The Zimaths competition

by Prof. Eduard Belinsky

There are two parts to this regular feature: Normal and Abnormal. Normal is open to any school student, while Abnormal is open to anyone, teachers included. Send us your answers with workings and the best entries will be mentioned in the next issue. Prizes are Z$50 and Z$30 for the Normal section and Z$75 and Z$50 for the Abnormal, and are again kindly partially sponsored by Mr & Mrs Farai Nyabadza. You are encouraged to send in your solutions even if you cannot answer all questions. Regrettably, prizes are only available readers in Zimbabwe.

Normal Section

1. Gina walks to the University and returns by bicycle in 1¹/₂ hours. Riding the bicycle to the University and back takes half an hour. How much time does Gina take to walk to the University and back?

2. Solve the following set of simultaneous equations:

Abnormal Section

1. Nine points are randomly placed in a unit square. Prove that three of these points form a triangle whose area is at most ¹/₈.

2. The graph shows a line with equation y = 2ax+b tangent to a curve with equation y = ax²+bx+c, where a ¹ 0. Why is this situation impossible?
3. How many different ways can be found in the pyramid below to read the word ``ZIMATHS''?

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