ACT Math Formulas Night‑Before Cram Sheet (with Test Strategy)

Exam Overview & Format

ACT (U.S. national test) = 4 required multiple‑choice sections + optional Writing (essay). No formula sheet is provided.

SectionQuestionsTimeQuestion type% of Composite*
English7545 minMCQ: grammar/usage, rhetoric~25%
Math6060 minMCQ: pre‑alg → trig~25%
Reading4035 minMCQ: passages~25%
Science4035 minMCQ: data, experiments, viewpoints~25%
Writing (Optional)140 minEssay (argument)Separate score

*Composite is the average of the 4 section scores (English/Math/Reading/Science), then rounded to the nearest whole number.

Total time (not counting instructions):

  • Without Writing: 2h 55m
  • With Writing: 3h 35m

Breaks (typical ACT schedule):

  • 10 minutes after Math.
  • If you take Writing, there is typically an additional 5‑minute break after Science before the essay.

Calculator & reference policies (high‑yield)

  • Math: calculators are allowed but must be ACT‑permitted (ACT maintains an official calculator policy list; models/features can change).
  • No formula sheet is provided on the ACT. You must know the key geometry/trig formulas.
  • Bring: approved calculator + fresh batteries, photo ID, admission ticket, #2 pencils (no mechanical pencils), acceptable eraser.

Critical: There is no penalty for guessing. Never leave a question blank.

Scoring & What You Need

How scoring works

  • Each multiple‑choice section earns a raw score = number correct.
  • Raw scores convert to scaled scores 1–36 via equating (varies by form).
  • Composite score (1–36) = average of the four scaled section scores (rounded).
  • Writing (optional) is scored separately on a 2–12 scale (essay readers score domains; ACT reports a combined Writing score).
  • ACT may also report:
    • STEM = average of Math + Science (1–36)
    • ELA = average of English + Reading (1–36)

“What score do I need?” (practical targets)

  • The ACT has no passing score. Required scores depend on your colleges/scholarships.
  • Useful night‑before target: focus on maximizing your Math raw points and avoiding avoidable errors; small gains can move your scaled score.

Guessing & omitted answers

  • No wrong‑answer penalty.
  • Best default: eliminate choices, then guess.

Score distribution (what’s safe to say without guessing)

  • ACT publishes annual national averages and percentiles that change year to year.
  • Historically, the national average composite has hovered around the high‑teens/low‑20s; check the most recent ACT report for current numbers.

Section-by-Section Strategy

English (75 Q / 45 min ≈ 36 sec/Q)

  1. Read with your pencil: for grammar questions, you usually only need the sentence + 1 line of context.
  2. Shortest is often best if it’s grammatical and preserves meaning (concise writing is rewarded).
  3. Punctuation rules > vibes: commas/semicolons/colons have strict jobs.
  4. Don’t “fix” what isn’t broken: if NO CHANGE is clean and clear, it’s frequently right.
  5. Time check: after 15 minutes you should be ~25 questions in.

Math (60 Q / 60 min = 60 sec/Q)

  1. Order matters: Q1–40 are usually quicker; bank time for the last 20.
  2. Don’t over‑algebra: plug in numbers, back‑solve from answer choices, or use the calculator when it saves time.
  3. Write mini‑work: one clean line per step prevents sign errors.
  4. Know when to bail: if you’re stuck at 60–75 seconds, guess strategically, mark it, move on.
  5. Time check: aim for ~30 questions by 30 minutes.

Reading (40 Q / 35 min ≈ 52 sec/Q)

  1. Passage first vs questions first: pick one and commit. Most students do best with passage first + quick margin notes.
  2. Line references are gold: when a question points to lines, go back—don’t rely on memory.
  3. Answer must be supported: eliminate anything not explicitly backed by the text.
  4. Don’t get trapped by “sounds right”: prefer literal, boring, text‑based choices.
  5. Time check: ~8–9 minutes per passage (including questions).

Science (40 Q / 35 min ≈ 52 sec/Q)

  1. It’s mostly data reading: treat it like “reading graphs/tables fast.”
  2. Go straight to the question: then scan the figure/table for exactly what you need.
  3. Units and axes first: many traps are unit swaps or reversed axes.
  4. Conflicting Viewpoints passage: read viewpoints like mini‑arguments; track who believes what.
  5. Skip dense setups: if the intro is long, jump to the question + figure.

Writing (Optional, 40 min)

  1. Pick a side fast: 5 minutes planning, 30 writing, 5 revising.
  2. Use a simple template: claim → reasons → counterargument → conclusion.
  3. Specific examples win: history/current events/personal observations—keep them clear.
  4. Paragraph structure: topic sentence + explanation + example.

Highest-Yield Content Review

ACT Math: the formulas you actually need (no formula sheet!)

1) Algebra essentials
TopicMust-know rule/formula
Slopem=\frac{y_2-y_1}{x_2-x_1}
Point-slopey-y_1=m(x-x_1)
Slope-intercepty=mx+b
Standard formAx+By=C
Distanced=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
Midpoint\left(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}\right)
Quadratic formulax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
Discriminantb^2-4ac (>0 two real, =0 one real, \<0 none real)
Exponent rulesa^ma^n=a^{m+n},\ \frac{a^m}{a^n}=a^{m-n},\ (a^m)^n=a^{mn},\ a^{-n}=\frac{1}{a^n}
Radicals\sqrt{ab}=\sqrt a\sqrt b (for $a,b\ge0$), rationalize denominators
Absolute value Percent change \%\ \text{change}=\frac{\text{new-old}}{\text{old}}\times100\% 2) Functions & graphs Concept One-liner you use on test day Function notation $f(x)$ = output when input is $x$ Composition $f(g(x))$ = plug $g(x)$ into $f$ Inverse Swap $x,y$ then solve for $y$; check domain restrictions Transformations $f(x-h)+k$: right $h$, up $k$; $-f(x)$ reflect over $x$-axis; $f(-x)$ reflect over $y$-axis Domain Inputs allowed (watch square roots/denominators) Range Outputs possible 3) Coordinate geometry (high frequency) Shape Key facts Parallel lines Same slope: $m_1=m_2$ Perpendicular Negative reciprocals: $m_1m_2=-1$ Circle Center-radius: (x-h)^2+(y-k)^2=r^2 Distance to axis-aligned point moves Horizontal/vertical distance is absolute difference in one coordinate 4) Plane geometry: areas/perimeters you can’t miss Figure Formula Rectangle $A=lw$, $P=2l+2w$ Triangle A=\frac12 bh Right triangle a^2+b^2=c^2 Equilateral triangle A=\frac{\sqrt3}{4}s^2 (rare but useful) Parallelogram $A=bh$ Trapezoid A=\frac12 (b_1+b_2)h Circle C=2\pi r,\ A=\pi r^2 Arc length s=r\theta (if $\theta$ in radians); or s=\frac{\theta}{360^\circ}2\pi r Sector area A=\frac12 r^2\theta (radians); or A=\frac{\theta}{360^\circ}\pi r^2 5) Solid geometry (volume/surface area) Solid Volume $V$ Surface Area $SA$ Rectangular prism $V=lwh$ $SA=2(lw+lh+wh)$ Cube $V=s^3$ $SA=6s^2$ Cylinder V=\pi r^2h SA=2\pi r^2+2\pi rh Cone V=\frac13\pi r^2h SA=\pi r^2+\pi r\ell Sphere V=\frac43\pi r^3 SA=4\pi r^2 6) Trigonometry (ACT-level) Topic Must-know SOHCAHTOA \sin\theta=\frac{\text{opp}}{\text{hyp}},\ \cos\theta=\frac{\text{adj}}{\text{hyp}},\ \tan\theta=\frac{\text{opp}}{\text{adj}} Pythagorean identity \sin^2\theta+\cos^2\theta=1 Special right triangles $45$-$45$-$90$: sides $x,x,x\sqrt2$; $30$-$60$-$90$: $x, x\sqrt3, 2x$ Degree basics $\sin 30=\tfrac12$, $\cos 60=\tfrac12$, $\tan 45=1$ 7) Probability, counting, statistics Topic Formula/Rule Mean \bar x=\frac{\text{sum}}{n} Median Middle value after sorting Mode Most frequent Range max − min Probability P(A)=\frac{#\ \text{favorable}}{#\ \text{total}} “And” (independent) P(A\cap B)=P(A)P(B) “Or” P(A\cup B)=P(A)+P(B)-P(A\cap B) Complement P(A^c)=1-P(A) Permutations ^{n}P_{r}=\frac{n!}{(n-r)!} Combinations ^{n}C_{r}=\frac{n!}{r!(n-r)!} 8) Quick conversion/ratio tools **Proportion:** \frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc **Rate:** \text{rate}=\frac{\text{distance}}{\text{time}} **Density:** \text{density}=\frac{\text{mass}}{\text{volume}} **Slope as rate of change:** $\Delta y/\Delta x$ Ultra-high-yield “methods” (these are worth points) **Plug In (numbers):** great for variables in answer choices. **Backsolve:** start with answer choice C, test, then go up/down. **Estimation:** especially with weird radicals/π; eliminate obviously wrong scales. **Dimensional analysis:** track **units** to prevent traps. Common Pitfalls & Traps **Rushing early Math questions** **What goes wrong:** you treat Q1–20 like freebies and make sign/operation errors. **Why wrong:** these are the easiest points on the test. **Fix:** slow down just enough to write one clean line; aim for **accuracy first 30–35 Q**. **Forgetting there’s no formula sheet** **What goes wrong:** you “know it’s somewhere” for volume/sector/special triangles. **Why wrong:** ACT doesn’t provide a formula page. **Fix:** memorize the tables above; especially **circle**, **triangle**, **cylinder/cone/sphere**, **special triangles**. **Misreading what the question is asking** **What goes wrong:** you solve for $x$ but they want $2x$ or $x+y$. **Why wrong:** ACT loves “last step” traps. **Fix:** underline the target (e.g., “**perimeter**,” “**probability**,” “**value of expression**”). **Not using answer choices strategically** **What goes wrong:** you grind algebra when answers could be tested quickly. **Why wrong:** time is the limiting factor. **Fix:** if answers are numbers, **backsolve**; if answers are expressions, **plug in**. **Calculator overuse** **What goes wrong:** you punch everything in and lose time (or mis-key). **Why wrong:** many items are faster by mental math/estimation. **Fix:** use calculator for messy arithmetic, trig values, or regression-like computation—not for $\frac{6}{3}$. **Domain/zero-division mistakes** **What goes wrong:** you cancel terms illegally or ignore restrictions (e.g., $x\ne0$). **Why wrong:** cancellation can remove invalid solutions. **Fix:** note restrictions from denominators and even roots; check final answers. **Slope/perpendicular confusion** **What goes wrong:** you use negative slope instead of negative reciprocal. **Why wrong:** perpendicular lines satisfy $m_1m_2=-1$. **Fix:** reciprocal + sign flip: $\frac{2}{3}\to -\frac{3}{2}$. **Probability “or” double-counting** **What goes wrong:** you add probabilities without subtracting overlap. **Why wrong:** overlapping outcomes get counted twice. **Fix:** use P(A\cup B)=P(A)+P(B)-P(A\cap B).$$

  • Reading/Science: answering from memory
    What goes wrong: you pick what “sounds right.”
    Why wrong: wrong choices are written to sound plausible.
    Fix: force yourself to point to the line/figure that proves it.

    • Memory Aids & Mnemonics

    MnemonicWhat it stands forWhen to use it
    PEMDASParentheses, Exponents, Multiplication/Division, Addition/SubtractionOrder of operations (still go left→right for ×/÷ and +/−)
    FOILFirst, Outer, Inner, LastMultiply two binomials $(a+b)(c+d)$
    SOHCAHTOA$\sin=\frac{\text{opp}}{\text{hyp}}$, $\cos=\frac{\text{adj}}{\text{hyp}}$, $\tan=\frac{\text{opp}}{\text{adj}}$Right-triangle trig
    “30-60-90: 1–\sqrt3–2”Short leg $x$, long leg $x\sqrt3$, hypotenuse $2x$Special triangle speed
    “45-45-90: 1–1–\sqrt2”Legs $x,x$, hypotenuse $x\sqrt2$Special triangle speed
    “Pythagorean triple 3–4–5”$3^2+4^2=5^2$Quick right triangles (also multiples: 6–8–10, 9–12–15)

    Important Dates & Deadlines (how to verify fast)

    ACT test dates and deadlines change by testing year and location (and some states/districts have additional school-day testing). To avoid giving you wrong dates, use this quick method:

    • Go to act.org → Register → choose your country/state → view the published test date schedule.
    • Rule of thumb: registration deadlines are often about 4–5 weeks before test day, with a late registration window afterward (fees apply). Score release timing varies by test date and delivery method.
    What you needWhere to checkWhat to look for
    Upcoming test datesACT registration portalYour region’s available Saturdays + any school-day tests
    Registration deadlineSameStandard vs late deadline + fees
    Score releaseACT scores pageFirst release window + potential delays

    Last-Minute Tips & Test Day Checklist

    Night before (15–30 minutes max)

    • Re-read the Math formula tables (circles, triangles, volume, trig, probability).
    • Do a 5-minute “methods reset”: plug-in, backsolve, estimate, eliminate.
    • Set your pacing plan: Math Q1–40 steady, Q41–60 bank time + guess smart.

    What to bring

    • Photo ID (acceptable per ACT rules)
    • Admission ticket (if required for your test mode)
    • 2–3 sharpened #2 pencils + good eraser
    • Approved calculator + spare batteries (or a backup calculator if allowed)
    • Watch (if permitted; must be silent—confirm local policy)
    • Water/snack for break

    What NOT to bring / do

    • Don’t bring prohibited electronics into the testing room (phone/smartwatch rules are strict; follow the proctor).
    • Don’t rely on “I’ll come back later” without marking the question number; lost time kills.

    In-section execution reminders

    • Bubble in batches (e.g., every 5 questions) to reduce mis-bubbles.
    • If you’re stuck: eliminate 2, guess, move. Protect your time.
    • In Math, if answers are increasing (A→E), use that to estimate and choose direction.

    Quick checklist (morning of)

    • [ ] ID + admission ticket
    • [ ] Calculator cleared/working + batteries
    • [ ] Pencils
    • [ ] Snack/water for break
    • [ ] Arrive early (parking + check-in)

    You don’t need to know everything—you need to cash the easy points and avoid the traps.