P5/P6 Math : Percentage Discount of 2 items with One Discount Known

The question type belows will provide total price of 2 items after discount.

One of the items' discount(amount saved) will be given.

From the information, students will need to find out either the original price of

- item A

- item B

- both items

and/or how much was the discount ( amount not percentage ) given.

Such questions usually appear in Paper 2.

Calculator usage is allowed.

During the summer sale,

Paul bought a TV and a fan, both at 25% discount.

He paid $930 altogether for both items after the discount.

He paid $50 lesser for the fan because of this discount.

What is the original price of the TV?

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P4 Math: Area and Perimeter of Square and Rectangle with Same Areas or Perimeters

This question type will show 2 shapes, a square and a rectangle.

Either the area or perimeter of both shapes will be the same.

From the values given, lengths or breadths or areas, students must be able to work towards the required answer(s).

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P5/P6 Math: Overlapping Triangles in a Rectangle

The concept of "Triangles in Rectangle" is commonly tested in P5 once the students have learnt how to find the area of triangles.

Such questions usually appear in P5 and P6 Paper 2.
Calculator usage is allowed.

(Diagram above may not be drawn to scale)

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P5/P6 Math: Starting Ratio and Ending Fraction of Total Given

This question type starts with the ratio of 2 parties given.

One of them undergo fractional decrease and the other one has a numeral decrease.

The remaining, which is a fraction of the total, will also be provided.

Such questions will appear in P5 SA2 and P6 exams Paper 2.
Calculator usage is allowed.

The ratio of money that Charles and David have are in the ratio of 4:5 respectively.
After Charles spent ¹/₂ of his money on lunch and David spent $28 on a taxi ride,
the total amount they have left is ¹/₃ of the total amount they had at first.

How much money did both have left at the end altogether?

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

The following question deals with "constant decrease".
The starting difference between 2 parties is known and both parties undergo constant decrease.

One party will be reduced to zero while the other will have some left.

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

Shane have 40 more flyers than Derek at first.

Every minute, Shane gave out 18 flyers and Derek gave out 15 flyers.

When Shane has given away all his flyers, Derek still has 35 flyers remaining.

How many flyers do they have altogether at first?

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Students may find these question types to be similar.

P5/P6 Math: Sharing the Workload Thus Lesser Time Needed

This question looks like an "Average" question
but it is not simply adding together and divided by 2.

When the job is shared, the time taken will always be lesser as the workload will be shared.

Such questions are common in P5 and P6 exams.
Calculator usage is not allowed.

Carol will need 5 hours to paint her bedroom.

If the room was painted by her father, he will only need 2 hours.

If both Carol and her father were to paint together,

how long will it take for them to paint her bedroom?
(Give your answer in hours using fraction in simplest form)

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P5 Math : Internal Transfer

This question requires students to be able to visualize a before and after model.

Before and after the transfer between both parties in the question,
the total will not change.

Such question often appears in P5 Paper 2.
Calculator usage is allowed.

Lester has thrice as many lego bricks as Patrick.
After Lester gave Patrick 60 lego bricks,
Lester now has twice as many lego bricks as Patrick.

How many lego bricks do they have altogether?

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P3/P4 Math: Set Method (Complete Sets without Remainders)

By the end of P3, students will be exposed to set method.

The basic components within 1 set will be given.

Such questions usually appear in from P3 SA2 and in P4 exam papers.

On a farm, there are ducks and pigs.
For every 1 pig, there are 3 ducks.
The ducks and pigs have a total of 80 legs.

How many pigs are there in this farm?

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P5 Math: Average of 2 groups of items

The topic of Average requires students to find out each fair share.

The question type below provides 2 sub-totals, 
from which, students must be able to derive first the total before they can process the average [ aka fair share ].

Such questions can appear in both paper 1 and 2.

Calculator usage is allowed if in Paper 2.

A group of 3 boys have a total of 17 die-cast toy cars.

Another group of 5 boys have a total of 39 die-cast toy cars.

What is the average number of die-cast toy cars owned by each of these 8 boys?

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P5/P6 Math: Discounted Price inclusive of GST given

This type of percentage question deals with the local Singapore tax system of GST ( aka Goods and Services Tax ), which is currently at 9% ( at March 2025).

A discount is given upon the purchase and the price of the discounted item includes the 9% GST.

Such questions will appear in P5 SA2 in Paper 2 and in P6 exams.

Calculator is allowed.

At a sports store, Alan bought a pair of sneakers at a 25% discount.

Alan paid $176.58, inclusive of the 9% GST, for the pair of sneakers.

What is the original price of this pair of sneakers?

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P5/P6 Math: Whatever Left is a Fraction of Total

This question type shows the denominator that represents the total are presented differently when used to represent the "fraction of total" that is represents on first item and the "fraction of total" that is left at the end.

Can the denominator that is used to represent the total in both statements be different numbers?

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

In a bag of red, blue, yellow and pink balloons,

²/₅ of the balloons are red.

There are 13 blue balloons and 27 yellow balloons.

The remaining ¹/₁₀ of the balloons are pink.

How many balloons are there in the bag altogether?

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P4/P5/P6 Math: Series of Repeating Pattern Numbers or Letters

Patterns are commonly tested since P3 for students to predict the next number in the sequence using Math.

The following question type deals with a repeating pattern of numbers or letters.

Suitable for P4, P5 and P6 students.

Calculator usage will not be necessary.

In a number series below,

1 , 4 , 7 , 2 , 7 , 1 , 4 , 7 , 2 , 7 , 1 , 4 , 7 , 2 , 7 , 1 , 4 , 7 , 2 , 7 , 1 , 4 .....

a) What would be the 54th digit?

b) From the first digit to the 74th digit,
how many times would the digit "7" have appeared?

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P5/P6 Math: Fractions and Ratio vs Repeated Identity

This following fraction/ratio question requires students to be able to identify the repeated identities in order to be able to make sense of the relationship between each ratio/fraction.

A starting ratio is given between 2 items.

Each of the item is then split again into 2 types via fractions.

The relationship between 2 of the split items are given with a comparison statement.

[eg more than, less than ]

Such questions usually appear in Paper 2 of P5 SA2 and P6 exams.

Calculator usage is allowed.

The ratio of boys to girls at the swim meet is 3:2.

¹/₄ of the boys and ¹/₃ of the girls are swimming
and the rest are not swimming.

There are 11 more boys than girls, whom are not swimming.

How many boys and girls are there altogether at the swim meet?

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P5/P6 Fractions (Before and After)

The following question type require students to understand what each numerator and denominator represents.

There will be 

fraction of the "total"
fraction of "one type"
fraction of "left"

Such questions usually appear in P5 SA2 and P6 exam papers in paper 2.

Calculator usage is allowed.

There are equal number of gray and brown jackets for sale in the store.

After ¹/₂ of the gray jackets and some brown jackets were sold,

the amount of jackets remaining was ¹/₃ of the total number of jackets for sale in the store.

What fraction of the remaining jackets are brown?

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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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P4/P5 Math: Sum of 2 not given

The following question type is an advance version of "Sum of 2 given".

Instead of giving a sum of 2 (out of 3 items) , the sentences are rephrased in another manner.

Such questions usually appears in Paper 1.
Calculator usage is not allowed.

The students of class 5A, each joined one of these 3 different clubs,
namely, a computer club, a nature club and an astronomy club.

15 students are not members of the computer club.
17 students are not members of the nature club.
12 students are not members of the astronomy club.

How many students are there in class 5A?

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P5/P6 Math: Perimeter of Multiple Squares/Equilateral Triangles

The question type below is common for P5 and P6 and often appears as the last question of Paper 1.

Calculator usage is not allowed.

Carpenter's ruler

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P5/P6 Math: Revisiting Value and Ratio Differences

This question is a variation of a tough P5/P6 Paper 2 high value question.
(A slightly more complex version of this question can be found here. )

2 different item of different quantities and individual values.

Only 4 information/numbers are given,

Namely

1) Total value of both items

2) Ratio between the quantity of both items

3) Individual value difference between both items

4) Total value difference between both items

Calculator usage is allowed. 

Tom has marbles placed in blue and red boxes.

The number of blue to red boxes is in the ratio of 7:6 respectively.

Each blue box contains 6 less marbles than a red box.

There are a total of 3834 marbles in both type of boxes.

The number of marbles in all the red boxes is 54 more than

all the marbles in the blue boxes.

How many marbles are there in each red box?

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P3/P4 Math: 3 Party Comparison Model Drawing ( within a same sentence )

Comparing 3 parties with 2 separate sentences is common in P3.

There are 13 more green than red ribbons.

There are 10 more blue than green ribbons.

In the later part of P3 and onto P4,
students are required to know how to draw comparison models with a single sentence such as one below.

Mark has 15 more cards than Reuben and 11 less cards than Bernard.
Who has the most and who has the least cards?

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P3/P4 Math: Reverse Model Drawing

To assist P3 and P4 Math students with comparison model drawing,
such visual aids may be useful.

Instead of having them draw the model, 
have them fill in a partially drawn model first.

If the student is able to fill in all the missing boxes, the model should be able to instruct them on how to find the answer.

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P5/P6 Math: Amount of Money Spent and Left of 2 Different Parties with Comparisons

This question type deals with 2 parties with a total sum of money.

There is a comparison with multiples on the amount of money spent between the 2 parties.
The amount of money left is also compared using multiples.

Such questions are suitable for P5 and P6.
These questions will usually appear in paper 2 in P5 SA2 and P6 papers.

Calculator usage is allowed.

Karlie and Lenny had a total of $1335.50 at first.

Karlie spent 4 times as much money as Lenny.

The amount of money that Lenny had left 

was $15 more than what he had spent.

The amount of money that Karlie had left was 

half as much as what Lenny had left.

How much did both have left altogether at the end?

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