Below are lists of the most important math
proficiencies needed in firstyear Calculus...
General
Proficiencies
Postsecondary instructors insist that the general
proficiencies in the table below are extremely important for anyone wishing to
succeed in a Calculus course. In many ways they are more valuable
proficiencies for the student entering a postsecondary Calculus course than are even a
large number of individual, specific mathematics skills. Although general
proficiencies are difficult to measure, the effects of these qualities and attitudes
towards success in any Calculus course is difficult to overemphasise.
General
Proficiencies Essential For Calculus 
General
Proficiency 
Related Proficiencies 
Comments 
Thinking Skills 
Critical, Logical Thinking 
Orderly, analytical, inquiring thought processes. 
Solving Word Problems 

Experience and comfort in setting up, solving and writing up word
problems. 
Multistep Problems 

Multistep problems involve two or more stages to arrive at a
solution. They are not necessarily word problems. 
Modelling 

Finding appropriate constructs or methods to solve a problem.
Example: writing a function that captures the components of a problem. 
Integration of Topics 
Combining concepts
Synthesising 
Using two or more concepts in combination. Example: the
concept of an inverse of a function with the exponential function. 
Abstracting/
Generalising 
Concept development 
Seeing common characteristics in separate settings.
Abstractions lead to the creation of a system of symbols. 
Symbolism 
Symbol Manipulation 
Familiarity and comfort with mathematical symbols. 
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Specific Proficiency Categories
The survey completed by college/university instructors listed broad
proficiency categories containing morespecific subproficiencies. These
main proficiency categories of specific mathematics topics that students typically
encounter in senior secondary courses are ranked in the table below. Each category
has also been given an importance rating of: Essential, Very
Important, Important, Nice to Know or
Not Important, in accordance with the survey results.
Code 
Mathematics Proficiency Categories Rated for Calculus 
L 
Understand and use the Function Concept. 
Essential 
A 
Understand and use Polynomial Expressions. 
Essential 
C 
Understand and use Exponential Expressions. 
Essential 
M 
Understand and use Straight Line and Linear
Functions. 
Essential 
E 
Solve Equations and Inequalities. 
Essential 
S 
Understand and use Circular Trigonometric
Functions. 
Essential 
B 
Understand and use Rational Expressions. 
Essential 
H 
Understand and use Triangle Trigonometry. 
Essential 
N 
Understand and use the Quadratic Function. 
Essential 
R 
Understand and use the Logarithmic Function. 
Essential 
D 
Understand and use Radical Expressions. 
Essential 
F 
Understand and use the Geometry of Lines and
Points. 
Essential 
Q 
Understand and use Polynomial Functions. 
Very Important 
P 
Understand and use Quadratic Relations. 
Very Important 
K 
Understand and use Sequences and Series. 
Very Important 
G 
Understand and use the Geometry of Circles. 
Very Important 
T 
Understand and use some Concepts of the
Calculus. 
Nice to Know 
J 
Understand and use Data Analysis. 
Nice to Know 
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Specific SubProficiencies  THE TOP 20
Each Specific Proficiency Category contains several, individual
subproficiencies. The twenty individual proficiencies rated highest
for entry to university/college Calculus are given below:
THE
TOP 20 MATH PROFICIENCIES FOR CALCULUS  IN ORDER OF IMPORTANCE 
Code 
Mathematics Proficiency 
Rating 
L1 
Understand and use function notation. 
Essential 
M1 
Graph and write the equations for linear
functions. 
Essential 
M2 
Understand and use the slope of a line. 
Essential 
A1 
Simplify polynomial expressions. 
Essential 
A2 
Add and subtract polynomial expressions. 
Essential 
A3 
Multiply and simplify polynomial expressions. 
Essential 
C1 
Use the Laws of Exponents to simplify
expressions. 
Essential 
E1 
Solve linear equations. 
Essential 
C2 
Write radical expressions in exponential form. 
Essential 
F3 
Understand and use the Pythagorean Theorem. 
Essential 
C3 
Apply the Laws of Exponents to expressions
with rational exponents. 
Essential 
E2 
Solve linear inequalities. 
Essential 
A4 
Factor binomials and trinomials. 
Essential 
B2 
Multiply and divide simple rational
expressions. 
Essential 
B3 
Add and subtract rational expressions. 
Essential 
H1 
Understand and apply the primary trig ratios
as related to triangles. 
Essential 
L3 
Graph basic RR functions like linear, absolute value, etc.on the Cartesian
plane. 
Essential 
E5 
Solve quadratic equations using the quadratic
formula. 
Essential 
B1 
Simplify rational expressions with polynomial
numerators and denominators. 
Essential 
R1 
Write exponential expressions in logarithmic
form. 
Essential 
Each of the above specific proficiencies is essential for success in a Calculus course.
The next 21 proficiencies are also rated as Essential. To view the specific
ratings and the entire list of topics, including ones not specifically mentioned in the
survey, you may use a pdf reader to download the entire Mathematics Proficiencies
Report from HERE.
The Mathematics Proficiencies for PostSecondary Mathematics/Statistics Courses
Project Report may be freely quoted when the source is credited.
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