Calculus Exam

MATH 210 – CALCULUS I EXAM 1 - A NAME DIRECTIONS: The purpose of this exam is to evaluate your knowledge of the topics covered in chapters 1 of the text. Read all directions carefully. Make sure to answer all parts of the question. Show all necessar y work to receive full credit. Do all work by hand. Circle and label all answers. This exam is worth 100 points and you have 75 minutes to complete it in. Good luck. (3) 1. Find the slope of the line through the points (2,1) and ( -3,4). (6) 2. Find the equation of the line through the point (2,1) parallel to the line 4x – 2y = 6. (6) 3. Find the equation of the line through the point (2,1) perpendicular to the line 4x – 2y = 6. (3) 4. State the domain for f (x) = . (3) 5. State the domain for f (x) = . (1) 6. Determine if y = x 4 + 4x 2 + 1 is odd, even, or neither. (1) 7. Determine if y = x 3 – x + 1 is odd, even, or neither. (1) 8. Determine if y = x 5 – 4x 3 + x is odd, even, or neither. (3) 9. If f (x) = x 2 – 5 and g (x) = x + 3, find f (g (3)). 16 - x 3 x 2 16 - x 2 (4) 10. If f (x) = x 2 + 1 and g (x) = 3x, find g (f (x)). (9) 11. State the domain, range, and intercepts for y = -2 – x – 1. (6) 12. Determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25% compounded quarterly. (8) 13. Determine if f (x) = is one -to -one. If it is , find its inverse. (3) 14. State the domain for y = ln x + 3. (3) 15. State the domain for y = log 3 (x – 1). (8) 16. Solve ln (y + 1) – ln 3 = x + ln x for y. 1 - 3x 1 x (8) 17. Given sin x = , x in , find the values for cos x and tan x. (3) 18. What is the period of y = sin (3x)? (3) 19. What is the period of y = cos (x – 3)? (7) 20. Use a reference triangle to find the angle for . 5 3 , 2 2 1 sin 1 - (7) 21. Given the parametric equations x = 4sin t, y = 5cos t, 0 t 2 , identify the path by finding the Cartesian equation for it. (4) 22. Find the parametric equations for the curve x = 3y 3 – 4y 2 + 2.