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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P4 Math: 2 Different Items bought at different quantities (Multiples of one another)

2 different items are bought at different quantites and the cost of one of the item is a multiple of the other.

Such questions are common in P4 exams and students will need to draw models so as to represent the numerical values given.

Alice bought 5 pens and Karen bought 2 books.

Each book costs thrice as much as each pen.

Both girls spent $66 on the books and pens altogether.

How much did Alice spend on her 5 pens?

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P5/P6 Math: A Total of 3 Given with Equal Ratio at the End

This question type starts with a known total of 3 parties.

Each party undergo either a fractional decrease or value increase/decrease and all 3 parties ends with equal ratio at the end.

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

Calculator usage is allowed.

Derrick, Lawrence and Patrick had $3025 altogether at first. 

After Derrick spent ⁵/₇ of his money and Lawrence spent ¹/₄ of his money 

and Patrick spent $155, each boy have the same amount of money left. 

How much did the 3 boys have altogether at the end?

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P5/P6 Math: Starting Ratio and Ending with Difference

Ratio, taught in P5, will appear with many "Before and After" type problem sums.

One of such problem sums presents itself with a known starting ratio between 2 parties.

After one of the party undergoes fractional decrease and the other going through an increase or decrease with a known value, the ending difference is given.

Such questions are common in P5 Paper 2.

Calculator usage is allowed.

Aaron and Kelvin have some sweets in the ratio of 4:5.

After Aaron ate ¹/₂ of his sweets and Kelvin bought 30 more sweets,

Kelvin now has 63 more sweets than Aaron.

How many sweets did they have altogether at first?

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P5/P6 Math: Average Difference if Only One Changed

An average score of a group of students is given.

If one of the student's score increases or decreases by a certain value, the average score changes accordingly.

Such questions are common in Paper 1 of P5 and P6 exams.

Calculator usage is not allowed.

After a Science Test, the average score of a group of students was 83.

Due to an error in marking, one of the students scored 68 instead of 88.

The new average of the group became 82 because of the adjustment.

How many students were there in the class?

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P4 Math: Writing down the number in Decimals with words given

0.1 is also known as 1 Tenth and 0.01 is also known as 1 Hundredth.

Students learn more about decimals in Primary 4 and are expected to write down the number in decimals with the words given, such as

12 thousands, 4 hundreds, 3 ones and 68 thousandths 

can also be written as 

12403.068 in decimals.

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

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P5/P6 Math: Starting Total Known with Both Parties undergoing Fractional Decrease

A total of 2 parties is given.

Each of the 2 parties undergo different fractional decrease.

The comparison between the amount left is given as multiple of another.

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

Calculator usage is allowed.

Similar questions of this type can also be found here.

Jayden and Keane have a total of $2024.

After Jayden spent ²/₅ of his money on a gaming console and

Keane spent ³/₄ of his money on a phone, 

Jayden has twice as much money left as Keane.

How much did Jayden have at first?

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