Basic Skills Test for Calculus II
N. Mackey
Purpose: Determine if your knowledge of simple differentiation and integration skills, learned
in Calculus I, are adequate for this course.
Passing this test quickly is IMPORTANT.
There will be 10 differentiation and 2 antidifferentiation problems. Each problem will be graded
correct or incorrect. Any mistake means that the answer is incorrect.
To pass, you must get 9 out of 12 problems correct.
You may take the test two times beyond the in-class testing. But it is STRONGLY advised that
you PREPARE for the test, and pass it QUICKLY.
If you do not pass after 3 tries, your final course grade will be lowered by a half letter grade at
the end of the course.
More information is available at
http://www.wmich.edu/math/academics/undergraduate/calculus-exam
Practise Problems
In each case, find an expression for the derivative. You do not have to simplify your
answers.
1. y(w) = √
√
1
− 2 w − 11w2 + π
3w
11
2. y = √ 2
2 x −x+9
3. f (x) =
3 − 2x11
x2 + 1
√
4. y =
5. y =
w
3
w −1
!7
t3 + 5
√
t t
2
6. y = ex + xe + e
7. y(u) = sec(3u)
!1230
8. h(t) = e−3t sin t
−1
9. y = etan
x
(x2 + 1)
10. y = cos3 (5x2 )
11. y = e2x sec(2x) tan(2x)
12. G(t) = ln(5t4 + 10)
13. f (u) = sin(1 − 4u2 )
√
14. y(t) = 5 t etan t
Find the following antiderivatives.
1.
2.
3.
4.
5.
√
1
2
2 t − 3t + 11t +
dt
e
Z 5
2
√ +
+ 11e−w
w
3w
Z
Z
Z
dw
(x2 − 4x + 4)(x − 1) dx
(2 − cos(3w) − sin w) dw
Z 1
(t2
0
6.
!
Z 1
3t
dt
+ 1)
2
−tet dt
0
7.
Z
1
dx
1 − 2x
2