P5P6 Math: Before and After (2 Equal Total at first with 2 different item types)

This question type is the slightly more complex version of the one shown here.

Both person start with the same total.

Each will use some of their total to make different quantities of 2 items.

The comparison between each of the 2 items and their respective remaining are given.

"Comparison models" will be needed to solve such questions.

Alan and Ben has equal amount of clay.

After Alan used his clay to make 10 bowls, he has 1.2kg of clay left.

After Ben used his clay to make 16 plates, he has 0.66kg of clay left.

Making 3 bowl uses the same amount of clay as 4 plates.

How much clay each boy have at first?

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P5P6 Math: Before and After (2 Equal Totals at First)

For this question type, there will be 2 equal totals, at first, belonging to two different persons.

Each will use some of their totals to make different quantities of the same items made and the remaining of each person are provided.

For such questions, students are expected to draw "Comparison Models" in order to solve.

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

Calculator usage is allowed.

Jake and Donna each have the same amount of flour.

Jake used some some of his flour to make 17 cookies and
had 45g of flour left.

Donna used some of her flour to make 8 cookies and
had 270g of flour left.

How much flour did each child have at first?

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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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Diagram may not be drawn to scale

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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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Diagram may not be drawn to scale

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