Calculus
2008/09 school year 

Unit A
 Functions 

Unit A1 – Characteristics, Limits,
Continuities 

A.1.1
 Function Characteristics 
increase/decrease/concavity/domain 
2L 
A.1.2
 Continuities 
piecewise fcns 
2L 
A.1.3
 Limits 
left/right/piecewise 
2L 
A.1.4
 Rates of Change 
average/instantaneous 
2L 
A.1.5
 Area Under Curves 
RAM,
trapezoids 
2L 
UNIT B  Differential Calculus 

Unit
B1  Derivatives & Differentiation Techniques 

B.1.1
 Limit Definition of a Derivative 
2L 

B.1.2
 Derivatives of Products 
1L 

B.1.3
 Derivatives of Rational Functions  The Quotient Rule 
1L 

B.1.4
 Derivatives of Composite Functions  The Chain Rule 
1L 

B.1.5
 Derivatives of Exponential Functions 
1L 

B.1.6
 Derivatives of Logarithmic Functions 
1L 

B.1.7
 Derivatives of Trigonometric Functions 
2L 

Unit
B2  Derivatives and Graphical Analysis 

B.2.1
 Graphical Differentiation 
2L 

B.2.2
 Increasing and Decreasing Functions 
1L 

B.2.3
 Relative Extrema 
1L 

B.2.4
 Absolute Extrema 
1L 

B.2.5
 Higher Derivatives, Concavity 
2L 

B.2.6
 Curve Sketching 
2L 

Unit
B3  Applications of Derivatives 

B.3.1
 Applications of Extrema 
3L 

B.3.2
 Implicit Differentiation 
2L 

B.3.3
 Related Rates 
2L 

B.3.4
 Differentials: Linear Approximations 
1L 

B.3.5
 NewtonRaphson Approximations 
2L 

Unit C  Integral Calculus 

Unit
C1  Basics of Integration 

C.1.1
 Antiderivatives 
1L 

C.1.2
 Area & the Definite Integral 
3L 

C.1.3
 The Fundamental Theorem of Calculus 
4L 

Unit
C2  Techniques and Applications of Integration 

C.2.1
 Integration by Substitution 
2L 

C.2.2
 Integration by Parts 
2L 

C.2.3
 The Area Between 2 Curves 
2L 

C.2.4
 Numerical Integration 
1L 

C.2.5
 Average Value of a Function 
1L 

C.2.6
 Volume 
3L 

Unit C3  Differential Equations 

C.3.1
 Differential Equations 
1L 

C.3.2
 Separable Differential Equations 
2L 

C.3.3
 Applications of Differential Equations 
4L 

C.3.4
 Slope Fields 
2L 