# Mcv4ua Practice Test Essay

1107 Words5 Pages

Calculus and Vectors MCV4U-A
Practice Test
Time: 2 hours
Total Marks: 101
Final Test Score _____ ÷ 101 × 100 = _____%
Instructions
• There is a label attached to this page. Compare the course code on the label with the course code printed on the Final Test to make sure that they are the same. Inform the Final Test supervisor immediately if they are not the same. • The Final Test pages are numbered 1 to 13. Check to see that all thirteen pages are attached. Inform the Final Test supervisor immediately if there are any pages missing.
• You may use a calculator during the Final Test. You may not use any books or notes.
• You must write your answers in the space provided.
• There are two parts to the test. A breakdown of the marks*…show more content…* (7 marks)
d) Indicate the intervals where the graph is concave up and concave down. (2 marks)
e) Sketch the graph of the function. (3 marks)
www.ilc.org
Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved.
page 8
Calculus and Vectors MCV4U-A
Practice Test
9.
An open-topped cylindrical water reservoir has a volume of 320πm3.
2
The material used for the bottom of the reservoir costs $5/m and the
2
material used for the vertical portion costs $8/m . Determine the radius and the height of the cylinder so that the cost is a minimum.
2
2
(Volume = πr h and Surface area = πr + 2πrh) (8 marks)
Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved.
www.ilc.org
Calculus and Vectors MCV4U-A
Practice Test
page 9
Part B: Vectors (39 marks) (approximate time: 40 minutes)
10. A chandelier with a weight of 100 N is suspended at a single point by two cables that make angles of 45° and 60° with the ceiling. Calculate the tension in each cable. (8 marks)
→
→
11. Find the angle between the vectors u = (–5, 1, 3) and v = (–2, 1, –2).
(5 marks)
www.ilc.org
Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved.
page 10
Calculus and Vectors MCV4U-A
Practice Test
12. Determine the scalar, vector, and parametric equations of the plane that passes through the points A(1, –1, 2), B(0, –1, 1), and C(1, 2, 1).
(9 marks)
Copyright © 2008 The Ontario Educational