Parts I, II, III of the RHIT Calculus Credit Exam are administered during orientation week, through prior appointment only. It is our recent experience that although 40% or more of students receive some form of mathematics placement, only a very small number of students per year do so through RHIT placement exams. This is not because the placement exams are unduly difficult but rather that most students likely to achieve advanced placement have already done so. Thus the RHIT Calculus Credit Exam Parts I, II and III will only be administered for students who have not had the opportunities for formal placement, or are seeking a higher placement than they have achieved through the formal programs. It is expected that the students will contact the department head in advance of arriving on campus for an appointment and commit to substantial self-study and preparation during the summer. 

The topics covered in the three exams are approximately as in the table below.

Part I -  Calculus I 

Part II -  Calculus II 

Part III - Calculus III 

  • functions, domains, ranges, and  graphing
  • ability to work numerically, algebraically and graphically with the following functions: polynomials, rational and algebraic functions,  exponential, logarithmic, and trigonometric functions 
  • inverse functions
  • parametric equations
  • limits, including L'Hopital's rule  
  • derivatives, including formal definition, higher derivatives, all derivative rules, implicit differentiation and derivatives of the above functions
  • velocity and acceleration as derivatives
  • tangent lines, slope and concavity 
  • max-min problems
  • related rate problems
  • curve sketching
  • simple integration up to the substitution rule
  • areas between curves
  • integration, Riemann sums,  Fundamental Theorem of Calculus
  • integration techniques including substitution rule, integration by parts and partial fractions
  • improper integrals
  • Trapezoidal and Simpson's rule
  • applications of integration including area,  volumes of revolution, surfaces of revolution, arclength, work, mass of a 1-dimensional objects  
  • solution of differential equations by separation of variables 
  • simple applications of differential equations:  population growth, exponential decay, cooling/heating, and falling bodies 
  • sequences and series, integral, comparison and ratio test
  • Maclaurin and Taylor polynomials and series
  • Calculus I topics that form the foundation of the above topics 
  • polar coordinates
  • vectors in the plane and space, including dot product, cross product, projections
  • lines and planes in space
  • velocity and acceleration, curvature, normal and tangential components of acceleration
  • partial derivatives, tangent planes, normal lines, gradient, chain rule, directional derivatives
  • maxima and minima, Lagrange multipliers 
  • double integrals in rectangular and polar coordinates
  • triple integrals in rectangular, cylindrical, and spherical coordinates
  • applications of multiple integrals including volume, mass, moments, centroids
  • Calculus I and II topics that form the foundation of the above topics

“Measure what is measurable, and make measurable what is not so.

- Galileo Galilei

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