ACT Math Advanced Concepts Night-Before Cram Sheet
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.
| 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: $an=a1+(n-1)d$; geometric: $an=a1r^{n-1}$ | 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 | $m=(y2-y1)/(x2-x1)$ | Parallel lines: same slope; perpendicular: negative reciprocals |
| Distance | $d=\sqrt{(x2-x1)^2+(y2-y1)^2}$ | Coordinate geometry staple |
| Midpoint | $\left((x1+x2)/2,(y1+y2)/2\right)$ | 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 |
| 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.