P6 Math: Same total quantity of 2 different items of different values

This question type is made famous during the 2021's Math PSLE exams.

The "Helen and Ivan" question.

2 items of different quantities and value are split into 2 groups containing same number of items. The individual value difference a between 2 items and the total value of one of the group [ containing different quantities of 2 items ] are given.

This is a P6 PSLE Paper 2 question.
Calculator usage is allowed.

Helen bought 64 pencils and some notepads.

Ivan bought 104 pencils and some notepads.

Both Helen and Ivan bought the same total number of notepads and pencils.

Each notepad costs $2.70 more than each pencil.

Helen spent a total of $1134 on their pencils and notepads.

How much did Ivan spend on all his pencils and notepads?

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P5 Math : Rates and Part Thereof

Rates are commonly taught after students are able to grasp the concepts of time and mutiples.

The term "Part Thereof" refers to a fixed portion, regardless consumed by part or whole, that is charged the same "rate".

Such questions are common in Paper 1 of P5 Math papers.
Calculator usage is not allowed.

The rates of taking a taxi ride ( based on distance ) is shown in the table below.

First 1 km	$3
Every 200m or part thereof	50 cents

How much will it cost to ride on this taxi for 2.3km?

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P6 Math: Splitting 2 groups to become 4

For questions like these, there will be a ratio to split a larger group into 2.

Each of the smaller group is divided into 2 smaller groups.
Students are required to make use of repeated identity concept in order to solve such questions.

These questions often appear in Paper 2.
Calculator usage is accepted.

The children in a dance hall are divided equally into 2 groups.

In the first group, there were 20 more girls than boys.

In the second group, there were 12 more boys than girls.

45% of all the children in the dance hall are boys.

How many children are there at the dance hall?

Vintage picture of children dancing in hall

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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

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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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