The Calculus Concepts Readiness (CCR) Test is a 25-question test designed to measure a student’s reasoning ability and knowledge of concepts that are central to precalculus and foundational for beginning calculus. These concepts include a strong understanding of rate of change, a process view of function, and the ability to use covariational reasoning to understand how two variables change together.
The test consists of 20 questions that do not involve trigonometry, and five trigonometry questions that are designed to indicate whether a student has a functional grasp of the subject.
The suggested time limit for the entire test is 30 minutes. If the five trigonometry questions are omitted, the recommended time limit is reduced to 25 minutes.
The test covers the following topics:
| Topic |
Number of Test Questions |
| Reasoning Strands |
Quantitative Reasoning involves identifying and relating measureable attributes of an object or situation in a problem context. |
9 |
Proportional Reasoning involves thinking about how two quantities change such that their ratio remains constant; attending to how one variable changes so that it is always a constant multiple of another variable. |
3 |
Covariational Reasoning involves thinking about how two quantities in a functional relationship are changing together; attending to how one variable changes while imagining successive amounts of equal changes in another variable. It involves coordinating two varying quantities that change in tandem while attending to how the quantities change in relation to each other. |
14 |
Process View of Function involves thinking of a function as an entity that accepts a continuum of input values to produce a continuum of output values; it views a function as a generalized process that accepts input and produces output, and appropriately coordinates multiple function processes. |
11 |
Notational Reasoning involves making sense of symbols used in mathematical expressions and giving meaning to the mathematical ideas communicated by conventional notation. |
9 |
| Graphical Reasoning involves making sense of graphs that represent functions, and interpreting the meaning of attributes of a graph that convey aspects of a function’s behavior. |
9 |
| Computational Abilities refers to facility with manipulations and procedures needed to evaluate functions, solve equations, compose functions, and invert linear and exponential functions, within the context of algebraic representations. |
6 |
|
| Content Areas |
| Proportions: Ratios of quantities in constant proportion |
2 |
| Algebra: Algebraic expressions, equations, inequalities |
9 |
| Functions: Concept, properties, operations |
13 |
| Representations of Functions: Symbolic, graphical, tabular, contextual (verbal) |
9 |
| Analytic Geometry: Circle, parabola, line |
7 |
| Trigonometry: Functions and applications |
5 |
| Models: Functions as models |
5 |
Note: Some questions are counted more than once. |
