## CLEP Calculus

The College-Level Examination Program® (CLEP) gives students the possibility to earn college credit at a cost far less ($80) than a college course.

The CLEP is developed by the College Board, as a college credit-by-exam program, and is recognized and used by more than 2,900 institutions of higher learning (including military installation). There are 33 CLEP exams that can be taken at over 1,900 universities and colleges.

The CLEP Calculus exam measures skills and understanding of concepts that are usually addressed in a 1-semester calculus course in college or university. Each CLEP Calculus examination takes around 90 minutes to complete and contains approximately 40% integral calculus, and 60% limits & differential calculus. The CLEP Calculus exam includes the functions of algebra, trigonometry, exponents, logarithm, and general functions.

The exam assesses primarily a student’s understanding of calculus, the methods used, and his or her experience with its applications. Students are required to master preparatory mathematics, such as geometry, trigonometry, analytic geometry, and algebra. The CLEP Calculus exam comes with 44 questions, divided into two sections, and students need to answer all questions in some 90 minutes. The time that candidates are spending on providing personal data and tutorials is added to their actual testing time.

- Section 1 contains 27 questions and takes 50 minutes. The use of a calculator is not permitted for this part.
- Section 2 contains 17 questions and takes 40 minutes. The use of an online graphing calculator (non-CAS) is permitted for this section, though not all questions require the use of the calculator.

**Graphing Calculator – **The CLEP Calculus exam comes with an integrated graphing calculator that students may use in Section 2, though just a few of the questions actually require the use of this graphing calculator, and applicants are supposed to understand when and how the calculator is used. Students can download the graphing calculator, and also some brief video tutorials, at no cost for a trial period of 30 days. In fact, students are expected to have downloaded the calculator prior to the exam and that they are familiar with the calculator’s functionality.

To be able to answer a number of the CLEP Calculus exam questions in section 2, applicants may require to use the available (online) graphing calculator. They can use it for:

- Performing calculations such as roots, exponents, logarithms, or trigonometric values
- Graphing functions & analyzing the graphs
- Finding zeros of functions
- Finding points of intersection of graphs of functions
- Finding minima/maxima of functions
- Finding numerical solutions to equations
- Generating a table of values for a function

To get all set for the CLEP Calculus exam, students should study at least one (but preferably more) introductory calculus textbook at college-level. You can find these books in practically all college bookstores, and online there great options as well. Consulting some more textbooks is advisable as the approaches to a number of topics may vary. When you pick out a textbook, see if the book’s table of contents matches the ‘Knowledge & Skills Required’ section for the exam (see the following paragraph).

**Knowledge & Skills Required**

Students must demonstrate the following knowledge and abilities if they want to answer the questions on the CLEP Calculus exam:

- Solve routine problems that involve the techniques of calculus (around 50% of the exam)
- Solve non-routine problems that involve understanding of the concepts & applications of calculus (around 50% of the exam)

The CLEP Calculus exam’s subject matter consists of the following topics (the indicated percentages are referring to the percentage of questions on that specific topic).

**Limits (10%)**

– Statement of properties (for example sum, limit of a constant, product or quotient)

**Integral Calculus (40%)**

**Antiderivatives & Techniques of Integration**

– Concept of antiderivatives

– Basic integration formulas

– Integration by substitution (change of variable, use of identities)

**Applications of Antiderivatives**

– Distance & velocity from acceleration with initial conditions

– Solutions of *y*′**5 ky** and applications to growth & decay

**The Definite Integral**

– Defining the definite integral as the limit of a sequence of Riemann sums & approximations of the definite integral using areas of rectangles

– Properties of the definite integral

– The Fundamental Theorem:

**Applications of the Definite Integral**

– Average value of a function on an interval

– Area, including area between curves

– Continuity

– Other (e.g., accumulated change from a rate of change

– Limit calculations, including limits involving infinity, e.g.:

**Differential Calculus (50%)**

**The Derivative**

– Definitions of the derivative:

– Derivatives of elementary functions

– Derivatives of sums, products & quotients (including **tan x** and

**cot**)

*x*– Derivative of a composite function (chain rule), e.g.

**sin(**

– Implicit differentiation

*ax*1*b*),*ae*, ln(*kx*)– Derivative of the inverse of a function (including

**arcsin**and

*x***arctan**)

*x*– Higher order derivatives

– Corresponding characteristics of graphs of

**ƒ**,

**ƒ**′ and

**ƒ**″

– Statement of the Mean Value Theorem; applications & graphical illustrations

– Relation between differentiability & continuity

– Use of L’Hôpital’s Rule (quotient & indeterminate forms)

**Applications of the Derivative**

– Slope of a curve at a point

– Tangent lines & linear approximation

– Curve sketching: increasing & decreasing functions; relative & absolute maximum & minimum points; concavity; points of inflection

– Extreme value problems

– Velocity & acceleration of a particle moving along a line

– Average & instantaneous rates of change

– Related rates of change

(Source: http://clep.collegeboard.org/exam/calculus)