Last-Minute Quick Reference

Course Roadmap

• Chapter 7 is a gateway to systems of linear equations and linear algebra; linear algebra is foundational for computing, ML, data science, etc.
• 7.1–7.3: Systems of linear equations.
• 7.4: Partial fraction decomposition (decomposing a rational expression into simpler fractions); useful in Calculus II and differential equations.
• The last part of the course covers trig functions (Chapters 4–6); trig is considered the hardest part.

Assessments and Schedule

• Assignment types: homework (open), quizzes (timed, often open on a limited window), exams (timed), workshop (5% of grade).
• Passwords to unlock quizzes/exams: often the word "ready" ( transcript also mentions "great" elsewhere; follow instructor guidance).
• Quizzes: typically open for 1 hour; due on calendar dates (often Mondays); once started, timer runs to submission.
• Exams: open on specified dates; duration about 2 hours.
• Retakes: exam by exam (optional); take retake on the following Monday if desired; higher of the two grades counts.
• Workshop: scheduled in the first week; counts 5% of final grade.
• Grade weights: Homework 10%, Quizzes 10%, Workshop 5%, each of three partial exams 25%; no final exam.
• Platform updates: grades updated nightly around 1 AM.

Policies and Procedures

• Drop deadline: October 31 (EW); after this date, drops follow College of Science policy; contact Rutgers office to drop.
• Extensions: HW extensions can be arranged via TA; quizzes and exams require instructor authorization and documentation for absences.
• Attendance: periodically checked; up to 4 absences could lead to withdrawal; attendance can influence borderline grades.
• Online exams: monitoring varies; future calculus courses may not have online exams.
• Respect and etiquette: late arrivals and early departures are tolerated; avoid distracting others; attendance can influence grading perception.

Course Logistics and Tools

• WebAssign: be careful with exact vs decimal answers; exact values are preferred unless rounding is specified.
• Exact vs decimal examples:
  • $\frac{1}{2} = 0.5$ (exactly equal).
  • $\sqrt{41}$ is the exact value; decimal expansion is an approximation.
• Rounding: if a problem asks for rounding, provide the specified number of decimals; otherwise supply the exact value.

Cartesian Plane and Distances (Key Concepts)

• Cartesian plane: 2D location with coordinates (x, y).
• Units/dimensions: 1D length, 2D area, 3D volume.
• Points and distances: distance between ((x1, y1)) and ((x2, y2)) is
  $d = \sqrt{(x<em>2 - x</em>1)^2 + (y<em>2 - y</em>1)^2}$
• Midpoint between two points: $M = \left( \frac{x<em>1+x</em>2}{2}, \frac{y<em>1+y</em>2}{2} \right)$
• Pythagorean theorem (right triangles): $c^2 = a^2 + b^2$
• Intuition: the distance is the hypotenuse of a right triangle formed by coordinate differences.

Quick Practical Notes for Exams and Problems

• Exact vs decimal again: provide exact value unless rounding is requested.
• When solving, remember the distance formula is a direct application of Pythagoras; the midpoint formula gives coordinates in the middle.
• Common geometry formulas (useful in later chapters):
  • Rectangle: $P = 2(a+b)\quad A = ab$
  • Circle: $A = \pi r^2;\quad C = 2\pi r$
  • Cylinder: $V = \pi r^2 h$
  • Sphere: $V = \tfrac{4}{3} \pi r^3$
• In-class approach: instructor emphasizes key ideas; harder problems may be solved in office or posted as solutions on Blackboard.

Quick Reference: Formulas in LaTeX

• Distance between two points: $d = \sqrt{(x<em>2 - x</em>1)^2 + (y<em>2 - y</em>1)^2}$
• Midpoint: $M = \left( \frac{x<em>1+x</em>2}{2}, \frac{y<em>1+y</em>2}{2} \right)$
• Right triangle: $c^2 = a^2 + b^2$
• Area of triangle: $A = \tfrac{1}{2} \text{base} \cdot \text{height}$
• Area of rectangle: $A = ab$
• Volume basics: $V_{box} = abc$

Homework and Practice Guidance

• Start early; some problems are time-consuming.
• If a problem is very time-consuming, discuss in office hours; otherwise I may post solutions on Blackboard.
• Take notes; they aid memory and understanding.