Mathematics 3CD: Further Examination Practice Questions
Mathematics 3CD – Further Examination Practice Questions.
1. [3, 3 and 3 = 9 marks] Consider the function i) Show that
ii) Determine the domain for which the function is increasing.
iii) Given that determine the values of x for which the function is concave downwards. 2. [1, 3 and 4 = 8 marks] Consider the functions and i) Find ii) Determine and state its domain and range iii) Find, algebraically, the values of x for which
3. (3, 2, 2 and 2 = 9 marks) Consider the system of equations shown; a) Reduce this system of equations algebraically or using an augmented matrix.
b) Determine the value(s) of ‘k’ for which the system of equations has i) No solutions ii) An infinite number of solutions
c) Determine the unique solution if k = 4.
4. (3, 3, 1, 3 and 3 = 13 marks) A company makes two types of bags, the shoulder bag and the backpack. Each day the company produces at least 60 bags, with a maximum of 50 backpacks. To keep up with demands the company must ensure that the number of backpacks produced is at least the same as or more than the number of shoulder bags produced.
Let x be the number of shoulder bags produced each day.
Let y be the number of backpacks produced each day.
a) Assuming x0 and y0, list the other three constraints on x and y as stated in the problem.
b) The graph displays the constraints listed in a).
Each backpack requires one tag and each shoulder bag requires two tags. To avoid an oversupply the company must use at least 80 tags each day. Write down this constraint and draw it on the graph above.
c) Shade the feasible region.
d) Each shoulder bag costs the company $12 to produce and each backpack costs the company $10 to produce. Determine the number of
1. [3, 3 and 3 = 9 marks] Consider the function i) Show that
ii) Determine the domain for which the function is increasing.
iii) Given that determine the values of x for which the function is concave downwards. 2. [1, 3 and 4 = 8 marks] Consider the functions and i) Find ii) Determine and state its domain and range iii) Find, algebraically, the values of x for which
3. (3, 2, 2 and 2 = 9 marks) Consider the system of equations shown; a) Reduce this system of equations algebraically or using an augmented matrix.
b) Determine the value(s) of ‘k’ for which the system of equations has i) No solutions ii) An infinite number of solutions
c) Determine the unique solution if k = 4.
4. (3, 3, 1, 3 and 3 = 13 marks) A company makes two types of bags, the shoulder bag and the backpack. Each day the company produces at least 60 bags, with a maximum of 50 backpacks. To keep up with demands the company must ensure that the number of backpacks produced is at least the same as or more than the number of shoulder bags produced.
Let x be the number of shoulder bags produced each day.
Let y be the number of backpacks produced each day.
a) Assuming x0 and y0, list the other three constraints on x and y as stated in the problem.
b) The graph displays the constraints listed in a).
Each backpack requires one tag and each shoulder bag requires two tags. To avoid an oversupply the company must use at least 80 tags each day. Write down this constraint and draw it on the graph above.
c) Shade the feasible region.
d) Each shoulder bag costs the company $12 to produce and each backpack costs the company $10 to produce. Determine the number of