# Grade 12 Calculus And Vector Algebra

PREREQUISITE: Advanced Function Analysis course must be taken prior to or concurrently with Calculus and Vector Algebra

AVAILABILITY: Full-time, Part-time, Private and Online

This course builds on student’s previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors, and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, rational, exponential, and sinusoidal functions; and apply these concepts and skills to modelling of real-world relationships. Calculus and Vector Algebra is intended for students who plan to study mathematics in university and who may choose to pursue careers in fields such as physics and engineering.

### UNIT ONE

Vectors

Essential Question: How can mathematics be used to explain orientation in space?

• In this unit, students will be studying a quantity known as a vector. It is simply your typical line segment with a direction, but what is surprising is the number of applications that make use of it. For example, in the field of physics there is position, displacement, velocity, acceleration, forces, momentum, fields and so on. Students will look at some vector applications and solve related problems both geometrically and algebraically by performing operations on vectors.

### UNIT TWO

Lines and Planes

Essential Question: How can two and three-dimensional models be used to imagine solutions to complex problems?

• In this unit, students will be required to combine the understandings from the previous unit with new concepts such as three-dimensional vectors and planes.

### UNIT THREE

Rates of Change

Essential Question: How can rates of change found in the real world be modeled using mathematics?

• In this unit, students will notice a shift in content as we move from the vectors portion of the course to the calculus portion. Students will be introduced to the idea of a rate of change. This is one of the most important concepts needed to understand calculus and will be used often throughout the course.

### UNIT FOUR

Derivatives

Essential Question: How can mathematical concepts be used to make sense of real-world problems?

• In this unit, students will be introduced to one of the most fundamental operations in the study of calculus – the derivative! Understanding the derivative will require the use of the understandings students developed throughout the first unit. A concrete understanding of the derivative is necessary to understand the remaining units in this course.

### UNIT FIVE

Curve Sketching

Essential Question: How can problem solving tools be used to represent functions visually?

• In this unit, students will develop the skills needed to sketch any given function. This unit will require students to connect algebraic concepts with graphical concepts in order to deepen their understanding of what the graph of a given function looks like.

### UNIT SIX

Derivatives of Exponential and Sinusoidal Functions

Essential Question: How can derivatives be used to analyze specific functions?

• In this unit, students will be required to apply their understanding of derivatives to analyze both exponential and sinusoidal functions.