Grade 12 Math Studies Calculus Option Comprehensive Test
Show your work!
page 1
[30 marks total]
(DL, 2002)
Name ................................................................... Date ...................................
1) If the velocity of a particle is given by
v(t )  6t 2  t 3 , find:
a)
The average rate of change of the velocity during the third second.
b)
Find the velocity at t = 2.1 and 2.01
v(2.1) =
c)
t = 2.1
[3]
[4]
v(2.01) =
Find the average acceleration between t = 2 and ...
[4]
t = 2.01
d)
From part (c), estimate the exact acceleration at t = 2
[1]
e)
Find the equation for a(t ) , acceleration as a function of time
[2]
f)
Hence confirm the exact acceleration at t = 2 (show how)
[2]
g)
If s(1)  6.8 , find the equation for s (t ) , displacement (position) as a function of time
[5]
Grade 12 Math Studies Calculus Option Comprehensive Test
Show your work!
page 2
[30 marks total]
(DL, 2002)
2) Choose only one of the following two problems (work and answers on another sheet): [4]
a)
b)
3) Draw a rough sketch below of the function from the information in the following table:
x
f (x)
f ' (x)
0
2
positive
2
4
0
4
...
positive
5
7
0
[5]
6
...
negative
What are the special names of each of
the two critical points?
y
(2, 4): ..............................................
(5, 5): ................................................
x
Grade 12 Math Studies Calculus Option Comprehensive Test
Show your work!
page 3
[30 marks total]
(DL, 2002)