SA Mathematics Olympiad 2025 – Senior Round 2 Solutions (Questions 11-16)

Описание: Complete worked solutions to the SA Mathematics Olympiad 2025 – Senior Round 2 (Questions 11-16).

Presented by Professor Poobhalan Pillay.

This video provides clear, step-by-step explanations to help learners prepare for the South African Mathematics Olympiad (SAMO) and strengthen advanced problem-solving skills.

Paper: 2025 Senior Section – Second Round
Section: Part B (5 marks per question)

Questions covered in this video:

Question 11: A trapezium has area 300 and parallel sides 𝑎 and 𝑏 . If the height ℎ between the two parallel sides is increased by 10%, and the lengths of both sides 𝑎 and 𝑏 are decreased by 10%, determine the area of the new trapezium.

Question 12: Find the value of 𝑥 if 𝑥 =
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Question 13: The probability that at least two of the three children in a family are girls is 5/16. The probability of having a girl or a boy is equal to 1/2. Determine the value of 𝑥.
(Use the exact symbol from the paper if it specifies a probability variable.)

Question 14: Four students each choose a number. When each student’s number is added to twice the mean of the other three numbers, the following sums are obtained: 42, 54, 66 and 78. Determine the mean of the four numbers chosen by the students.

Question 15: The vase-like shape in the sketch is formed by six circular arcs, 𝐴𝐵, 𝐵𝐶, 𝐶𝐷, 𝐷𝐸, 𝐸𝐹 and 𝐹𝐴, each of which is a quarter of the circumference of a circle with radius 6, all joined together. What is the area of the vase?

Question 16: Contestants in a singing competition must each select two songs from a list of 20 to perform. What is the least number of contestants that need to enter the competition to be certain that at least two contestants make the same selection?

Timestamps:
0:01 Question 11
6:54 Question 12
9:51 Question 13
14:27 Question 14
22:32 Question 15
36:45 Question 16

This video forms part of the SA Mathematics Olympiad 2025 Junior Round 2 Solutions series (2018–2025).

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• SA Mathematics Olympiad (Junior & Senior)
• Round 1, Round 2 and Round 3
• Team Round Solutions