Limits Derivatives Integrals Infinite Series Parametrics Polar Coordinates Conics
Limits
Epsilon-Delta Definition
Finite Limits
One-Sided Limits
Infinite Limits
Trig Limits
Pinching Theorem
Indeterminate Forms
L'Hopitals Rule
Limits That Do Not Exist
Continuity & Discontinuities
Intermediate Value Theorem
Derivatives
Power Rule
Product Rule
Quotient Rule
Chain Rule
Trig and Inverse Trig
Implicit Differentiation
Exponentials & Logarithms
Logarithmic Differentiation
Hyperbolic Functions
Higher Order Derivatives
Differentials
Slope, Tangent, Normal...
Linear Motion
Mean Value Theorem
Graphing
1st Deriv, Critical Points
2nd Deriv, Inflection Points
Related Rates Basics
Related Rates Areas
Related Rates Distances
Related Rates Volumes
Optimization
Integrals
Definite Integrals
Integration by Substitution
Integration By Parts
Partial Fractions
Improper Integrals
Basic Trig Integration
Sine/Cosine Integration
Secant/Tangent Integration
Trig Integration Practice
Trig Substitution
Linear Motion
Area Under/Between Curves
Volume of Revolution
Arc Length
Surface Area
Work
Moments, Center of Mass
Exponential Growth/Decay
Laplace Transforms
Describing Plane Regions
Infinite Series
Divergence (nth-Term) Test
p-Series
Geometric Series
Alternating Series
Telescoping Series
Ratio Test
Limit Comparison Test
Direct Comparison Test
Integral Test
Root Test
Absolute Convergence
Conditional Convergence
Power Series
Taylor/Maclaurin Series
Interval of Convergence
Remainder & Error Bounds
Fourier Series
Study Techniques
Choosing A Test
Sequences
Infinite Series Table
Practice Problems
Exam Preparation
Exam List
Parametrics
Parametric Curves
Parametric Surfaces
Slope & Tangent Lines
Area
Arc Length
Surface Area
Volume
Polar Coordinates
Converting
Slope & Tangent Lines
Area
Arc Length
Surface Area
Conics
Parabolas
Ellipses
Hyperbolas
Conics in Polar Form
Vectors Vector Functions Partial Derivatives/Integrals Vector Fields Laplace Transforms Tools
Vectors
Unit Vectors
Dot Product
Cross Product
Lines In 3-Space
Planes In 3-Space
Lines & Planes Applications
Angle Between Vectors
Direction Cosines/Angles
Vector Projections
Work
Triple Scalar Product
Triple Vector Product
Vector Functions
Projectile Motion
Unit Tangent Vector
Principal Unit Normal Vector
Acceleration Vector
Arc Length
Arc Length Parameter
Curvature
Vector Functions Equations
MVC Practice Exam A1
Partial Derivatives
Directional Derivatives
Lagrange Multipliers
Tangent Plane
MVC Practice Exam A2
Partial Integrals
Describing Plane Regions
Double Integrals-Rectangular
Double Integrals-Applications
Double Integrals-Polar
Triple Integrals-Rectangular
Triple Integrals-Cylindrical
Triple Integrals-Spherical
MVC Practice Exam A3
Vector Fields
Curl
Divergence
Conservative Vector Fields
Potential Functions
Parametric Curves
Line Integrals
Green's Theorem
Parametric Surfaces
Surface Integrals
Stokes' Theorem
Divergence Theorem
MVC Practice Exam A4
Laplace Transforms
Unit Step Function
Unit Impulse Function
Square Wave
Shifting Theorems
Solve Initial Value Problems
Prepare For Calculus 1
Trig Formulas
Describing Plane Regions
Parametric Curves
Linear Algebra Review
Word Problems
Mathematical Logic
Calculus Notation
Simplifying
Practice Exams
More Math Help
Tutoring
Tools and Resources
Learning/Study Techniques
Math/Science Learning
Memorize To Learn
Music and Learning
Note-Taking
Motivation
Instructor or Coach?
Books
Math Books

You CAN Ace Calculus

17calculus > exam list > calc2 exam C1

### Calculus Main Topics

Single Variable Calculus

Multi-Variable Calculus

### Tools

math tools

general learning tools

other exams from this semester

exam C1 -

complete exam list

Calculus 2 - Exam 1 ( Semester C )

Exam Overview

This is the first exam for calculus 2. The material covered in this exam includes area between curves, moment and center of mass of a planar lamina, work moving water out of a container, volume of revolution, arc length and linear motion.

Exam Details

Tools

Time

2.5 hours

Calculators

no

Questions

6

Formula Sheet(s)

2 pages, 8.5x11 or A4

Total Points

100

Other Tools

ruler for drawing graphs

Instructions:
- For each problem, correct answers are worth 1 point. The remaining points are earned by showing calculations and giving reasoning that justify your conclusions.
- Correct notation counts (i.e. points will be taken off for incorrect notation).

Question 1

[15 points] A stone is thrown vertically into the air off the edge of a bridge 160ft above a river. If the initial velocity of the rock is 48ft/sec (upward) and the acceleration is a constant -32ft/sec2 (downward), find the following. a. The velocity v(t) after t seconds. b. The position s(t) of the stone above the river. c. The velocity at which the stone hits the water.

solution

Question 2

[10 points] Calculate the length of the arc $$y=2x^{3/2}$$ from $$x=1/3$$ to $$x=8/3$$.

solution

Question 3

[10 points] Consider the region bounded by $$y=\ln(x)$$ and the line with slope $$m=(3+\ln(5))/5$$ and y-intercept at $$x=-3$$ above the x-axis as shown in the plot. Set up and but do not evaluate one integral that calculates the shaded area.

solution

Question 4

[20 points] Consider the region R bounded by $$y=x^3$$ and $$y=\sqrt{x}$$. a. Calculate the area of the region R. Sketch a plot and shade the region. b. Calculate the moments Mx and My. c. Determine the center of mass.

solution

Question 5 [ exam link ]

[20 points] For the region R bounded by the graphs of $$y=2x$$, the x-axis and $$x=1$$, consider the solid generated by revolving the region about the line $$y=3$$. Sketch a different plot of region R for each method, clearly showing the region by shading, the axes of revolution, the representative rectangle, R, r, p and h. a. Set up the integral to calculate the volume using the disc-washer method. b. Set up the integral to calculate the volume using the shell-cylinder method. c. Calculate the volume of the solid by evaluating one of the integrals you set up in parts a and b.