Calculus Semester Exam Outline – December 2014
Unit 0: Review of Algebra – Chapter P
 Graphing linear equations (P.1)
 Sketching the graph of a function (P.1)
 Find the intercepts of a graph (P.1)
 Test a graph for symmetry (P.1)
 Find the points of intersection of 2 graphs (P.1)
 Writing equations of lines. (From a graph, given two points, given slope
and a point, given point and parallel line, given point and perpendicular
line) (P.2)
 Determining domain and range of functions (P.3)
 Determining if relations are functions
(From an equation or from a graph) (P.3)
 Finding zeros of functions (P.3)
 Predicting transformations of graphs from changes in the equation of the
function (P.3)
 Writing equations for combinations and compositions of functions (P.3)
Unit 1: Limits and Continuity
 Understanding the Tangent Line Problem (1.1)
 Estimate a limit using a numerical or graphical approach (1.2 E.g. 1 - 2)
 Explore limits that fail to exist (1.2 E.g. 3 - 5)
 Evaluate basic limits (1.3)
 Evaluating limits of a polynomial, of a rational function, of a composite
function, and of trigonometric functions (1.3)
 Find limits of a function analytically (1.3 E.g. 6 – 10)
 Determine continuity at a point and on an open interval (1.4)
 Evaluating one-sided limits and continuity on a closed interval (1.4)
 Evaluating infinite limits from the left and from the right (1.5)
 Determining removable and non-removable discontinuities of functions
(1.5)
 Find and sketch vertical asymptotes of functions (1.5)
Unit 2: Introduction to Derivatives
 Find the slope of a tangent line to a curve at a point (2.1)
 Use the limit definition to find the derivative of a function (2.1)
 Use the derivative to find the slope at a point (2.1)
 Understand differentiability and Continuity (graphs with sharp turns &
graphs with vertical tangent lines) (2.1 E.g. 3 - 4)
 Find the derivative of a function using the power rule, therefore find the
slope and the equation of tangent lines (2.2)
 Find the derivative of sums and differences (2.2)
 Find the derivative of sine and cosine (2.2)
 Find velocity of falling objects (2.2)
 Know the position function and use the derivative to find velocity (2.2)
 Find the derivative using the Product Rule (2.3)
 Find the derivative using the Quotient Rule (2.3)
 Find the derivative of trigonometric functions (2.3)
 Find higher order derivatives (2.3)
 Find acceleration due to gravity using derivatives (2.3)
 Find the derivative of a composite function using the chain rule (2.4)
 Simplify the derivative of a function using algebra (2.4)
 Find the derivative of trig functions using the chain rule (2.4)
 Distinguish between functions written in implicit form and explicit form
(2.5)
 Use implicit differentiation (2.5)
 Find a related rate and use them to solve real life problems, involving
length, area, volume, velocity, angles of elevation and angular speed
verses Linear speed (2.6)
Unit 3: Applications of Differentiation
 Understand the definition of extrema of a function on an interval (3.1)
 Understand the definition of relative extrema of a function on an open
interval (3.1)
 Find extrema on a closed interval (3.1)
 Understand and use Rolle’s Theorem (3.2)
 Understand and use the Mean Value Theorem (3.2)