# MUFY semester 1 mathematics trial examination 2012

Otherwise, two straight lines are perpendicular to each other if the product of their slopes is –1. MEASUREMENT Area of triangle Area of circle Area of trapezium Curved surface area of a cylinder Volume of rt. circular cylinder, height h Volume of right circular cone, height h Volume of sphere Volume of right pyramid, base area A, height h Question 1 [5 + 3 = 8 Marks] Consider the function (a) Find the derivative of the function, to the simplest form. (b) Hence, show that the graph of the function has no stationary points. Question 2[4 + 2 = 6 Marks]

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Find the following, to the simplest form: (a) (b) Question 3 [7 + 6 = 13 Marks] (a) Find and hence evaluate the exact value of (b) Find and hence evaluate the exact value of Question 4[5 + 5 + 3 = 13 Marks] (a) Given below is the graph of On the same axes, sketch the graph of . (b) Given below is the graph of On the same axes, sketch the graph of (c) Given below is the graph of On the same axes, sketch the graph of Question 5 [1 + 5 = 6 Marks] Given above is the graph of (a) Explain why c = 3. 5. (b) Calculate the exact values of a and b. Show complete working.

Consider the function (a) Factorize the function completely. (b) Hence, find the axial intercepts of the graph of (c) Find the coordinates of the stationary points of the graph of using your graphic calculator. Give your answer correct to 1 decimal place. (d) On the axes below, sketch the graph of Label all the important features. y x Question 7 [2 + 4 + 3 + 4 = 13 Marks] The number of bacteria present in a lasagne, t minutes after it was found contaminated, can be modelled by At time t = 0, the number of bacteria is 300 and when t = 10 minutes, the number increased to 450. (a) Find (b) Find the value of k, correct to 2 decimal places. (c) Find the rate of change in the number of the bacteria after for 1 hour. (d) How long will it take for the number of bacteria to be 600? Give answer correct to the nearest minute. Question 8 [2 + 5 + 1 + 7 = 15 Marks] Consider the function where (a) Find the largest possible value of t, so that exists. Hence, state the range of function (b) Find the rule of inverse function, and state its domain and range.

Using your graphics calculator, find the coordinates of the point of intersection of both the graphs of and Give answer correct to two decimal places. (d) On the axes below, sketch the graphs of and Label all the important features. y x Question 9 [5 + 6 + 3 = 14 Marks] A special container is used to fill a certain chemical that is used for the production of a medicine. Volume (V ) of chemical in the container is given by and surface area (S ) of the chemical is where x is the depth of the chemical in the container. Initially (at time t = 0), the container is empty.

The chemical is then poured in at a constant rate of (a) Express the rate of increase in the depth, x, of chemical with respect to time, t. Hence, how fast is the chemical rising when x = 4. Give an exact answer. (b) Find when Describe the rate of change in surface area of the chemical when (c) The container is 6 cm high. How long will it take for the chemical to fill the container, to the nearest second. Question 10 [5 + 2 + 1 + 7 = 15 Marks] Given and (a) On the axes below, sketch the graphs of and y x (b) Using your graphics calculator, find the points where both the graphs.