本课程是以学生先前的函数的经验和对变化率认识为基础的学生将解决涉及到向量的几何和代数表示以及在三维空间内线和平面的表示的问题;扩宽了学生对变化率的理解，包括对多项式的导数，正弦函数，指数函数，有理数函数以及根函数理解;运用对真实世界关系的建模的概念和技巧学生也完善了高中数学成功所需的数学过程的使用该课程是为那些选择在科学，工程，经济学领域，及商业的一些领域追求事业的学生，同时包括那些要求学习大学水平的微积分，线性代数，或物理课程的学生开设的。
A. RATE OF CHANGE
OVERALL EXPECTATIONS
By the end of this course, students will:
- demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;
- graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;
- verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.
B. DERIVATIVES AND THEIR APPLICATIONS
OVERALL EXPECTATIONS
By the end of this course, students will:
- make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;
- solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.
C. GEOMETRY AND ALGEBRA OF VECTORS
OVERALL EXPECTATIONS
By the end of this course, students will:
- demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;
- perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications;
- distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space;
- represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.
