ACT Math Advanced Concepts Night-Before Cram Sheet

Transition alert: ACT is in a format transition. Check MyACT/admission info tonight:
Traditional ACT Math: 60 questions / 60 minutes / 5 answer choices
Enhanced ACT Math: 45 questions / 50 minutes / 4 answer choices
If you know which one you’re taking, your pacing gets much easier.

Exam Overview & Format

Official format	Section	Questions	Time	Question type	% of composite
Traditional ACT	English	75	45 min	MCQ grammar/usage + rhetoric	25%
	Math	60	60 min	MCQ math (usually 5 choices)	25%
	Reading	40	35 min	MCQ passage-based reading	25%
	Science	40	35 min	MCQ graphs/data/experiments/conflicting viewpoints	25%
	Writing (optional)	1 essay	40 min	Persuasive essay	0% (separate)
Enhanced ACT (rolling out 2025–26)	English	50	35 min	MCQ grammar/usage + rhetoric	about 33%
	Math	45	50 min	MCQ math (4 choices)	about 33%
	Reading	36	40 min	MCQ passage-based reading	about 33%
	Science (optional/separate)	40	40 min	MCQ graphs/data/experiments/conflicting viewpoints	separate report
	Writing (if offered/registered)	1 essay	40 min	Persuasive essay	separate

Traditional total testing time: 2 hr 55 min without Writing; 3 hr 35 min with Writing.
Enhanced core testing time: 2 hr 5 min without Science/Writing; 2 hr 45 min with Science; 3 hr 25 min with Science + Writing.
Expect a supervised break after Math. If you take Writing, expect another short break before the essay.
Calculator policy: calculator is allowed only on Math. No formula/reference sheet is provided.
Allowed calculator types: most standard 4-function, scientific, and graphing calculators. Not allowed: phones/tablets, smartwatches, QWERTY-keyboard calculators, or calculators with prohibited CAS/internet-style features.
Materials: bring your photo ID, required test-center materials from MyACT, and for paper testing No. 2 pencils. Use only paper/materials the test center allows or provides.

Scoring & What You Need

Multiple-choice scoring: every correct answer earns 1 raw point; raw scores convert to scaled section scores from 1–36.
No penalty for guessing. Wrong and blank both hurt equally, so bubble something for every question.
Traditional composite: average of English, Math, Reading, Science, rounded to the nearest whole number.
Enhanced composite: average of English, Math, Reading; Science is reported separately if you take it.
Writing: scored separately on a 2–12 scale; it does not affect your composite.
ACT also reports subscores and many colleges accept an ACT Superscore.
There is no official passing ACT score. Your goal is your colleges’ middle 50% range.

Useful score targets

Score fact	What it means
National average composite (recent graduating class): about 19.4	A 20 is roughly average nationally
ACT College Readiness Benchmarks	English 18, Math 22, Reading 22, Science 23
24+ composite	Solid score for many public universities
30+ composite	Strong/selective-college range
34+ composite	Highly selective range

Writing score quick note

Essay is graded across Ideas & Analysis, Development & Support, Organization, Language Use & Conventions.
Two raters score the essay; the reported Writing score is 2–12.

Important: ACT raw-to-scale conversions vary by test form. You are not competing against other students in the room; the scale is set for that test version.

Section-by-Section Strategy

English

Move fast and trust standard grammar. You have about 36 seconds/question on traditional, a bit more on enhanced.
Read only what you need. For sentence-level grammar, you usually do not need the whole paragraph.
Shortest correct answer often wins on redundancy questions—but only if it is fully grammatical.
For organization questions, ask the paragraph’s job. Is it introducing, supporting, contrasting, or concluding?
Don’t overthink style. If two answers sound fine, pick the one that is clearer, more precise, and less wordy.

Math

Use a two-pass plan. Questions usually get harder as you go.
- Traditional: try to reach Q30 by 30 min, Q45 by 45–48 min.
- Enhanced: try to reach Q15 by 16–17 min, Q30 by 33–35 min.
Bank time early. The first half should feel straightforward. Don’t donate 3 minutes to one ugly problem at Q52 or Q41.
Use the answer choices. Backsolve and plug in numbers whenever algebra looks messier than the choices.
Use your calculator selectively. Great for arithmetic, checking graphs, and quick estimates; bad for symbolic problems that need a theorem or identity.
Circle the ask before solving. ACT loves making you solve for $x$ and then asking for $x+2$, a side length, an angle measure, or the number of solutions.

Reading

Do the passage type you like first if your format allows you to flip within the section.
Stay text-faithful. ACT Reading rewards what the passage says, not what seems plausible.
Use line references aggressively. If an answer can’t be pointed to, it’s probably wrong.
Traditional pace: about 8.5 minutes/passage. Enhanced pace: about 10 minutes/passage.
Main idea last is often easier. Answer the specific questions first; they build the big picture for you.

Science (if your test includes it)

Read graphs before prose. Start with axes, units, legends, and trends.
Most questions are data-reading, not science-content questions. Don’t panic if the topic feels unfamiliar.
For conflicting viewpoints, track who believes what. Make a mini T-chart of claims.
Traditional pace: about 5–6 minutes/passage. Enhanced pace: about 6–7 minutes/passage.
Estimate direction and relative size. Many science answers fall from reading the graph shape, not exact computation.

Writing (if you registered for it)

Take a clear position fast. Don’t write a “both sides” essay with no thesis.
Address the perspectives in the prompt, even if briefly.
Use a simple structure: intro with thesis, 2–3 body paragraphs, quick conclusion.
Time split: about 8 minutes plan, 25 minutes write, 5–7 minutes revise.

Highest-Yield Content Review

What ACT Math officially emphasizes

ACT Math reporting category	Approx. share	Night-before priority
Preparing for Higher Math	57–60%	Core Algebra II / functions / geometry / stats
Number & Quantity	7–10%	exponents, radicals, complex numbers
Algebra	12–15%	linear, quadratic, systems, inequalities
Functions	12–15%	notation, composition, inverse, transformations
Geometry	12–15%	triangles, circles, coordinate geometry, trig
Statistics & Probability	8–12%	counting, probability, averages, spread
Integrating Essential Skills	40–43%	ratios, percents, rates, interpreting tables/graphs
Modeling	more than 25%	turning words into equations and sensible estimates

Algebra / functions / polynomials

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a},\qquad x_{\text{vertex}}=-\frac{b}{2a},\qquad D=b^2-4ac$

Topic	Must-know fact	Why it matters
Quadratics	Vertex form: $y=a(x-h)^2+k$	Max/min questions and graph shifts
Discriminant	$D=b^2-4ac$	$D>0$: 2 real roots; $D=0$: 1 real double root; $D<0$: no real roots
Vieta’s formulas	Sum of roots $=-b/a$, product $=c/a$	Fast root questions without solving
Remainder theorem	Remainder on division by $(x-a)$ is $P(a)$	High-yield advanced algebra trap
Factor theorem	If $P(a)=0$, then $(x-a)$ is a factor	Turns evaluation into factoring
Exponents	$a^m a^n=a^{m+n}$, $(a^m)^n=a^{mn}$, $a^{-n}=1/a^n$	Easy points lost by sign mistakes
Radicals	Even roots require nonnegative radicand; rationalize with conjugates	Domain + simplification traps
Functions	$(f\circ g)(x)=f(g(x))$	Very common late-middle question type
Inverse functions	Swap $x$ and $y$, then solve for $y$	Watch domain restrictions
Sequences	Arithmetic: $a_n=a_1+(n-1)d$; geometric: $a_n=a_1r^{n-1}$	Regular ACT advanced pattern
Absolute value	Solve by splitting into cases	Remember it represents distance

Coordinate geometry / geometry / trig

Topic	Must-know fact	Why it matters
Slope	$m=(y_2-y_1)/(x_2-x_1)$	Parallel lines: same slope; perpendicular: negative reciprocals
Distance	$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$	Coordinate geometry staple
Midpoint	$\left((x_1+x_2)/2,(y_1+y_2)/2\right)$	Midpoint and partition problems
Circle equation	$(x-h)^2+(y-k)^2=r^2$	Center/radius recognition
Triangle area	$A=\tfrac12 bh$	Also use coordinate/altitude logic
Special triangles	$45$-$45$-$90$: $x,x,x\sqrt2$; $30$-$60$-$90$: $x,x\sqrt3,2x$	Huge ACT time-saver
Pythagorean theorem	$a^2+b^2=c^2$	Also know common triples: $3$-$4$-$5$, $5$-$12$-$13$, $8$-$15$-$17$
Trig basics	$\sin=\text{opp}/\text{hyp}$, $\cos=\text{adj}/\text{hyp}$, $\tan=\text{opp}/\text{adj}$	Right-triangle questions and exact values
Radians	$180^\circ=\pi$ radians	Convert before using arc/sector formulas
Arc length / sector area	$s=r\theta$, $A=\tfrac12 r^2\theta$ when $\theta$ is in radians	Common advanced circle question

Warning: ACT figures are not necessarily drawn to scale unless the problem tells you otherwise.

Probability / statistics / counting

Topic	Must-know fact	Why it matters
Basic probability	$P(A)=\text{favorable}/\text{total}$	Start here before overcomplicating
Independent events	Multiply: $P(A\text{ and }B)=P(A)P(B)$	Coin/spinner/die style questions
Dependent events	Update the denominator after each draw	“Without replacement” trap
Permutations	$nP r=n!/(n-r)!$	Order matters
Combinations	$nC r=n!/[r!(n-r)!]$	Order does not matter
Mean	Sum divided by number of terms	Weighted-average setups show up often
Median	Middle value after sorting	Don’t forget to sort first
Spread	More spread = larger standard deviation	Usually conceptual, not computational

Fast stem clues → best tool

If the question says…	Think…
remainder when divided by $x-a$	plug in $a$ using the Remainder Theorem
maximum / minimum of a parabola	use the vertex
how many arrangements	permutations
how many groups / committees	combinations
perpendicular line	negative reciprocal slope
tangent to a circle	radius is perpendicular to tangent
number of integer solutions	solve the inequality/equation, then count integers carefully
function of a function	composition: plug one into the other

Rare-but-fast points if they appear

Complex numbers: $i^2=-1$, and powers of $i$ cycle every 4: $i,-1,-i,1$.
Matrices: multiply row by column.
Logs: know that $\log_b(b^k)=k$ and products turn into sums.

Common Pitfalls & Traps

Wrong target — You solve correctly for $x$, but the problem asks for $x+3$, a side length, or the number of solutions. Fix: circle the exact quantity asked before you compute.
Trusting the picture — You assume a side looks longer or an angle looks right. ACT diagrams are often not to scale. Fix: use labels, equations, and stated relationships only.
Forgetting domain restrictions — You allow a negative inside an even root or a zero denominator. Fix: check restrictions before and after solving.
Keeping extraneous solutions — Squaring both sides, clearing denominators, or solving radicals can create fake answers. Fix: plug your answer back into the original equation.
Permutation vs. combination mix-up — Students multiply when order doesn’t matter. Fix: ask, “Would these two arrangements count as different?” If no, use combinations.
Degree/radian mismatch — You use arc length or sector area with degrees when the formula expects radians. Fix: convert first or use the degree version intentionally.
Overusing the calculator — You burn time graphing or typing when the problem is really about a property like vertex, slope, or factor. Fix: identify the concept first, then use the calculator only if it saves time.
Sign mistakes in transformations — In $y=(x-h)^2+k$, students move the graph the wrong way. Fix: inside is opposite, outside is same: right $h$, up $k$.
Leaving blanks — There is no guessing penalty. Fix: always guess, especially in the last 20 seconds.

Memory Aids & Mnemonics

Mnemonic	What it stands for	When to use it
SOHCAHTOA	$\sin=\frac{\text{opp}}{\text{hyp}}$, $\cos=\frac{\text{adj}}{\text{hyp}}$, $\tan=\frac{\text{opp}}{\text{adj}}$	Right-triangle trig
ASTC	All Students Take Calculus	Signs of trig functions by quadrant
FOIL	First, Outer, Inner, Last	Expanding two binomials quickly
Opposite inside, same outside	In $y=(x-h)^2+k$, horizontal shift is opposite sign, vertical is same sign	Function transformations
Order matters = Permutation	Arrangement/lineup/ranking → permutation	Counting questions
Committee = Combination	Group/selection with no order → combination	Counting questions
$i$ cycles by 4	$i,-1,-i,1$	Complex-number powers

Important Dates & Deadlines

Use MyACT for exact dates, center availability, and current fees. ACT updates the exact calendar each year, and school-day/international schedules can differ. The U.S. national ACT follows this general cycle:

U.S. national test month	Regular registration usually closes	Late registration usually closes	Score release timeline
September	about 5 weeks before test day	about 2–3 weeks before test day	typically begins about 2 weeks after the test; may continue up to 8 weeks
October	about 5 weeks before	about 2–3 weeks before	same general release window
December	about 5 weeks before	about 2–3 weeks before	same general release window
February	about 5 weeks before	about 2–3 weeks before	same general release window
April	about 5 weeks before	about 2–3 weeks before	same general release window
June	about 5 weeks before	about 2–3 weeks before	same general release window
July	about 5 weeks before	about 2–3 weeks before	same general release window

Writing scores typically post after the multiple-choice scores, often about 2 additional weeks.
Enhanced ACT rollout milestones: national online rollout began April 2025, national paper rollout began September 2025, and school-day/state-district rollout begins spring 2026.
Late registration usually requires an extra fee; verify the current amount in MyACT before registering.

Last-Minute Tips & Test Day Checklist

Tonight

Do one clean review pass of formulas, pacing, and traps—not a marathon of new content.
Memorize these cold: special triangles, quadratic basics, slope/distance/midpoint, circle equation, permutation vs combination.
Put your calculator in your bag with fresh batteries.
Check MyACT for your exact format, test center, and any center-specific instructions.
Sleep beats one more hour of random practice.

Bring

Acceptable photo ID
MyACT/admission details and whatever your center specifically requires
Approved calculator
No. 2 pencils for paper testing
Snack + water for break
A simple watch only if it is allowed and not a smartwatch

Do NOT bring / use

Phone, smartwatch, earbuds, tablet, or other smart device
Notes, formula sheets, or your own scratch paper
Prohibited calculator models/features
Anything that makes noise or connects to the internet

In the room

Start each Math problem by asking: What concept is this?
If stuck after about 45–60 seconds, mark it, guess strategically, move on.
Come back only if you’ve banked time.
On your last pass, prioritize easy misses over heroic saves.
Bubble every question.

You do not need perfection tomorrow—just clean decisions, steady pacing, and no free mistakes.