P6 Math: Circles with Rectangles and Diagonals

A rectangle is drawn inside a circle with one of its corner at the center of the circle.

The diagonal length of the rectangle between 2 corners is provided together with its length and breadth.

Students are expected to find the area of the circle using the information from the rectangle(within the circle).

Such questions often appear in P6 Paper 2 during the Prelims.
Calculator usage is allowed.

The semi-circle below has a rectangle inside of it.
The rectangle was drawn from the center of the circle.

What is the area of this semi-circle?

Take π to be 3.14

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

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P6 Math: Composite figure of Square formed around the edges of a Rectangle

The question below is a relatively uncommon one.

2 pairs of squares are drawn along the edges of a rectangle.
The total area of the 4 squares and the perimeter of the rectangle is known.
With that, students must find out what is the area of the rectangle in the middle.

Such questions appear in Paper 2 of P6 Prelim papers.
Calculator usage is allowed.

Composite rectangles in real life

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P5/P6 Math: Figure of 2 Overlapping Triangles

2 overlapping triangles sharing the same base but with different heights shares a common overlapped area.

Such questions requires students to know that the sum of the area of both triangles will definitely be more than the actual area of the figure shown.

Such questions are common in Paper 1 of P5/P6 exam papers.
Calculator usage is not allowed.

Triangular shaped support structures at the Eiffel Tower

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P6 Math: Different Percentage Discounts causing Different items to be Same Price

2 different items for sale at different discount percentages but has the same price after their respective discounts.

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

A pen was for sale at a 15% discount and a vase was selling at a 20% discount.
Both items were sold at the same price after the discount.

Lisa wanted to buy both discounted items but was short of $36.

If she only bought the pen at the discounted price, she'd have $100 left.

How much more will she need if she were to buy both items without discount?

An intricate antique Chinese vase

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

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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: Before and After ( Starting Difference with Ending Ratio)

Such questions are common for P5 and P6 exams.

Where the starting difference is known and the ending ratio is given after some numerical increase/decrease is applied to both parties.

As these appear mostly in Paper 2,

calculator usage is allowed.

A similar "before and after" type question can also be found here.

Eric has 450 more items listed on his online store than Kelvin.

After Eric sold 45 items and Kelvin listed 3 more items for sale,

the ratio of Eric's items for sale to Kelvin's items for sale became 3:2.

How many items did both have listed for sale at first?

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

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P6 Math: Redistribution of same total to lesser parties with left over

The same total meant to be equally distributed, is now distributed to lesser parties, with each party getting sligjhtly more than before. There will also be some left over after the "re-distribution" due to lesser shares.

A relatively similar question can also be found here.

Such questions are common in P6 Paper 2.

Calculator usage is allowed.

Miss Tan have 560 sweets to give to her class of 35 students.

Each student was supposed to get the same number of sweets.

Because some students were absent that day,

Miss Tan had 38 sweets left after distributing 2 more sweets
to all whom were present.

How many of her students were present that day?

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

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