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Lab 0 - Algebra Review & PEMDAS Quick Reference

Lab structure and grading

  • Labs: weekly practice problems, not graded. Homework (online) is graded; labs are for practice.
  • Homework zero: due this Sunday at 11:59 PM; only the homework folder labeled with the backpack icon is to be completed and submitted online.
  • Access: materials under HuskyCT → Labs → Chapter Zero questions. Printable copy available for download/record; use the online version for submission.
  • Answers: posted after Friday on HuskyCT.
  • Attendance: labs are practice; missing labs may impact performance on homeworks/exams.

Quick access and workflow

  • Where to find: HuskyCT → Labs → Chapter Zero questions. Download as needed.
  • Printable copy is for your records; do not submit it.

Core rules: PEMDAS (order of operations)

  • PEMDAS order:
    \text{PEMDAS} = \text{Parentheses}, \text{Exponents}, \text{Multiplication/Division (left-to-right)}, \text{Addition/Subtraction (left-to-right)}
  • Examples:
    • 10 - \frac{10}{5} + 1 = 9
    • 2 + 3 \times 5 = 17
  • Tip: enter expressions as written in calculators; use parentheses to enforce a desired order.

Scientific notation and decimal notation

  • Negative exponent conversion:
    • 1.34 \times 10^{-4} = 0.000134
    • Move decimal left by the exponent magnitude; pad zeros as needed.
  • Positive exponent conversion:
    • 2.1 \times 10^{3} = 2100
    • Move decimal right by the exponent magnitude; pad zeros as needed.

Intervals: midpoint, width, and representations

  • Definitions for interval [(\text{lower}, \text{upper})]
    • Midpoint: \text{mid} = \frac{\text{lower} + \text{upper}}{2}
    • Width: \text{width} = \text{upper} - \text{lower}
    • Midpoint form: [\text{lower}, \text{upper}] = \text{mid} \pm \frac{\text{width}}{2}
    • Conversion: from midpoint form to lower-upper, a \pm b \rightarrow [a-b, a+b]
  • Example patterns (conceptual): between -5 and 20, mid = 7.5, width = 25, so 7.5 ± 12.5; between 5 and 20, mid = 12.5, width = 15, so 12.5 ± 7.5 (use formula rather than memorized numbers).

Linear model notation and evaluation

  • Model: \hat{y} = \beta0 + \beta1 x
  • Example substitution: \beta0 = -5, \beta1 = 2, x = 5 \Rightarrow \hat{y} = -5 + 2 \times 5 = 5
  • Note: equivalent form in other notation is \hat{y} = b0 + b1 x with the same interpretation.

Solve for x from a ratio equation

  • Given: z = \frac{x - m}{s}, solve for x:
    • Multiply both sides by s: zs = x - m
    • Add m: x = zs + m
  • Alternative equivalent form: x = m + zs
  • Key idea: linear rearrangement yields the same result regardless of the order of multiplication due to commutativity.

Proportion in a sample (basic statistics)

  • Given: sample size n = 522 and proportion p = 0.55
  • Compute number of voters: x = p\,n = 0.55 \times 522 \approx 287.1 \Rightarrow 287 (rounded to integer)

Quick reminders

  • Homework zero is the only item graded online; labs remain practice.
  • Be on track with every lecture and lab to avoid gaps before exams.
  • If unclear, ask questions during or after the session.

Important dates recap

  • Homework zero due: Sunday 11:59 PM
  • Lab answers posted after Friday on HuskyCT