SAT-98: The Formula Sheet Hack

SAT-98: The Formula Sheet Hack

Description: Every SAT math section gives you a reference sheet of formulas. Knowing exactly what's on it (so you don't memorize those) — and, more importantly, what's not on it (so you do) — is a quiet but real advantage.

What the reference sheet gives you

• Area of a circle: A = πr²; circumference: C = 2πr.
• Area of a rectangle and triangle; the Pythagorean theorem.
• Volumes: rectangular box, cylinder, sphere, cone, pyramid.
• Special right triangles (the 30-60-90 and 45-45-90 ratios).
• The fact that a circle has 360°, and a triangle's angles sum to 180°.

(Oʻzbekcha: maʼlumotnomada doira yuzasi, hajmlar, Pifagor teoremasi va maxsus uchburchaklar bor.)

What is NOT on the sheet (you must know these)

• The slope formula and slope-intercept form y = mx + b.
• The quadratic formula and the discriminant.
• The distance and midpoint formulas.
• Percent change, exponential growth (a·b^x), and SOH-CAH-TOA.

Memorize these, because the sheet won't help you. (Oʻzbekcha: nishab, kvadrat formula, masofa formulasi — bular varaqda yoʻq, ularni yodlang.)

Worked Example 1 — use a given volume formula

A cylinder has radius 3 and height 10. Find its volume (V = πr²h is on the sheet).

• V = π(3)²(10) = π·9·10 = 90π. You just look up the formula and plug in.

Worked Example 2 — recall a NOT-given formula

Find the slope between (1, 2) and (5, 10). (The slope formula is NOT on the sheet.)

• slope = (10 − 2)/(5 − 1) = 8/4 = 2. You must know this from memory.

(Oʻzbekcha: nishab formulasi varaqda yoʻq — yoddan bilishingiz kerak.)

Worked Example 3 — combine sheet + memory

A sphere has volume 36π. Find its radius (V = (4/3)πr³ is on the sheet).

• 36π = (4/3)πr³ → 36 = (4/3)r³ → r³ = 27 → r = 3.

Worked Example 4 — don't waste time re-deriving

You need the area of a circle with radius 5. Should you derive it?

• No — A = πr² is on the sheet. Just use it: A = π(25) = 25π. Save your time for the formulas you had to memorize.

Strategy: at the start, glance at the reference sheet so you know what's there. Spend memorization energy on the formulas that are NOT provided. (Oʻzbekcha: varaqda nima borligini bilib oling — yodlashni varaqda yoʻq formulalarga sarflang.)

The hidden cost of relying only on the sheet

Even for provided formulas, the sheet helps only if you know which one applies and what each letter means. It won't tell you that a "can" is a cylinder, or that you need the cone formula rather than the cylinder one. So the real skill is matching the situation to the right formula and identifying r, h, and so on from the problem. Treat the sheet as a memory aid for the equation's form, not a substitute for understanding the shape. (Oʻzbekcha: varaq formulani beradi, lekin qaysi shaklga mosligini va harflar maʼnosini oʻzingiz aniqlashingiz kerak.)

Practice 1

A cylinder has radius 2 and height 7. Find its volume (use the sheet's V = πr²h).

Practice 2

Which of these must you memorize because it's NOT on the reference sheet: area of a circle, or the quadratic formula?

Key words — Kalit soʻzlar

• Reference sheet — maʼlumotnoma varagʻi
• Formula — formula
• Provided / Given — berilgan
• Memorize — yodlash
• Volume — hajm
• Slope — nishab
• Quadratic formula — kvadrat tenglama formulasi
• Distance formula — masofa formulasi
• Cylinder / Sphere — silindr / shar

Summary

• The sheet gives areas, volumes, the Pythagorean theorem, and special-triangle ratios — don't memorize those.
• Memorize what's missing: slope, quadratic formula, distance/midpoint, SOH-CAH-TOA, percent change.
• Glance at the sheet early; use it instead of re-deriving provided formulas.