Principal Math Items Kr (1)

By Kasozi Rattibu 740281457 PRINCIPAL MATH TOPICAL PRACTICE ITEMS I WISH YOU ALL THE BEST Contact me for any Assistance TOPIC 1: NUMERICAL CONCEPTS Item 1 Nakato is a mobile money agent in her village, Mukono . When she started in January 2024, she had 50 regular customers. She observed that her customer base seemed to grow exponentially each month. By the end of March 2024 (after 3 months), she had 135 regular customers. She wants to predict her customer growth to plan for liquidity (cash and e -float) and potentially hire an assistant. Assume the growth follows the model 𝑁 = 𝑁0× 𝐾𝑡, where N is the number of customers after t months, 𝑁0 is the initial number of customers, and 𝐾 is the monthly growth factor. Tasks: a) Help Nakato in determining her monthly gr owth factor, 𝐾. Express your answer to 3 significant f igures. b) Determine the number of customers Nakato can expect by the end of December 2024 (after 12 months) if this growth rate continues. c) Nakato estimates she needs UGX 10,000 in float per regular customer per month. Using the predicted number of customers for December 2024, calculate the total float she would need. Express this amount using index notation in terms of powers of 10. Item 2 Mr. Okello is weaving a traditional Ugandan mat (ekikeeka) with intricate geometric patterns. One key element involves f itting square tiles made of dyed reeds into a rectangular border. The side length of each square tile needs to be exactly (√5−√2 )𝑐𝑚 for the pattern to align perfectly. The rectangular border has a length of (10√5 + 5√2 )𝑐𝑚 and a width of (8√5− 4√2 ) 𝑐𝑚. Tasks: a) Calculate the exact area of one square tile. Express your answer in the simplest surd form …