mathematical mathematical, Summaries of Law

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1. Find the value of ( 101 + 234 + 567 ) × ( 234 + 567 + 89 ) − ( 101 + 234 + 567 + 89 ) × ( 234 + 567 )
2. The figure shows 4 overlapping circles with each circle passing through the centres of its adjacent 2 circles. The figure measures 60 cm vertically from top to bottom as shown below. Find the total area of the shaded parts. (Take 𝜋 = 3. 14 )

1. Mrs. Tan and Mrs. Ong were having a conversation at a park. Mrs. Tan: “Hi, how are you? How are your children? You have three if I remembered correctly. How old are they now?" Mrs. Ong: “Yes, I have three children. The product of their ages is equal to 96. The sum of their ages is equal to the number of trees in this park.” Mrs. Tan counted the number of trees in the park, thought for a while and said, “I still could not figure out the ages of your children.” Mrs. Ong simultaneously replied, “Pardon me, for I have to pick up my children from the school across the park. We can catch up again soon. Goodbye.” Finally, Mrs. Tan managed to figure out all the ages of Mrs. Ong’s children. How old is Mrs. Ong’s youngest child?

1. The diagram below shows two squares 𝐴𝐵𝐶𝐷 and 𝐷𝐸𝐹𝐺 where 𝐴𝐷𝐺 is a straight line and point 𝐸 lies on 𝐷𝐶. The length of each side of square 𝐴𝐵𝐶𝐷 is 8 cm. What is the area of triangle 𝐴𝐶𝐹?
2. What is the remainder when 6 × 2017 !"!#^ is divided by 11?

1. 9 natural 3 - digit numbers, represented by 9 different letters 𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑝, 𝑞 and 𝑟, formed an addition sequence shown in the diagram below. Find the smallest possible value of 𝑟. 𝑎 + 𝑐 = 𝑒

𝑏 + 𝑑 = 𝑓 = = = 𝑝 + 𝑞 = 𝑟

1. Given that 𝐴 𝐵

where 𝐴 and 𝐵 are positive integers, find the value of 𝐴 + 𝐵. Note that 2 −

2 −^20232024

is the 1 st^ layer. 2024 layers

1. In the following figure, 𝐴𝐵𝐶𝐷 is a square, 𝐵𝐷 is parallel to 𝐸𝐶 and 𝐵𝐷 = 𝐵𝐸. Find ∠𝐵𝐸𝐶 in degrees.

1. There are 6 red points labelled R1, R2, R3, R4, R5 and R6, and 6 green points labelled G1, G2, G3, G4, G5 and G6. Using straight lines, each red point is connected to at least one green point and each green point is connected to at least one red point. The number of green points connected to R1, R2, R3, R4 and R5 is 5 , 4 , 3 , 2 and 2 respectively. The number of red points connected to G1, G2, G3, G4 and G5 is 4 , 3 , 2 , 1 and 1 respectively. Find the number of red points connected to G6.