Minsi MATHEMATICS OLYMPIAD ROUND ONE - LEVEL THRE (GRADES 10, 11 AND 12) - \( 10^{\text {ch }} \) MARCH 2025 Timet 60 Minutes ( \( \$ 1 \) to \( \# 15: 3 \) Marlss each ) Total Marks: 45 Which of these is the largou number? A) \( 2+0+1+3 \) B) \( 2 \times 0+1+3 \) C) \( 2+0 \times 1+3 \) D) \( 2+0+1 \times 3 \) E) \( 2 \times 0 \times 1 \times 3 \) What is the 'hundreds' digit of: \( 2025^{2}=2025 \) A) 0 B) 1 C) 4 D) 5 E) 6 The numbers \( x \) and \( y \) satisfy the cquations \( x(y+2)=100 \) and \( y(x+2)=60 \) What is the value of \( x-y \) A) 60 B) 50 C) 40 D) 30 E) 20 In a 'ninety nine' shop, all items cost a number of rands and 99 cents. Susan spent R665, 76. How many ltems did she buy? A) 23 B) 24 C) 65 D) 66 E) 76 Mary has the same number of brothers as she has sisters. Ench one of her brothers has \( 50 \% \) more sisters than brothers. How many children are in Mary's famtily? A) 5 B) 7 C) 9 D) 11 E) 13 Which of the following is equivalent to \( (x+y+z)(x-y-z) \) ? A) \( x^{2}-y^{2}-z^{2} \) B) \( x^{2}-y^{2}+z^{2} \) C) \( x^{2}-x y^{2}+x=-z^{2} \) D) \( x^{2}-(y+z)^{2} \) E) \( x^{2}-(y-z)^{2} \) How many two-digit numbers have remainder 1 when divided by 3 and remainder 2 when divided by 4 ? A) 8 B) 7 C) 6 D) 5 E) 4
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Math enthusiasts throughout history have celebrated the beauty of problem-solving, with notable early civilizations like the Babylonians and Egyptians laying the groundwork for algebra and geometry. They used sophisticated techniques, such as the base-60 system and geometric approaches, which inform modern mathematics. Olympiads, like the one you're preparing for, continue this legacy, challenging thinkers to stretch their limits and explore creative solutions to complex problems. If you're looking to sharpen your problem-solving skills, a great tip is to always verify the rules of arithmetic. Remember, multiplication takes precedence over addition and subtraction! Common mistakes involve miscalculating these priorities, which can skew results. For instance, in expressions with both addition and multiplication, ensure you handle multiplication first, just like prioritizing tasks in life to avoid chaos!