P6 Math : Buying 2 different items in Different Quantity and Different Value with known Ratio

This question type is similar to the one practiced here.

2 different items are sold in bags of different quantities and not sold individually.
Each bag of items have different value.
A ratio of the number of items bought is given and the difference between the total values of the 2 items are also known.

Such questions require the knowledge of "set method" and "common multiples" and "ratio".

As these questions appear in Paper 2 of P6 exam papers,
calculator usage is allowed.

Carnations and roses are sold in bunches at a market stall.

A bunch of 12 roses are sold at $27.

A bunch of 9 carnations are sold at $23.

The number of roses that Alexis bought to the number of carnations
that Belle bought was in the ratio of 2:3.

Belle paid $76 more for her carnations than Alexis for her roses.

a) How much did Alexis pay for her roses?

b) How many bunches of carnations did Belle buy?

Did you know?
Freshly cut carnation flowers last longer than roses

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

The question below will randomize with different numbers every hour. 

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P6 Math: Fraction of Remaining with Before and After

Many P6 Math Paper 2 questions in Mid Year and Prelim exams makes use of 2 concepts learnt in P5.

Concepts such as "Fraction of Remaining" and "Before and After" and other ratio concepts are often combined to produce a question like the one below.

Such questions will appear in Paper 2.
Calculator usage is allowed.

In a farm, ²/₅ of the animals were chickens.

⁹/₁₀ of the remaining animals were pigs and the rest were ducks.

There were 112 more pigs than chickens at first.

After the farmer sold some of the chickens,

4/5 of all the animals left were pigs and ducks.

How many chickens were sold?

Animal Farm by George Orwell
All young adults should read this at least once

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P5/P6 Math: Repeated Identity (Ratios as Fractions)

The question presents 3 unique items of different quantities and each or 2 of them are compared with the total using "fractions".
2 of such comparison statements are given and the total is also known.

Questions like these requires students to use "ratio" methods to solve a seemingly "fraction" problem sum.

Cocepts such as "total unchanged" and "repeated identity" are required to solve such questions.

These questions will usually appear in Paper 2 of P5 and P6 exam papers.

Calculator usage is allowed.

Patricia has a collection of 135 books, stickers and pens.

²/₃ of these items were not pens.

³/₅ of these items were either books or pens.

a) How many items of Patricia's collection were stickers?

b) What is the ratio of her stickers to pens?

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P6 Math: Area of Triangle in a Rectangle

A rectangle or square is presented with a triangle inside the shape.
The 3 corners of the triangle are touching the sides of the rectangle/square.

Such questions require students to use the concept that triangle is half of the area of the rectangle/square that it shares its base and height with.

These questions appear can appear in both Paper 1 and in Paper 2.

For the purposes of this practice,
calculator usage is allowed.

Triangular and other shaped dices

The figure below consists of a square with an area of 200 cm².

Triangle BDF has its 3 corners touching the sides of the square.

AB, AF, BC and EF have the same length as each other.

What is the area of triangle BDF?

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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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P4/P5 Math: Fraction with units and without units

P4 and P5 Fractions is a relatively large topic.

One of the type of question requires student to be able to tell the difference between the following fraction problem sum.

Malcolm has 3/5 kg of sugar.	Malcolm has 3/5 kg of sugar.
He gave away 1/2 kg of the sugar.	He gave away 1/2 of the sugar.
What is the mass of sugar he has left?	What is the mass of sugar he has left?

Can you spot the difference between the 2 fraction problem sums above?

Both will produce different answers due to this subtle difference.

Such questions often appear in Section B or P4 Papers or Paper 1 of P5 Papers.
Calculator usage will not be allowed.

A more advanced version of this question can also be found here.
An expert version of this question can be found here.

Spot the difference arcade game

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P4/P5 Math: Before and After with Starting Total and Ending Equal

Questions like these require students to be able to use model drawing to visualize how the ending became both the same amount.

The total at first is given. Both parties undergo a change [ increase and decrease respectively.

And both parties have the same at the end.

Such questions will appear in Section C of P4 and Paper 1 of P5.

Calculator usage is not allowed.

There are a total of 140 red and green bottles at first.

After 12 red bottles are discarded and 20 green bottles were added,

there are now equal number of red and green bottles.

How many green bottles were there at first?

Green bottles due for recycling

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