2 Different Items

The question type below deals with a container with limited space for both items.
Such questions are common in P5 SA1 and SA2 and appears in Paper 1.

No calculator allowed.

A school bus can board either 20 adults or 28 children. After 5 adults boarded the empty bus,

how many more children can this bus take?

Why are school buses in America painted yellow?

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P6 Math: Catching up by Adding More every time

The question below starts with 2 parties, one with more and one with less.

The one with less will add more each time in order to catch up with the one with more.

Such question will usually appear in P6 and will appear in paper 2.
Calculator usage is allowed.

Hannah have a collection of 45 seashells and

Oliver have a collection of 72 seashells at first.

Each week, Hannah will add 9 seashells to her collection and 

Oliver will add 6 seashells to his collection.

How many weeks will it take Hannah to have the same number of seashells as Oliver?

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P5/P6 Math: Revisiting Fractions of Equal Value

The question below deals with the concept of equal value fractions.
Such questions will appear in exams once after ratio techniques are taught in P5.

Similar Fractions of Equal Value questions can also be found here

Calculator usage is allowed.

In a school canteen, there were 37 more boys than girls.

³/₇ of the boys and ²/₅ of the girls wore spectacles.

An equal number of boys and girls do not wear spectacles.

How many children were there at the canteen altogether?

Natural ways to improve your eyesight without surgery

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P5/P6 Math: Ratio: Both Parties Change

The question below deals with the ratio, where both parties undergoing changes via addition or subtraction. Both the starting ratio and ending ratio will be given.

Such questions will appear in exams once after ratio techniques are taught in P5.

Calculator usage is allowed.

A similar version of this question can also be found here.

Jason and Alan each bought some flowers

in the ratio of 1:3 respectively.

Jason gave away 12 flowers and Alan gave away 18 flowers.

The ratio of Jason's flowers to Alan's flowers became 2:9.

How many flowers did they buy altogether at first?

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P4/P5/P6 Math: Fraction With And Without Units

Questions like these need students to understand that 

"fraction of total" and "fraction of a kg"(or any other units of measure)

needs to be processed differently.

Such questions usually appears in P4 section C and will also be tested for P5 and P6.

Heather has ⁷/₈ kg of flour.

She gave ¹/₄ of her flour to Ben

and used ¹/₂ of her flour to bake a cake.

How much flour does she have left?

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P4 Math: Before and After (Intermediate)

The question type below deals with "P4 before and after" comparison models.
One of the models will remain the same.

Such questions often appear in P3/P4 exam papers in Section C.

Samy has thrice as many books as Darius at first. After Darius gave away 18 books, Samy has 6 times as many books as Darius.

How many books does Samy have?

Book binding process (video link)

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P5/P6 Math : Repeated Identity Ratio (Basic)

Questions of these type will start to appear in tests and exam papers once the students have been exposed to REPEATED IDENTITY and RATIO.

Such questions usually appear in Paper 2.
Calculator usage is allowed.

Gerald, Thomas and Brandon shared the cost of a present.

The ratio of Gerald's share to Thomas' share was 2:3.
The ratio of Thomas' share to Brandon's share was 1:2.

Brandon paid $48 more for his share than Gerald.

How much was the present?

Some history about Christmas

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P5/P6 Math: Fractions of Equal Value

The question below deals with the concept of equal value fractions.
Such questions will appear in exams once after ratio techniques are taught in P5.

Calculator usage is allowed.

Evelyn and Heather collected some seashells from the beach.

¹/₃ of the seashells that Evelyn had collected 

was equal to ²/₅ of Heather's seashells.

How many seashells did they collect altogether

if Evelyn collected 13 more seashells than Heather?

Why we must not pick seashells from the beach

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P5/P6 Math : Sharing the Shortage/Excess

The question type below is about evenly distributed items in multiple containers.

When some of the containers were removed, the items will be redistributed evenly into the remaining containers.

Such questions often appear in paper 2 for P5 after SA2 
and also for P6 mid year and prelim.

Calculator usage is allowed.

In a hall, chairs were arranged into 18 equal rows.
3 rows of chairs were removed and
these chairs were arranged equally into the remaining rows.
Each of the remaining row now has 12 more chairs.
How many chairs were there in the hall?

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P6 Math: One Party Reduced to Zero with Starting Ratio Given

The question type below deals with 2 parties with different ratios given at the start.
Each will have different amount deducted every instance until one party reaches zero.

Such questions often appear in P6 paper 2 during SA1 and prelim.

Calculator is allowed.

Geraldine has red and blue pins in the ratio of 3:4 respectively.

For every 5 red pins she used, 3 blue pins will also be used.

After all the red pins were used, there were 132 blue pins remaining.

How many red and blue pins did Geraldine have altogether at first?

20 of the most visited countries in the world

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Students may find these question types to be similar.