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P5/P6 Math: Advance Assumption with 3 variables consisting of 1 accumulation and 2 deductions

In a former "Assumption Method" example shown here, the element of "deduction" is introduced and students will have to use a slightly different way to address the "deductions" when performing calculations using the "Assumption" method.

This question type below, requires students to be able to handle another variable and remove it from the total number of marks before using the "Assumption" method(with subtraction).

Such questions are now common in P5 SA2 Paper 2.
Calculator usage is allowed.

Alison took Mathematics Quiz containing 40 questions.
For each correct answer, 3 points will be awarded.
For each wrong answer, 2 points will be deducted.
For each question without answer, 1 point will be deducted for a blank answer.
Alison scored a total of 64 points with 9 questions that she left blank.

How many questions did Alison answer correctly?


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P5/P6 Math: 3 Item Types with Different Quantities and Values

Such questions uses fraction and multiples(ratio) to give a breakdown of the distribution of 3 different items. Each of the item have different values and the total value of all quantities of 3 items is also provided.

Such questions are common in Paper 2 of P5 exams.
Calculator usage is allowed.

Erica bought a number of durians,watermelons and jackfruits 
from the market and spent $620 altogether.
1/2 of all the fruits bought were durians.
The ratio of the number of watermelons to jackfruits bought was 3:2.
Each durian costs $20, each watermelon $4 and each jackfruit was $6.

How many durians did Erica buy?



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P4 Math: Quantity Difference and Total Value Given

This is an easier version of a common P5 question shown here.

There are 2 types of items purchased and one of the items bought is slightly more than the other.
The cost of each type of item is given and the difference between the quantities of the 2 types of items bought is also know.

Such question requires students to use "set method" to solve.
These questions are common in Section C of P4 exam papers and will be more apparent in P5 exams.

Calculator usage is not allowed.

Siew Lee bought 3 more apples than pears and 
paid $71 altogether for all the apples and pears.
Each apple cost $5 and each pear cost $3.

How many apples did Siew Lee buy?


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P6 Math: Bill shared by 3 people but one of them paid first

A bill is shared equally by 3 people whom have different amounts of money at first.

This is a very unique question that requires students to make use of "Total Unchanged" to visualize the models between all 3 parties.

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

Mary, Roger and Ken shared the cost of a gift for their father equally.
If Mary paid for the gift first, the amount she have remaining will 
be 4/9 of the amount of what Roger have at first. 
If Roger paid first, the amount he have remaining will 
be 11/15 of the amount of what Mary have at first.
If Ken paid first, he'd have no money remaining.

If Roger had $126 more than Mary at first,
how much did the gift cost?


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P5/P6 Math: Cutting into pieces with a tool

The question below requires students to see that one cut can cut a single length into 2 pieces.
And 2 cuts into 3 pieces.

Such questions are common in Paper 1 of P5 and P6 exams.
Calculator usage is not allowed.

Questions of a similar nature can be also found here.

A carpenter using a hacksaw can saw a length of wood into 3 pieces in 3 minutes.
How long will it take for the carpenter to saw the same length of wood into 9 pieces?
(*Hint* The answer is not 9 minutes.) 

A Hacksaw



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P3/P4 Math: Fitting Equal Quantities into Containers with Remainder

The following question requires basic division so as to find out how many containers can be fitted with equal quantities but there will be some remainder after performing the division.

Such questions are common in P4 exams in Section A or B.

Mrs Lim is planning an excursion for her 60 students.
She needs to ferry the students and herself to the Science Center.
A mini-bus can sit up to 12 people.

What is the least number of mini-buses needed 
to ferry the students and herself to the Science Center?

Typical 12-seater mini-bus

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P5 Math: Percentage and Ratio to describe 3 Values

Once students are taught percentage and ratio, these 2 concepts can be presented in the same problem sum such as the one below.

Students must make use of the "repeated identity" method to solve.

Such questions are common in WA2 and SA2 of P5 exams.
Calculator usage is allowed.

There are oranges, pears and apples for sale at a fruit stall.
15% of the fruits at the stall are oranges.
The ratio of pears to apples at the stall is 12:5.
There are 150 more apples than oranges at the stall.

How many fruits are there altogether at the fruit stall?


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P6 Math: 2 Different Comparisons between 3 Parties

The relationship of 3 values are being compared by using the sum of first two to compare with the third.
2 of such comparisons are given with the known differences.

Such questions are common in Paper 2 of P6 Prelims.
Calculator usage is allowed.

Ahmad, Balu and Canaan, each have some marbles.
Ahmad's marbles make up 1/4 of their total number of their marbles.
Ahmad and Balu together, have 66 more marbles than Canaan.
Canaan and Ahmad together, have 24 more marbles than Balu.

How many marbles do they have altogether?


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P5/P6 Math: Fraction of Shaded Triangle in a Square Grid

A triangle occupies space in a grid container many smaller squares.

Students are expected to find out the fraction of the grid that is shaded (or unshaded) without knowing the dimensions of the square grid.

Such questions are common in Paper 1 of P5 and P6 exams,
Calulcator usage is not allowed.

In each of the figures, what fraction of the figure is unshaded?




P5/P6 Math: Ratio of 4 Triangles in a Rectangle

A rectangle as a composite figure containing 4 triangles.
The relationship between the triangles and rectangles are given in both fractions and ratio.
A value of the area of one of the shapes is also given.

Such questions are common in P5 and P6 Paper 2.
Calculator usage is allowed.


Triangular window panes forming rectangles and squares



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