P6 Math: Before and After Ratio made Equal at the end

This question type starts with a ratio and after both values undergo some decrease, a new ratio is given.

Both values undergo another addition and that causes both values to become the same at the end.

Such questions are common in P6 Prelim Paper 2.

Calculator usage is allowed.

Benedict and Erica has erasers in the ratio of 5:7 respectively.

After Benedict gave away ³/₇ of his erasers and Erica sold some erasers,

the ratio of Benedict's to Erica's remaining erasers became 10:7.

Benedict then bought another 60 erasers and Erica bought 240 erasers.

Each have the same number of erasers at the end.

How many erasers does Erica have at first?

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P5 Math: Uneven Ratio becomes Equal after Both Decrease

This question provides the ratio of 2 items at first.
After both undergo different decrease in value, both ends up being equal with one another.

Such questions are common in WA2(mid year) for P5.

Calculator usage may be allowed.

A similar but "inverted" version of this question can also be found "here".

Alan and Rick each have pencils in the ratio of 5:8.

After Alan gave away 32 pencils and Rick sold 77 pencils.

They have equal number of pencils remaining.

How many pencils did Rick have at the end?

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P4/P5 Math: Starting Multiples and Ending Multiples After Equal Decrease in Value

"Before and After Comparison Models" are staple for P3 to P6 Math.

The folowing question type presents one party to be a multiple of another at first.

After both undergo an equal decrease in value, the ending comparison is another multiple of one another.

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

Calculator usage is not allowed.

Kenneth has thrice as many baseball caps as Hiroshi at first.

After each gave away 45 caps,
Kenneth still has 8 times as many baseball caps as Hiroshi.

How many caps did both have altogether at first?

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P5/P6: Ratio : Difference Unchanged (Age)

Age comparison questions are common in P4 but in P5 ratio will be used(instead of fractions or multiples) to compare the ages.

These questions requires the concept of "Difference Unchanged".
Similar questions can be viewed here.

Such before and after questions will usually appear in Paper 2 of P5 exams.

Caculator usage is allowed.

The ratio of Hannah's age to Grace's age was 5:6 at first.

10 years ago, the ratio of their age was 5:8.

How old is Grace now?

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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: Overlapping Areas of 2 Shapes

The concept of overlapping shapes requires ratio knowledge, constant difference and knowing that the overlapped area is the same value for both individual shapes.

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

Overlapping shadows due to multiple light sources

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P5/P6 Math: Two Overlapping Identical Rectangles

The concept of overlapping shapes can also be found over in these questions.

Such questions require the concept of constant difference and will usually appear in Paper 2.

Calculator usage is allowed.

Overlapping of Red and Blue and Green lights to obtain White light

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P6 Math: Overlapping Areas of 2 Shapes ( Triangle and Rectangle )

This question type presents 2 overlapping shapes.
The areas of both shapes are not given but certain dimensions of the shapes are given.
The question will ask for the area difference between 2 non-overlapped regions.

Such questions are common in both paper 1 and paper 2 of P6 exam papers.

Calculator is allowed if such questions appear in Paper 2.

Overlapping leaves of the forest canopy to capture as much light as possible

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P6 Math: Overlapping Shapes with Ratios

The following question presents 2 shapes that are overlapping each other.

Such overlapping shapes questions often appear in P6 Paper 2.
Calculator usage is allowed.

The comparison of each whole shape's area with another is respresented using a ratio.
The ratio of the are that is not overlapping each other is also provided.

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P4/P5 Math: Before and After Age ( Multiples given at First and Total give at the End)

Such questions about age, requires students to understand that the age gap remains constant (ie constant difference) and that both ages need to add (or subtract) the same amount when talking about the number of years to the future (or the past).

A comparison using multiples will be given at first.
A total of the sum of the ages is also provided at the end (either a few years into the future or to the past).

Such "before and after" questions usually appear in Section C of P4 and Paper 1 of P5.
Calculator usage is not allowed (for P5).

Similar questions such as this(but not dealing with age) can also be found "here".

Ben is thrice as old as Alan now.

In 3 years time, Ben and Alan have a total combined age of 54.

How old is Ben now?

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P5/P6 Math: Same Container Filled with Different Fractions of Liquids

Such questions refreshes the concept of P4 constant difference where the student cannot ignore the presence of the container that is holding the items within.

Questions like these usually appear in Paper 1 of P5 and P6 exams.
Calculator usage is not allowed.

Similar versions of this concept with varying difficulties can also be found "here".

A bottle, when completely filled with water, has a mass of 1000g.

The same bottle, when only ¹/₂ filled, is 600g.

a) What is the mass of the empty bottle?

b) What is the mass of the bottle if ¹/₄ filled with water?

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