IB Diploma Programme – Firebaugh High School
UNIT 4 OUTLINE:
APPLICATIONS OF DIFFERNTIAL CALCULUS
IB Mathematics SL – Year 2
IB Topics Addressed: Topic 6 - CALCULUS
Common Core Standards Addressed: CALCULUS:
4.0 Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability:
4.2 Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use
derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function.
7.0 Students compute derivatives of higher orders.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which
the function is increasing and decreasing.
11.0 Students use differentiation to solve optimization (maximum-minimum problems) in a variety of pure and applied contexts.
12.0 Students use differentiation to solve related rate problems in a variety of pure and applied contexts.
Lesson
Title
1
Introduction to
Kinematics – Velocity &
Acceleration (17A)
2
Motion of a Particle –
Day 1 (17A)
3
Motion of a Particle –
Day 2 (17A)
Stndrds
Assignment
4.0, 4.2
17A.1: #1 – 4
4.0, 4.2
7.0, 9.0
17A.2: #1 – 3
4.0, 4.2
7.0, 9.0
17A.2: #4 – 8
Students work together in tutorial teams to study,
review and get questions answered about
topics/problems/concepts that they struggled with
4.0, 4.2
7.0, 9.0
Bring 2 problems that
you had questions on
SWBAT find the rate of change of a substance with
respect to time (or other variable) by using the
derivative function and its properties.
4.0, 4.2
7.0, 9.0
12.0
SWBAT find the optimal solution of a real-world
problem by using the first and second derivatives.
4.0, 4.2
7.0, 9.0
11.0
Review
SWBAT demonstrate mastery of concepts learned
throughout the entire unit.
All Above
Assessment
Test: 3 Parts (A = Group, B = Non-GDC, C = GDC)
All Above
Tutorials
4
Rates of Change – Day 1
(17B)
5
Rates of Change – Day 2
(17B)
6
Optimization – Day 1
(17C)
Optimization – Day 2
(17C)
7
Objective
SWBAT find the instantaneous velocity &
instantaneous acceleration of a particle that is
moving in a straight line by using the derivative
functions.
SWBAT determine where a moving particle is located,
the direction of motion, where a change of direction
occurs and when the particle’s velocity is increasing or
decreasing by using a sign diagram.
17B: #1 – 4
17B: #5 – 8, 13, 15
17C #1 – 5
17C #8 – 14
Review 17A
Review 17B
IB Diploma Programme – Firebaugh High School
UNIT 4 ESSENTIAL QUESTIONS:
PROPERTIES OF CURVES
Lesson
IB Mathematics SL – Year 2
Essential Question
1
How do I find the instantaneous velocity? Instantaneous acceleration? What is the relationship between the two?
2
What is the relationship between s(t), v(t) and a(t) ? What do they represent?
3
What do the signs of s(t), v(t) and a(t) tell me about the motion of a particle?
4
What does the derivative of a displacement function tell us? Describe the benefits of finding the derivative of the
displacement function?
5
6
7
What are the tests for optimal solutions? What do we need to have in order to use these tests?
UNIT 4 VOCABULARY
Displacement
Displacement Function
Motion Graph
Average Velocity
Instantaneous Velocity
(Velocity Function)
Acceleration
Average Acceleration
Instantaneous Acceleration
Initial Conditions
Speed
Sign Test
Rate of Change
Optimum Solution
Optimization
Local Maximum
Local Minimum
Sign Diagram Test
Second Derivative Test
Graphical Test