COVENANT CANADA ACADEMY
COURSE CODE: MCV4U
Teacher(s): Rui Zhang
Student: ______________________
Date:_____________________
Duration: 2 Hours
Number of Pages (excluding cover page): 4
Instructions
Ensure that your exam has the correct number of pages.
Write the answers to Parts A ,B, C and D in the space provided with each question.
Every key step should be shown. Marks will lose even if the answer is correct.
Write your name on each page.
Mark Distribution
Part A: Multiple Choices
24
Part B: Short Answer
30
Part C: Graph
10
Part D: Application
36
Total Marks:
K/U
30%
T/I
20%
C
20%
A
30%
/100
Page 1 of 5
Part A: Multiple Choices [24]
1. Determine lim f ( x ) , where
x 2
A 6
B -6
C -2
D 2 E the limit does not exist
2. For which value(s) of x is the tangent to f ( x )
A x=1
B x= -3,1
C x= -1,3
x2 3
horizontal?
x 1
D x= 3 E x= 3
3. If A goes from (x1, y1) to (x2, y2), what is A ?
A
( x2 x1 ) 2 ( y2 y1 ) 2
B
( x2 x1 ) 2 ( y2 y1 ) 2 C
D
( x2 x1 ) 2 ( y2 y1 ) 2
E Need more information
( x2 x1 ) 2 ( y2 y1 ) 2
4. Given that a [1, 2, 7] and b [10, 4, 2] What is a 2b ??
A 16
B 22
C 32
D 44
E 56
5. If A is any non-zero vector, a unit vector in the same direction of A would be
A A A
1
B A
A
1
C A
A
D A A
E 1
6. If 5 A 15 , then what is A ?
A 3
B 45
C 15 D 5
E 20
Page 2 of 5
Part B: Short Answer [30]
7. Evaluate the following limits [10]
a) lim ( x 3 3 x 1)
x 1
b) lim
x2
6 x 2
x2
8. Find the derivatives [10]
3x 2 1
a) f ( x )
2x2
b)
f ( x ) sin(cos(e 2 x 1 ))
2
9. Given a [ 1, 2, 3] ， b i j k and c 2i 4 j k [10]
Page 3 of 5
a)
2( a c ) 3(2b c )
b)
d c a and DETERMINE the projection of d on b
Part C: Graph [10]
10. Sketch the graph of f ( x ) x 3 81x
Part D: Application [36]
11. A pilot flies on a heading of N 30 W with an airspeed of 240 km/h. Her actual ground velocity is 250
km/h at a bearing of 300 . [15]
a) Draw a vector diagram to show the air velocity, ground velocity and wind.
b) Calculate the speed and direction of the wind.
Page 4 of 5
12. A closed rectangular storage box with a square base is to be constructed so the volume is 3000cm 3 .
Determine the dimensions of the box that minimize the amount of material needed to make the box. [10]
13. Determine the intersection of these lines[11]
l1 :[ x, y ] [3,1] t[2, 4]
l1 :[ x, y ] [1, 0] s[1, 1]
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Page 5 of 5
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