P5P6 Volume of Partially Filled Tank with Unknown Height

Volumes of partially filled containers will require students to make use of the given values such as the available "Lengths", "Breadths". "Heights" and "Volumes" in order to calculate the required value that is not given.

Such questions are common in P5 and P6 exams in Paper 2.

Calculator usage is allowed.

A rectangular tank as the following dimensions.

Length : 30 cm

Breadth : 24 cm

This tank is filled with water up to a height of 48 cm.

The tank is ²/₇ filled with water.

a) How much water is needed to fill the tank?

b) What is the volume of the tank?

 

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P6 Math: 3 Different Fractions of 3 Different Totals

This question type shows 2 fractions of 2 different totals.

The 3rd fraction shows the relationship between the 2 numerators above.

Such questions are common in Paper 1 of P6 Exams(Mid Year and Prelims)

Calculator usage is not allowed.

Mr Teo owns an aquarium that sells goldfish and guppies.

On a particular day, he sold ¹/₃ of the goldfish and ⁵/₁₁ of the guppies.

⁸/₁₃ of the fish sold that day were goldfish.

What fraction of all his fish were sold that day?

                                                1)    ²⁶/₃₃

                                                2)    ²⁶/₃₅

                                                3)    ¹³/₃₅

                                                4)    ⁶/₁₁

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P4/P5 Pie Chart (Fractions of Different Denominators)

These questions shows that the Pie Chart have 3 sections and each section is denoted by a fraction with its own unique denominator.

Students have to make use of common denominator so all the sections' fractions add up to become one whole.

Such questions are common in Section C of P4 exams and also in Paper 1 of P5 exams.

Calculator usage is not allowed.

More similar questions on Pie Charts here.

Is this a Pie Chart or a picture of a pyramid?

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P4P5P6: Set Method (1 free with every multiple of)

Set method of many variations are taught since P3.

Such questions require students to count in multiples of certain number and use those multiples to calculate the value of such sets.

For the type of questions shown below, students will also need to understand what are "Complete Sets" and "Incomplete Sets".

Such questions are common in Section B and C of P4 exams and also in Paper 1 of P5 and P6 exams.

Calculator usage is not allowed.

At a fruit stall, apples are sold at $2 each.

For every 4 apples sold, an apple is given free.

a) What is the minimum amount needed to buy 21 apples?

b) What is the most number of apples that can be bought with $84?

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P5P6 Math: Value and Multiples and Differences

This is a question type that will provide 4 of the listed information below for 2 different items of different quantities,

1. Total value of 2 items
   
   
2. Difference between 2 item's totals
   
   
3. Unit Difference between 2 items
   
   
4. Multiples of 1 item compared with another 

Similar questions using ratio to represent the multiples can also be found here and here.

Such questions are common in Paper 2 of P5 and P6 exams.

Calculator usage is allowed

Samy bought thrice as many books as pens.

He spent a total of $3850 on all the books and pens.

Each book cost $5 more than each pen.

He paid $2030 more for all the books than for all the pens.

How many books did Samy buy?

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P5P6 Math: Before and After (One Party Change) Fractional Comparison

Such questions are very similar to before and after "ratio" comparison where only one of the values changed, but the ratios are expressed using fractions. 

Such questions are common in Paper 2 of P5 and P6 exams.

Calculator usage is allowed.

Similar Ratio (One Party Change) questions can be found here.

Ben and Lenny each have some baseball cards.

At first, Ben has ²/₅ as many cards as Lenny.

After Ben bought 36 more cards,

Ben has ²/₃ as many cards as Lenny.

How many cards did both boys have altogether at first?

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P6 Math: Fraction of Remainder with Guess and Check

This question type requires students to be able to use part/whole models to visualize "Fraction of Total" and "Fraction of Remainder". The "Guess and Check" table will also be required here.

Such questions are common in Paper 2 of P6 exams.

Calculator usage is allowed

Teddy bought some apples from the market.

After he threw away 152 apples and gave ¹/₅ of the remaining apples to his sister, 

he was left with ⁴/₇ of the apples bought. 

He packed the apples he had left into large boxes of 12 and small boxes of 8.

All the boxes were full without any apples left over.

What was the least number of boxes used by Teddy?

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P6 Math: Before and After Average Expert (Average Decreased after some left)

The meaning of "Average" is 

"the number that is calculated by adding quantities together and then dividing the total by the number of quantities" 

according to Britannica dictionary.

For this "Before and After" Average question type, the total is not given and the average decreased if some parties were excluded from the count.

This question is very similar to another one published here.(where the average increased instead). More of such "before and after average" questions here.

Such questions are common in P6 Prelim Paper 2.

Calculator usage is allowed.

A group of girls have an average of 66 stickers in their collection.

If 3 girls with an average of 70 stickers stickers were excluded from the group,

the remaining girls will have an average of 64 stickers instead.

How many girls were there in this group?

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P6 Math: Before and After Average Expert (Average Increased after some left)

Average is about equal sharing. 

When the average is given but not the total number of parties to be shared with, the question becomes more complex.

Such "before and after" average questions will often appear in Paper 2 of P6 Prelim exams.

Calculator usage is allowed.

More of such before and after Average questions here and here.

Class 6C took a Math test recently and the class scored an average of 81 marks.

If the results of 4 students with average of 64 marks are excluded, 

the remaining students will have an average of 83 marks for this test.

How many students are there in class 6C?

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P6 Math: Before and After (3 changes to percentage between 2 values)

This question type show the percentage changes at every step of the "internal transfer" that happens between 2 values.

Such questions are common in Paper 2 of P6 Prelim exams.

Calculator usage is allowed.

Shane and Kirsten have a total of $8640 at first.

Shane gave Kirsten some of his money and Kirsten's amount increased by 60%.

Kirsten then gave Shane some of her money and Shane's amount increased by 30%.

Then, Shane gave Kirsten some of his money and Kirsten's amount increased by 80%.

Both had equal amount of money in the end.

Find the percentage increase of the amount of Kirsten's money.

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