# Thinking and Inquiry

MCV4U Grade 12 Thinking/Inquiry 18 Communication 6 Total Marks 24 Part A- Thinking and Inquiry( 18 marks) Communication (6 marks) 1. Determine the maximum volume of a square-based box with an open top that can be constructed with 3600 cm2 of cardboard. MCV4U Grade 12 2. A store sells 380 frozen yogurt cakes per week at a price of $12.50 each. A market survey indicates that for each $0.25 decrease in price, five more cakes will be sold each week. a) Write the demand function. b) Write the revenue function. c) Determine the marginal revenue. d) For what price is the marginal revenue zero? Interpret the meaning of this value. MCV4U Grade 12 3. A man starts walking north at a speed of 1.5 m/s and a woman starts at the same point P at the same time walking east at a speed of 2 m/s. (6 marks) a) How far is the man, m, from his starting point after one minute? b) b) How far is the woman, w, from her starting point after one minute? 4. The sum of two positive numbers is 12. If the product of one number cubed and the other number is a maximum, find the two numbers. MCV4U Grade 12 5. A farmer wants to fence an area of 2 240,000m in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. How can be done to minimize the cost of the fence? MCV4U Grade 12 6. A pebble is dropped into a pond and waves begin to spread. The radius of the circle of waves grows at a rate of 1 m/s. Find the rate of increase of the area of the circle at the instant the radius is 8 m. Nucleus High School Derivatives Chapter: 2.1 – 2.5 Course Code:MCV4U1 Name: Date: Note: Steps in each question will be marked as COMM. T/I will be marked in Q2 and Q6. 1. Differential the following K/U 4 marks

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