AP Calculus
AP Calculus is equivalent to a first year university calculus course and follows the College Board Advanced Placement curriculum. Students who take the Calculus AB or BC exams and receive a score of four or five receive Calculus 12 AP credit. Taking this course is shown to significantly improve your results in your first year of university. This is why taking AP Calculus is highly recommended for anyone that is considering majoring in any course that requires calculus.
Incentive Math
The Incentive program in Palmer provides enriched and accelerated courses for strong students. Students take an enriched Math 8/9 course in Grade 8 and Math 9/10 in Grade 9, which compresses content from Grades 8-10 in a span of two years, along with a mandatory Pascal contest in Grade 8. This allows students to finish their courses early. Pre-calculus Enriched 11 builds upon the Incentive courses or Grade 10 content, accelerating and going deeper into topics than the average Pre-calculus 11 course. Admission to this course requires students to have an 86% (A) or above in previous courses and is also based on recommendation.
The Main Ideas of Calculus
Limits
Limits describe the value that a function approaches as its input gets closer to a specific number.
Differentiation
Differentiation is the process of finding the derivative of a function. Derivatives measure how a quantity changes with respect to changes in the input, typically representing instantaneous rate of change or slope.
Derivatives of Trigonometric and Logarithmic Functions
These derivatives follow specific rules: derivative of sin(x) is cos(x), derivative of ln(x) is 1/x.
Curve-Sketching
Curve-sketching uses derivatives and other function properties to estimate a graph’s behaviour. This includes identifying intercepts, increasing/decreasing intervals, concavity, asymptotes, and critical points to produce an accurate sketch of the function.
Anti-Derivatives
An anti-derivative is a function whose derivative gives the original function if you have the it's derivative. It represents the reverse process of differentiation and is the basis of integration.
Integration
Integration computes the accumulated total of a quantity, such as area under a curve. It includes both indefinite integrals (general antiderivatives) and definite integrals (numerical accumulation over an interval).
Maximum/Minimum Problems
These problems use derivatives to identify points where a function reaches its highest or lowest value. They are essential in optimization tasks across mathematics and applications.
Rate Problems
Rate problems, often involving related rates, use derivatives to describe how one changing quantity affects another. They model real time changes such as motion, fluid flow, or growth.
Growth/Decay Problems
Growth and decay problems use differential equations to model processes that increase or decrease over time, such as population growth or radioactive decay. Solutions often involve exponential functions.