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P3/P4 Before and After One Party Unchanged (Start Multiples, End Difference)

Such questions presents 2 values to be multiples of each other at first.

One of the value undergo a change(addition/subtraction) and the resulting difference is given after the chance.

Such questions require students to use "Before and After Comparison Models" to visualize the changes and to also be aware that one of the values "did not change".

These questions are common in Section C of P3 and P4 exam papers.

There were thrice as many boys as girls whom were in the school hall at first.
After 15 boys left the school hall to go toilet, 
there were still 17 more boys than girls remaining in the hall.

How many students were there altogether in the school hall at first?


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P3/P4 Before and After One Party Unchanged (Start Same, End Multiples)

In such questions, 2 values are being presented to be equal at first.
One of the values undergo a change (add/subtract) and it results with the larger value becoming a multiple of the smaller value at the end.

Before and After questions are staples for P3 and P4 students as they would need to know how to visualize these questions using "Before and After Comparison Models".

Such questions are common in Section C of P3 and P4 exam papers.

Harold and Kumar has the same number of sweets at first.
After Harold ate 45 sweets, 
Kumar now has 4 times as many sweets as Harold.

How many sweets did both have altogether at first?


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P5P6 Math: Starting Difference Given with Both ending Equal at the End

This type of question begins with a value given(usually the difference between 2 parties).
Each of the value undergo fractional decrease and both ends up to be equal in the end.

Such questions are common in Paper 2 of P5 and P6 Math exams.
Calculator usage is allowed.


Rachel has $105 more than Phoebe at first.
After Rachel spent 2/3 of her money and Phoebe spent 1/4 of her money,
both girls have equal amount of money left.

How much did Rachel spend?




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P6 Math: 3 Parties Before and After with Uneven Ratio at the End

A total of 3 parties are given at first.
Each of the party undergo increase or decrease and the end ratio is given.
Some of the increase/decrease are fractional and some are numerical.

Such questions are common in Paper 2 of P6 exams
Calculator usage is allowed.

An easier version of this question can be found here.


Elizabeth, Wendy and Lindy had a total of $483 at first.
Elizabth was give some more money by her parents and had double of what she had at first.
Wendy spent $67 on a pair of ballet shoes and Lindy's brother gave her another $94.
In the end, the ratio of remaining money of Elizabeth to Wendy to Lindy was 5:4:2.

How much did Lindy have at first?


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P5/P6 Math: Before and After with Percentage and Fractional Decrease

This question type begins with the total of 2 values given at first.
One of the value undergo percentage decrease and the other a fractional decrease.
Both values become equal at the end.

Students will need to work backwards in order to solve such questions.

These questions are common in Paper 2 of P5 and P6 exams.
Calculator usage is allowed.

Mr Tan and Mr Lee had a total of $418 at first.
After Mr Tan spent 75% of his money on a gift and Mr Lee spent 1/3 of his money on lunch, both men had equal amount of money remaining.

How much did each have remaining at the end?


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P5/P6 Math: Triangle sharing Base and Height with Rectangle

The area of a triangle are actually expressed as half the area of a rectangle or square.

This above concept requires students to know that regardless of how the triangle looks like, it's area will be half of a rectangle that shares the same base and height as it shares the same length and breadth of a rectangle.

Such questions are common in Paper 1 of P5/P6 exams.
Calculator usage is not allowed.




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P5/P6 Math : 3 Parties Before and After with Equal Amounts at the End

This Before and After problem sum starts with the total of 3 parties given.
Each party undergo either numerical increase, numerical decrease and/or fractional decrease. The problem sum ends with each party having equal ratio in the end.

Such questions are common in P5 and P6 Paper 2.
Calculator usage is allowed.

Ben, Carl and Dave have a total of 1021 marbles at first.
After Ben halved his number of marbles by giving some away, 
Carl bought 118 more marbles and Dave threw away 1/5 of his marbles,
each boy have the same number of marbles left.

How many marbles did Dave have at first?


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P4P5 Math: Before and After Start Same End Multiples

One of the "Before and After" problem sums where the 2 parties start with equal value.
After each undergo a decrease, one of value remaining is a multiple of the other.

Such questions are common in P4 and P5 exams.
They either appear in Paper 1 of P5 or Section C of P4 papers.

Calculator usage is not allowed.

Evelyn and Kathy each have the same number of stamps at first.
After Evelyn sold 24 stamps and Kathy gave away 100 stamps,
Evelyn now has thrice as many stamps remaining as Kathy.

How many stamps did Evelyn have at first?


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P4P5 Math: Before and After Start Multiples End Same

Such problem sums starts with 2 parties, one being a multiple of another at first.
Both parties undergo addition or subtraction and results in both having equal value at the end.

This type of problem sum will require student to use before and after models to represent visually the starting multiples of one another at the "Before" model and the "After" model to represent the changes and how both became "Equal".

These questions are common in Section C of P4 exams and Paper 1 of P5 exams.
Calculator usage is not allowed.

Chris have 3 times as many buttons as Bailey at first.
After Chris used 30 buttons making shirts and Bailey used 4 buttons for making pants,
they had the same number of buttons left.

How many buttons did Chris have at first?


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P4P5 Math: Fraction of Remaining(Simpler)

"Fraction of remaining" is a concept that requires students to be able to understand that in the 2 fractions given, one represents "Fraction of Total" and the other represents "Fraction of Remaining".

The denominators of both fractions need not be made to be the same as both represents a different value.

Such questions usually appear in Section C of P4 exam papers.
Calculator is not allowed. (for P5 students attempting this question)

Similar question for P4 can be found here.
A tougher version for P5 can be found here.


Calvin has a collection of precious gemstones.
1/4 of his gemstones are green in colour.
1/3 of his remaining gemstones are red and the rest are blue.
He has 24 blue gemstones.

How many gemstones does Calvin have altogether?


If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 
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