# Calculus Placement Exam

## Department of Mathematics

In order to take MATH 2413: Calculus I, you must meet at least one of the following prerequisites:

- A grade of C or better in a precalculus course (MATH 2312 or equivalent) or a department-approved trigonometry course (MATH 1316 or equivalent).
- Pass a placement test administered by the UT Tyler Testing Center with a score of at least 80 points. Information on scheduling this exam is listed below. It is suggested that you study for this test.
- Score of 710 or higher on the SAT (quantitative section) or 27 or higher on the ACT (math section).
- If you do not satisfy requirements 1 or 3 then you MUST take the placement test, or else enroll in MATH 2312 (Precalculus) prior to enrolling in MATH 2413 (Calculus).

Anyone who plans to take MATH 2413 (Calculus I) and who has not already taken MATH 2312 (Precalculus), MATH 1316 (Trigonometry), or a course equivalent to one of these two will need to take the precalculus exam. If you had a course in trigonometry in high school and want to go directly into Calculus I, you must take the placement test. If you have never taken a course that covers trigonometry, it is recommended that you enroll in Precalculus prior to enrolling in Calculus I.

Mathematics, biology, chemistry, computer science and engineering majors must take Calculus I (MATH 2413), so students in these majors may need to take the placement test if they have not already had a college precalulus course or equivalent.

### When and Where?

Students who complete the Calculus Placement Exam with a score of at least 80 points will be allowed to enroll in MATH 2413 (Calculus I). The Calculus Placement Exam is offered by appointment only and is administered by the UT Tyler Testing Center. To schedule your exam, please call the Testing Center at (903) 565-5693.

### How can I study?

The placement exam covers material you would be expected to learn in a standard precalculus course. In particular, it assesses your algebra skills and your knowledge of trigonometry in order to determine whether both are adequate for admission into Calculus I.

Below is a more detailed breakdown of the topics that may appear on the placement exam. When applicable, there are links to some free online resources (including an online textbook that we have used in our Precalculus course at UT Tyler).

#### Algebra

**Basic algebra techniques**(see the Algebra Review Guide from Paul's Online Math Notes)- Be able to simplify an algebraic expression by distributing and combining like terms.
- Expand an algebraic expression using the FOIL method.
- Manipulate fractions and rational expressions.

**Functions**(Chapter 1 of OpenStax Precalculus)- Be comfortable with function notation.
- Find the domain of a function.
- Write down a simplified formula for the composition of two function.
- Determine how basic transformations affect the graph of a function.

**Linear equations and functions**(Chapter 2 of OpenStax Precalculus)- Find the slope and/or equation of a line through two points.
- Solve a linear equation.

**Quadratic equations and functions**(Section 3.2 of OpenStax Precalculus)- Factor quadractic expressions.
- Rewrite quadratic expressions by completing the square.
- Solve a quadratic equation by factoring, completing the square, or using the quadratic formula.
- Identify the vertex of a quadratic function by completing the square.
- Graph a quadratic function.

**Rational functions and expressions**(Section 3.7 of OpenStax Precalculus)- Find the domain of a rational function.
- Identify the vertical and horizontal asymptotes of a rational function.
- Determine the x-intercepts and y-intercept of a rational function.
- Solve a rational equation.

**Exponential and logarithmic functions**(Chapter 4 of OpenStax Precalculus)- Be comfortable working with exponential functions and logarithms.
- Simplify exponential expressions using the rules of exponents.
- Identify the graphs of exponentials and logarithms.
- Use logarithms to solve an exponential equation.
- Simplify logarithmic expressions using the rules of logarithms.

#### Trigonometry

**Angles and radian measure**(Section 5.1 of OpenStax Precalculus)- Be familiar with the idea of drawing an angle in standard position, as well as reference angles and coterminal angles.
- Be able to convert angle measures in degrees to radians and vice versa.

**Definitions of trig functions**(Sections 5.2, 5.3, and 5.4 of OpenStax Precalculus)- Given the side lengths of a triangle, find the sin, cos, tan, cot, sec, and/or csc for a designated angle of the triangle.
- Given that a point (x,y) lies on the terminal side of an angle in standard position, find the sin, cos, tan, cot, sec, and/or csc for that angle.

**Evaluation of trigonometric functions at special angles**(Section 5.2 of OpenStax Precalculus)- Given an angle that is a multiple of 30 or 45 degrees, be able to find the sin, cos, tan, cot, sec, and/or csc of that angle measure.
- Given an angle that is a multiple of π/6 or π/4 degrees, be able to find the sin, cos, tan, cot, sec, and/or csc of that angle measure.

**Right triangles**(Section 5.4 of OpenStax Precalculus)- Be able to determine the values of the six trigonometric functions for an angle in a given right triangle.
- Be able to solve for the missing sides of a right triangle.

**Identities**(Section 7.1 of OpenStax Precalculus)- Know the fundamental identities tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x).
- Know the reciprocal identities sec(x) = 1/cos(x), csc(x) = 1/sin(x), and cot(x) = 1/tan(x).
- Know the Pythagorean identities sin
^{2}(x) + cos^{2}(x) = 1 and tan^{2}(x) + 1 = sec^{2}(x). - Given a trigonometric expression, be able to simplify this expression using the fundamental, reciprocal, and Pythagorean identities.
- Be able to use the fundamental, reciprocal, and Pythagorean identities to find values of the six trigonometric functions given the value of one of the six trigonometric functions at an angle and the quadrant in which this angle lies.

**Graphing**(Sections 6.1 and 6.2 of OpensStax Precalculus)- Identify the graphs of sin, cos, tan, sec, csc, and cot.
- Given the graph of trigonometric equation, be able to identify the formula corresponding to that graph and vice versa.

**Inverse trig functions**(Section 6.3 of OpenStax Precalculus)- Be able to find inverse trigonometric function values for given real numbers corresponding to angles at multiples of π/6 or π/4 degrees.

**Trig equations**(Sections 7.1 and 7.5 of OpenStax Precalculus)- Be able to solve equations involving trigonometric functions.