P6 Math: Overlapping Triangles (Advanced)

The question presents 2 overlapping triangles sharing the same base but with different heights.

Such questions requires students to understand the concept of "constant difference" on top of knowing how to calculate the basic area of triangle using the known formula.

Such questions may appear in Paper 2 of P6 exams.

Calculator usage is allowed.

More overlapping triangles questions here.

Triangles on roller coasters' structures provides strength in its support

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P5/P6 Math: Before and After ( Starting Difference with Ending Ratio)

Such questions are common for P5 and P6 exams.

Where the starting difference is known and the ending ratio is given after some numerical increase/decrease is applied to both parties.

As these appear mostly in Paper 2,

calculator usage is allowed.

A similar "before and after" type question can also be found here.

Eric has 450 more items listed on his online store than Kelvin.

After Eric sold 45 items and Kelvin listed 3 more items for sale,

the ratio of Eric's items for sale to Kelvin's items for sale became 3:2.

How many items did both have listed for sale at first?

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

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P6 Math: Redistribution of same total to lesser parties with left over

The same total meant to be equally distributed, is now distributed to lesser parties, with each party getting sligjhtly more than before. There will also be some left over after the "re-distribution" due to lesser shares.

A relatively similar question can also be found here.

Such questions are common in P6 Paper 2.

Calculator usage is allowed.

Miss Tan have 560 sweets to give to her class of 35 students.

Each student was supposed to get the same number of sweets.

Because some students were absent that day,

Miss Tan had 38 sweets left after distributing 2 more sweets
to all whom were present.

How many of her students were present that day?

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

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P4 Math: First fraction of total given

Questions like these require students to be able to draw model to represent the first fraction of total before processing the rest of the numerical values to represent the remainder.

A part whole model will allow students to be able to process the remaining using the given numerical values.

Such questions often appear in Section C of P4 exam papers.

Gianna drank ¹/₅ of the milk in the carton.

Her father drank 115ml and her brother finished drinking the remaining 81ml.

What is the volume of milk in the carton at first in millilitres?

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

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P5 Fractions : Mixed numbers undergo fractional decrease

A mixed number is used to represent the mass of a substance.

This mixed number next undergo fractional decrease.
The fractional decrease may or may not include the units of measure.

Such variation will result in different method of solving and the answers will be different.

Such questions usually appear in Paper 1 of P5 Papers.
Calculator usage will not be allowed.

An easier version of this fraction problem sum can be found here.
An expert version of this question can be found here.

Sean has 2 3⁄4 litres of milk.	Melissa has 2 3⁄4 litres of apple juice.
He drank 1⁄2 litre of the milk.	She drank 1⁄2 of the apple juice.
What is the volume of milk he has left?	What is the volume of juice she has left?

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P4 Math: Before and After Fractions (One Party Changed)

This question type shows that one of the parties changed, causing the fractional comparison to become different at the end.

The solution requires students to make use of "Before and After" comparison models. 

Such questions are common in P4 exams, often appearing in Section C of the paper.

Abigail has 6 times as many stickers as Belinda.

After Belinda bought 450 more stickers,

Belinda now has ¹/₃ as many stickers as Abigail.

How many stickers did both have altogether at first?

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

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P5 Math: Splitting 2 Groups to become 4

A group of items is being split into 2 using fractions.
Each of the group is being sub-divided again using another pair of fractions.

Such questions require the student to recognise the repeated identity in order to ensure that the fractional split in each group is correctly processed.

These questions often appear in Paper 2 of P5 and P6 exams.
Calculator usage is allowed. 

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

At first, ¹/₃ of the fruits in the basket are red grapes, the rest are green grapes.

¹/₂ of the red grapes and ¹/₄ of the green grapes are sold.

150 red and green grapes were sold altogether.

How many grapes were there at the basket at the start?

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

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