Targeted math clean-up: hardest topics review set

1. Reinforce your two weakest math domains

You’re building a cheatsheet that’s basically a custom power-up for the exact math areas that trip you most often. This starts with choosing the right two domains and deciding what belongs on one tight page.

1.1 Pick your two weakest domains (with intention)

You want “weakest” to mean: “where I miss points most often,” not “what I dislike the most.”

Common domains you might see:

• Linear equations and inequalities
• Quadratics and polynomials
• Functions and graphs
• Geometry (triangles, circles, 3D)
• Word problems / systems
• Exponents and radicals
• Statistics and probability

Pick two where:

• You miss several questions in practice sets or diagnostics
• You feel slow or unsure on real test-style problems
• Mistakes repeat (same pattern of error)

1.2 Decide what GOES on the cheatsheet for each domain

Your cheatsheet should not be a mini-textbook. It’s a fast reminder tool. For each domain, capture:

1. Core formulas / rules you actually use

   • Linear: slope formula, point-slope form
   • Quadratic: vertex form, quadratic formula, discriminant
   • Geometry: area/volume formulas, special right triangles
   • Exponents: product/power/quotient rules, negative and fractional exponents

2. Typical “move” or method (step pattern)

   • Example: “Solve word problem linear equation”
   • Pattern: define variable → write equation → solve → check units

3. Top 2–3 personal traps

   • Sign errors (- lost)
   • Distributing exponents incorrectly
   • Confusing radius vs diameter
   • Mixing up permutations vs combinations

4. 1–2 medium-level example problems per domain

   • With a full solution showing the steps you want to remember
   • Not trivial; should resemble real exam difficulty

Think of each domain’s section like:

• Tiny formula box
• 1 short “how to attack” checklist
• “Watch out” line of pitfalls
• 1–2 solved examples

Tiny reference layout example

Imagine your two weakest domains are quadratics and geometry. A rough cheatsheet sketch:

• Top half: “Quadratics”

  • Formulas: ax^2 + bx + c, x = (-b ± √(b^2 - 4ac)) / (2a), vertex = (-b / 2a, f(-b/2a))
  • Method: “To solve ax^2 + bx + c = 0 → check factorable → else quadratic formula”
  • Pitfalls: forget to divide whole numerator by 2a; wrong sign on b
  • Example: a full solved quadratic typical of your tests

• Bottom half: “Geometry – triangles & circles”

  • Area formulas, Pythagorean theorem, special triangles (3–4–5, 5–12–13, 30–60–90 ratios)
  • Method: draw picture → label knowns → choose formula → solve → sanity-check units
  • Pitfalls: using diameter instead of radius in circle formula; mixing degrees and radians (if relevant)
  • Example: right triangle word problem; circle with inscribed angle

1.3 Mechanism: why narrowing to two domains works

Cause → effect:

• Cause: You select just two domains and pack them with high-yield reminders.
• Effect: Your brain gets dense repetition on the same concepts and error patterns, wiring those neural paths stronger.

Versus spreading across 6–7 domains:

• You touch more topics but never enough times to “burn in” the patterns.
• You keep re-making the same mistakes on your weakest domains because they don’t get enough targeted practice.

By focusing:

• You see the same formulas and traps every session.
• You start predicting the right approach as soon as you recognize the question type.
• Questions in those domains begin to feel familiar instead of scary.

1.4 Quick example domain section (runnable by hand)

Say one weak domain is linear word problems. A cheatsheet mini-section might contain:

Formulas / forms

• Slope: m = (y2 - y1) / (y1 - y2) (and a note: “rise over run”)
• Point-slope: y - y1 = m(x - x1)
• Slope-intercept: y = mx + b

Procedure: translate word problem to equation

1. Define variables clearly.
2. Write expressions for what’s changing.
3. Set up equation from “total,” “difference,” or “rate × time” statements.
4. Solve for the variable.
5. Interpret answer in context (do units and size make sense?).

Pitfalls

• Forget to convert units (minutes vs hours, etc.).
• Neglect negative rates (like decreases, losses).

Example problem (you can run this)

A gym charges a sign-up fee of $25 plus $15 per month.

(a) Write an equation for total cost C after m months.

(b) After how many months will the total cost be $160?

Solution

(a) Sign-up fee is a one-time constant: 25. Monthly rate is 15.
Equation:
C = 15m + 25

(b) Set C = 160.
160 = 15m + 25
160 - 25 = 15m
135 = 15m
m = 135 / 15 = 9

So after 9 months, total cost is $160.

You want 1–2 examples like this per weak domain, in your own handwriting/words, on the sheet.