My 12-Week College Algebra Study Plan

Posted on in Learning

I’m rebuilding my maths foundation for physics/astro without video courses. This plan is book-only, exercise-first, and fits into three 1-hour sessions per week over 12 weeks, using:

Primary text: Schaum’s Outline of College Algebra, Fifth Edition (Spiegel & Moyer)

How I’m running this

  • Schedule: Monday, Wednesday, Friday (1 hour each)
  • Session format (1 hour):
    • 5 min warm-up: I redo one problem from a prior session.
    • 20 min reading + worked examples.
    • 30 min problem practice (I check answers at the back).
    • 5 min reflection: I write one key idea to remember.
  • Pacing: I’ll cover all 9 chapters in about 10 weeks, then use Weeks 11–12 for mixed review and consolidation.

Week 1 — Real Numbers & Algebra Basics (Ch. 1)

  • Mon: Sets of numbers; properties of real numbers. Practice: simplifying expressions.
  • Wed: Exponents and radicals. Practice: rules of exponents and radical manipulation.
  • Fri: Scientific notation; operations with radicals. Practice set focusing on accuracy.

Week 2 — Linear Equations & Inequalities (Ch. 2)

  • Mon: Linear equations in one variable; proportional reasoning.
  • Wed: Graphs of lines; slope–intercept and point–slope forms; I sketch several lines.
  • Fri: Linear inequalities and absolute-value equations; solution sets on the number line.

Week 3 — Systems of Linear Equations (Ch. 2 cont.)

  • Mon: Two-equation systems (substitution and elimination).
  • Wed: Three-equation systems; consistency and uniqueness.
  • Fri: Word problems: mixture, rate, and investment-style systems.

Week 4 — Quadratic Equations (Ch. 3)

  • Mon: Factoring and the quadratic formula; using the discriminant for insight.
  • Wed: Completing the square; vertex form; nature of roots.
  • Fri: Graphing parabolas; modelling problems with quadratics.

Week 5 — Polynomials & Rational Expressions (Ch. 4)

  • Mon: Polynomial operations; degree and leading coefficient.
  • Wed: Long and synthetic division; remainder and factor theorems.
  • Fri: Rational expressions: simplify, restrict domains, and solve simple rational equations.

Week 6 — Exponential & Logarithmic Functions (Ch. 5)

  • Mon: Exponential functions; growth/decay intuition.
  • Wed: Logarithms; change-of-base and log identities.
  • Fri: Solving exponential/log equations; common algebra traps I’ll avoid.

Week 7 — Functions & Graphs (Ch. 6)

  • Mon: What is a function? domain, range, and evaluation.
  • Wed: Composition and inverse functions; when inverses exist.
  • Fri: Transformations: shifts, stretches, reflections; quick sketching practice.

Week 8 — Matrices & Determinants (Ch. 7)

  • Mon: 2×2 and 3×3 determinants; properties and computation.
  • Wed: Cramer’s rule for small systems; interpreting results.
  • Fri: Matrix operations and inverses

Week 9 — Sequences & Series (Ch. 8)

  • Mon: Arithmetic sequences and partial sums.
  • Wed: Geometric sequences and sums.
  • Fri: Binomial theorem; coefficients and pattern spotting.

Week 10 — Probability Essentials (Ch. 9)

  • Mon: Basic probability rules; complements and unions.
  • Wed: Permutations; ordering and arrangements.
  • Fri: Combinations; selections; simple binomial probability applications.

Week 11 — Mixed Review (Chs. 1–4)

I revisit real numbers, linear equations/inequalities, systems, quadratics, polynomials, and rationals.
I build a one-page formula sheet for Chapters 1–4 (exponent/log rules, quadratic formula, factoring patterns).

Week 12 — Mixed Review (Chs. 5–9)

I revisit exponentials/logs, functions, matrices, sequences/series, and probability.
I extend my formula sheet with log identities, inverse/compose rules, determinant shortcuts, binomial coefficients, and permutations/combinations.

Study habits I’m following

  • I write everything out neatly—clean steps reduce errors.
  • I check and correct using answer keys to understand why I missed something.
  • I spiral back: if a topic feels shaky, I note a micro-plan to revisit it.
  • I track progress with a simple log (date, section, problems attempted/solved, confidence 1–5).
  • If sets feel easy, I add challenge problems from the end of each chapter.

What I’ll do next

After this 12-week block, I’ll move to:

  • Schaum’s Outline of Trigonometry (another 12 weeks at 3 hrs/week)
  • Then Calculus (e.g., Thomas’ Calculus or Strang: Calculus if Stewart isn’t available)

By sticking to this cadence, I’ll have a solid algebra base, ready for trig and then calculus—exactly what I need before diving deeper into physics and astrophysics.

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