Math Proficiencies Required for Success in First Year

Below are lists of the most important math proficiencies needed in first-year Calculus...

General Proficiencies

Post-secondary 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 post-secondary 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 over-emphasise.

General Proficiencies Essential For Calculus

General Proficiency

Related Proficiencies


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.
Multi-step Problems   Multi-step 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
Using two or more concepts in combination.  Example:  the concept of an inverse of a function with the exponential function.
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 more-specific sub-proficiencies.  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.


Mathematics Proficiency Categories Rated for Calculus

L Understand and use the Function Concept.


A Understand and use Polynomial Expressions.


C Understand and use Exponential Expressions.


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 Sub-Proficiencies - THE TOP 20

Each Specific Proficiency Category contains several, individual sub-proficiencies.  The twenty individual proficiencies rated highest for entry to university/college Calculus are given below:


Code Mathematics Proficiency Rating
L1 Understand and use function notation.


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 Post-Secondary Mathematics/Statistics Courses Project Report may be freely quoted when the source is credited.

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