advertisement

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