Gina Wilson’s All Things Algebra 2016 – Unit 11 Overview
Unit 11 of Gina Wilson’s All Things Algebra course focuses on a blend of combinatorial counting, motion concepts, and quadratic analysis. The material is delivered through concise video recordings created with Screencast‑O‑Matic, allowing students to review the key ideas at their own pace. This unit equips learners with the tools to solve real‑world problems involving permutations, combinations, the counting principle, and the fundamentals of kinematics and dynamics. A special emphasis is placed on recognizing symmetry in geometry, a powerful strategy for simplifying complex AMC‑style questions.
Permutations, Combinations, and the Counting Principle
Understanding how to count arrangements is essential for tackling probability and combinatorics problems. The unit begins with the fundamental counting principle, which states that if one event can occur in m ways and a second event can occur in n ways, then the two events can occur in m × n ways. From here, students explore:
- Permutations – ordered selections where arrangement matters.
- Combinations – unordered selections where order is irrelevant.
- Applications to real‑life scenarios such as arranging books, selecting teams, or creating passwords.
Example practice: “How many ways can a 5‑letter password be formed from the letters A, B, C, D, and E if repetition is allowed?” Students apply the counting principle to calculate \(5^5 = 3125\) possible passwords.
Kinematics: Position, Displacement, Distance, Velocity, Speed, and Acceleration
The motion segment of Unit 11 introduces the core concepts of kinematics. By using the standard equations of uniformly accelerated motion, learners can translate between position, displacement, velocity, speed, and acceleration. Key points include:
- Distinguishing displacement (vector) from distance (scalar).
- Understanding the difference between velocity (vector) and speed (scalar).
- Calculating acceleration as the rate of change of velocity.
- Graphical interpretation of motion using position‑time and velocity‑time graphs.
Sample problem: “A car accelerates from 0 to 60 mph in 10 seconds. What is its average acceleration?” Students compute \(a = \frac{60 \text{ mph}}{10 \text{ s}}\) after unit conversion, demonstrating the practical use of the formula.
Dynamics: Resultant Force and Equilibrant
In dynamics, the unit covers how forces combine. The resultant force is the single force that has the same effect as multiple forces acting simultaneously. Its counterpart, the equilibrant, is the force that would bring a
