P6 Math: Catching up (Savings vs Spent vs Allowances)

Advance P6 questions such as these requires students to compare between daily differences and accumulated differences.

Such questions are common in P6 Prelim Paper 2.

Calculator usage is allowed.

An easier version of the question can be found here. (use for building concepts)

Esther's daily allowance is $0.40 more than Valerie's daily allowance.

Each girl spends the same amount of $1.50 every day and saves their remaining allowance.

When Esther saved $40, Valerie only managed to save $20.

How much was Valerie's daily allowance?

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P6 Math: Combination of Sets and Individual Units

This question type shows a total value resulting from a combination of multiple sets and mutiple single units without sets. 

These questions are common in Paper 2 of P6 exam papers.

Calculator usage is allowed.

Ivan is a fishmonger at the local market.

Each customer that buys 3 fish will get one free.

Each fish is sold at $12.

Last week, his customers either bought 1 or 3 fish.

Ivan collected $888 from the sale of his fish last week and gave away 21 free fish.

How many of his customers bought only 1 fish?

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P6 Math: Fraction of Remainder with Addition and Ratio at the End

Fraction of remainder questions will be more complex at P6 level.

The following question type adds on to the difficulty by including an addition and provides the ratio comparing between the total at first and the total at the end.

Such questions usually appear in Paper 2.

Calculator usage is allowed.

Devinder has some money at first.

He spent ³/₈ of this money to buy a ruler and

²/₇ of the remaining money on a book.

After he was given $9.20 by his uncle, the ratio of his

money at the end to his total amount of money at first became 5:2.

How much did Devinder spend on his ruler?

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P5P6 Math: Percentage Decrease of One Value vs Percentage Decrease of the Total

While percentage simply means a fraction of 100, the concept of percentage becomes complex when the terms such as percentage increase or decrease is in play.

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

Calculator usage is allowed.

In June, Alan was given an allowance of $200.

Alan spent 20% of his allowance on food and 30% of the allowance on transport.

He saved the remaining of the allowance in June.

In July, he was given less allowance.

So he spent 20% lesser on food but spent the same amount on transport and saved the same amount as in June.

What was the percentage decrease of his allowance in July?

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P6 Math: Equal Quantity after 2 Parties undergo Fractional Decrease

The question presents 2 different items, each of different value and quantity.
After each undergo a fractional decrease, both items have the same number remaining.

The unit value of each item and the total value of the remaining items are provided.

Such questions require students to make use of "Equal Value Fractions" in order to solve.

These type of questions will usually appear in Paper 2 of P6 exams.

Calculator usage is allowed.

Craig has a stack of $2 and $10 notes.

After using ²/₉ of the $2 notes and ³/₅ of the $10 notes to buy a figurine,

he has equal number of $2 and $10 notes remaining.

He has $672 left at the end.

How much money did Craig have at first? 

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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?

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

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