Test Day and Reference: ACT Math Lesson

Plan your calculator, Desmos, scratch work, and checklists for ACT Math test day, then review the key relationships in one compact reference.

ACT Math Test Day

A testing room is never perfect. The clock might sit at an awkward angle, the room might run warm, a proctor's instructions might take longer than expected, and none of that is worth spending energy on, because it happens to everyone in the room and it is not part of the mathematics. Math adds one layer the rest of test day does not: a set of equipment and interface decisions that are entirely solvable before you ever leave home. A calculator problem on test day is rarely about not owning a calculator. It is usually about discovering, too late, that the one you brought is unfamiliar, low on power, not permitted, or doing something you do not know how to undo.

This lesson separates official ACT requirements from ordinary room experience. Where a rule is official, it is stated plainly. Where a pattern is common but not universal, such as a preference for paper over digital testing, it says so honestly instead of declaring one format superior.

The night before

Remove every decision you can the night before, so the morning of the test is execution, not decision-making. Confirm the test center, date, and whether you are testing on paper or online. Check for any last updates from ACT. Bring an acceptable photo ID. ACT also recommends bringing the admission ticket because it contains useful registration and, for online testing, launch information, but the ticket itself is not required for admission. If testing on paper, pack several sharpened pencils with erasers.

Then handle the Math-specific layer directly. Verify your calculator's exact model against current ACT policy, not against a classroom rule, an SAT rule, or an old forum list. Charge it fully or confirm the batteries are reliable. Pack a backup calculator or extra batteries if you have them; ACT recommends this, and testing staff do not provide a handheld calculator if you forget one. Do not plan to share a calculator with another student; sharing is not permitted. If you are testing online, know that Desmos is built into the Math section, and decide your fallback in advance: a familiar handheld calculator, hand algebra, or both, in case it lags or is briefly unavailable. If you are using a BYOD device, complete any required device or software setup ahead of time, and pack it fully charged along with its charger. Do not pack personal scratch paper; the format you are testing in determines how scratch work happens, and personal paper is not part of either version. Know going in that there is no general Math formula sheet waiting for you; if a quick review of the reference page feels useful, do it early, then stop studying. Do not install a new calculator program or change familiar settings the night before a test.

Calculator readiness

Handle the calculator itself as its own checklist item, not an afterthought folded into packing. Confirm the exact model is currently permitted; verify it is charged or has fresh batteries; bring a backup if one is available; and use the calculator you actually practiced with, not a more powerful one you are less familiar with. A powerful calculator used slowly is worse than a familiar one used automatically. Check ordinary settings before test day and avoid last-minute changes. CAS functionality is prohibited, and some stored programs or documents may require removal under current policy; verify this ahead of time instead of discovering it in the room. Some calculator models require specific modifications, such as removing a cover or disabling a feature; check the current model-specific policy if this applies to your device. And again: sharing is not permitted, so a friend's calculator is never a valid backup plan.

Desmos readiness

The current online National ACT Math section includes a built-in Desmos graphing calculator, reachable through the Math section's own tools menu. This is current, official fact. Students report that it is generally reliable, though occasional lag, zoom oddities, or a slow-to-open tool are not unheard of. That is worth knowing, not fearing: if Desmos is briefly unavailable or awkward on a specific question, the algebra underneath it is usually still solvable by hand or with a permitted handheld calculator, and the section has not disappeared along with the tool.

If you have used a generic version of Desmos or a different platform's version before, spend some time in ACT's own online practice environment specifically, since menu layout and behavior are not guaranteed to be identical across platforms. Online testers may also bring a permitted handheld calculator; some students use Desmos for graphing and intersections and a familiar handheld for other work, or as a backup if Desmos is having a bad moment.

No formula sheet

There is no general Math reference sheet provided, on paper or on screen. When a question requires a complex or unfamiliar formula, the formula is supplied within that specific item. This is current official policy, not a gap to fill by memorizing an exhaustive formula list the night before. Know the relationships you have already learned, and expect that anything genuinely unusual will be handed to you inside the question that needs it.

Scratch work by format

Scratch work works differently depending on how you test, and neither version involves bringing your own paper. On paper, work happens directly in the test booklet; personal scratch paper is not permitted. Online, the testing site supplies scratch paper, which is collected afterward; you do not bring your own sheets, and there is no fixed guaranteed quantity to expect, so follow the site's or proctor's procedure if you need more. Students genuinely disagree about which format is easier here. Some feel more exposed without the ability to graph or check work digitally; others make fewer mistakes writing directly on a printed page than copying figures and expressions back and forth between a screen and supplied paper. The useful question is not which format is objectively better. It is which workflow you have actually practiced under timed conditions.

BYOD readiness

If your test site uses a bring-your-own-device model, complete every required setup and readiness check before test day, not the morning of. Bring the device fully charged, and bring its charger. Sites are not required to provide a backup device if yours fails, which is exactly why the setup checks and the charge matter as much as they do. Bring your admission ticket; it can contain login information you will want on hand. If a technical problem happens during the test itself, alert the proctor immediately instead of spending timed minutes troubleshooting it yourself. If a calculator tool alone fails while the rest of the device works, continue with a permitted handheld calculator or hand work where practical, following the proctor's directions.

Math is second: using the break deliberately

On the current national test structure, Math is the second section, and the scheduled break comes immediately afterward. Know that going in, so the last few minutes of Math are spent on remaining questions and final answer selections, not on managing the transition to a break that is coming regardless. When the break arrives, use it physically: restroom, a familiar snack, water, a real reset. Do not spend it calculating how many Math questions you think you missed. That number is not knowable from inside the test, and replaying it costs you focus that the next section needs.

If the Math setup isn't ideal

A few specific problems are common enough on this section to plan for directly, instead of improvising in the moment.

Common setup problems and responses
Problem	Immediate response
Handheld calculator won't turn on before testing begins	Switch to a backup or fresh batteries if available; tell staff if needed. Testing staff do not provide a handheld calculator, which is why the backup was packed.
Forgot a calculator on a paper test	Testing staff do not provide one. Continue without a calculator if admitted; every Math question can be solved without one, even if some are slower that way.
Desmos won't open or is lagging	Alert the proctor if it appears to be a platform issue. Use a permitted handheld calculator or hand work instead of repeatedly reopening the same tool.
Online scratch paper is running low	Follow the site's or proctor's procedure and request more if needed. Do not use personal paper.
BYOD device fails before the section starts	Tell staff immediately. Readiness checks and a full charge beforehand are the real prevention here.
A technical failure happens mid-test	Flag it for staff right away. Do not spend timed minutes trying to fix it yourself.
Calculator is in the wrong mode or shows a strange graph window	Use the recovery method you've practiced, or switch to a different route or tool instead of fighting an unfamiliar screen.
Can't recall a formula	Check whether the item itself supplies it, which it usually does if the formula is genuinely uncommon. Otherwise, reason from a relationship you do know, or mark it and return.
Testing on paper but wishing for Desmos	Do not change your plan mid-section. Use the paper methods you actually practiced.
Testing online and finding copying figures onto scratch paper awkward	Copy only the specific labels or relationships you actually need, not the entire figure.

Night-before checklist

Confirm test center, date, and paper-versus-online format. Check for any last updates.
Acceptable photo ID packed. Admission ticket printed and packed if available; ACT recommends bringing it, although it is not required for admission.
If testing on paper: several sharpened pencils with erasers.
Calculator model verified against current policy, fully charged or with fresh batteries confirmed, backup calculator or extra batteries packed if available. No plan to share a calculator. No new calculator programs or major setting changes tonight.
If testing online: know Desmos is built into Math, and know your fallback if it lags.
If using BYOD: device setup complete, fully charged, charger packed.
No personal scratch paper packed; the format's own rule is already known.
No general Math formula sheet exists; a short review of the reference page is fine if useful, then stop.
A permitted watch or timing device packed if desired.
Normal snack, water, layers, and breakfast or caffeine plan in place.

Test-morning checklist

Do not switch calculators because another student claims theirs is faster. Before leaving, verify the calculator turns on and, if using BYOD, that the device is charged; bring the charger regardless. Arrive before the current cutoff with ID and ticket accessible. Once seated, follow staff directions before taking anything out or changing any settings. On paper, use the bubbling method already practiced. Online, locate the timer, scratch paper, marking tools, and Desmos once the interface makes them available, and do not panic if a Math-specific tool isn't visible during general directions. Once Math begins, use the same hand, handheld, Desmos, and hybrid decisions you practiced with. Don't let a calculator or interface issue consume several questions before flagging it for the proctor. Before time expires, make sure every remaining question has an answer selected. At the break immediately after Math, stop replaying it: restroom, snack, water, reset.

What this lesson is not saying

A few claims are worth ruling out directly, because they are easy to assume and not quite accurate. Desmos is current and generally reliable, but it is not guaranteed to work perfectly on every single question. Digital testing is not automatically easier just because it includes Desmos, and paper testing is not automatically safer just because it avoids a screen; students genuinely differ on which workflow suits them, and the honest answer is that the one you have actually practiced under timed conditions is the one to trust. No formula sheet is provided in either format. No calculator model is uniquely mandatory; what matters is legality and familiarity, not brand. And installing anything new, whether a program or a changed setting, the night before a test creates risk that removing decisions in advance is designed to avoid.

Once these decisions are made ahead of time, an imperfect room stops being part of the test. A prepared Math tester already knows the format, already knows the calculator and Desmos plan, already knows how scratch work functions, and already knows there is no formula sheet to search for. What is left, once the section actually begins, is the mathematics itself.

ACT Math Reference

This reference teaches nothing new. Every fact below was already taught in full, with worked examples and practice, somewhere earlier in the course. Its only job is to put the relationships you will want to recall quickly in one place, organized by content area, so a quick review before test day does not mean flipping back through thirty units.

Remember what the test day lesson established: there is no general Math formula sheet on the current test. When an item needs a genuinely unfamiliar or complex formula, that formula is supplied inside the item itself. Everything below is the kind of relationship worth knowing automatically, not a substitute for a reference sheet that does not exist on the actual test.

Number and Quantity

Number and Quantity
Relationship	Where it was taught
$i^2=-1$ ; multiply by the conjugate to divide complex numbers	Real and Complex Numbers
When defined in the real numbers, $x^{m/n}$ can be interpreted using an $n$ th root and the power $m$ ; with an even root, the radicand must be nonnegative. Check candidate solutions after raising both sides of an equation to an even power	Exponents and Radicals
Matrix multiplication requires columns of the first to equal rows of the second; determinant of $\begin{bmatrix}a&b\\c&d\end{bmatrix}=ad-bc$	Vectors and Matrices

Algebra

Algebra
Relationship	Where it was taught
Multiplying or dividing an inequality by a negative reverses the inequality sign	Linear Equations, Inequalities, and Systems
Discriminant $b^2-4ac$ : positive gives two real solutions, zero gives one, negative gives two complex solutions; vertex at $x=\frac{-b}{2a}$	Quadratics and the Discriminant
Factor by grouping; if $x=a$ is a zero, $(x-a)$ is a factor; rewrite exponential equations with a common base	Polynomial, Radical, and Exponential Equations
$\|\text{expression}\|=k$ splits into two cases; an absolute value can never equal a negative, so any case producing one is rejected	Absolute Value

Functions

Functions
Relationship	Where it was taught
$f(g(x))$ means evaluate the inner function first; domain excludes zero denominators, negative values under an even root, and non-positive arguments of a logarithm	Notation, Evaluation, and Composition
Roots, zeros, and $x$ -intercepts name the same feature; end behavior is controlled by degree and leading-coefficient sign	Linear, Quadratic, and Polynomial Functions
After common factors are canceled, a zero that remains in the denominator gives a vertical asymptote; a canceled denominator factor gives a hole. For horizontal asymptotes: numerator degree smaller gives $y=0$ ; equal degrees gives the ratio of leading coefficients; numerator degree larger gives no horizontal asymptote	Rational, Radical, Exponential, and Logarithmic Functions
$f(x+h)$ shifts horizontally, $f(x)+k$ shifts vertically, $-f(x)$ reflects over the $x$ -axis, $f(-x)$ reflects over the $y$ -axis	Transformations and Piecewise Functions
An inverse is found by swapping $x$ and $y$ and solving for the new $y$ ; verify with $f(g(x))=x$ and $g(f(x))=x$	Inverse Functions
Arithmetic series: $S_n=\frac n2(a_1+a_n)$ ; geometric series: $S_n=\frac{a_1(1-r^n)}{1-r}$ for $r\ne1$ ; $\Sigma$ substitutes each index value in turn and adds the results	Sequences and Series
For $b>0$ and $b\ne1$ , $\log_b(x)=k$ is equivalent to $x=b^k$ . In the real-number setting, logarithm arguments must be positive. Where all logarithms are defined: $\log(ab)=\log a+\log b$ ; $\log\frac ab=\log a-\log b$ ; $\log(a^n)=n\log a$	Logarithm Properties and Equations

Geometry

Geometry
Relationship	Where it was taught
Interior angles of a triangle sum to $180^\circ$ ; an exterior angle equals the sum of the two remote interior angles	Lines, Angles, and Triangles
Similar figures have proportional sides and equal corresponding angles; scale factor applies directly to length and perimeter, and its square to area	Congruence and Similarity
$\sin=\frac{\text{opposite}}{\text{hypotenuse}}$ , $\cos=\frac{\text{adjacent}}{\text{hypotenuse}}$ , $\tan=\frac{\text{opposite}}{\text{adjacent}}$ ; $a^2+b^2=c^2$	Right Triangles, Trigonometry, and the Unit Circle
$(x-h)^2+(y-k)^2=r^2$ for a circle; arc length $=$ radius $\times$ central angle in radians	Circles and Conics
Area and volume of composite figures are found by adding or subtracting the areas or volumes of their pieces	Area, Volume, and Composite Figures
Distance $=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ ; midpoint $=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ . Parallel nonvertical lines have equal slopes. Perpendicular nonvertical, nonhorizontal lines have negative-reciprocal slopes; horizontal and vertical lines are the special perpendicular pair	Coordinate Geometry
$\sin^2\theta+\cos^2\theta=1$ ; Law of Sines: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ ; Law of Cosines: $c^2=a^2+b^2-2ab\cos C$	Trigonometric Identities and General Triangles
Rotation, reflection, and translation preserve size and shape; dilation by scale factor $k$ multiplies coordinates by $k$ , and multiplies area by $k^2$	Geometric Transformations
An inscribed angle is half the central angle intercepting the same arc; intersecting chords and secant/tangent segments follow power-of-a-point relationships	Circle Theorems
A conditional statement's contrapositive shares its truth value; a counterexample disproves a statement by meeting its hypothesis but not its conclusion	Proof, Reasoning, and Constructions

Statistics and Probability

Statistics and Probability
Relationship	Where it was taught
Mean is sensitive to outliers; median usually is not; $\text{IQR}=Q_3-Q_1$ ; right skew typically pulls the mean above the median, left skew below it	Center and Spread
A randomized experiment supports a causal conclusion; an observational study supports only an association	Data Collection and Study Design
Residual $=$ actual $-$ predicted; a strong correlation does not by itself establish causation; random residual scatter suggests a model fits well, a patterned residual suggests it does not	Bivariate Data and Models
$P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$ ; $P(A\text{ and }B)=P(A)\cdot P(B\mid A)$ , which reduces to $P(A)\cdot P(B)$ when $A$ and $B$ are independent	Probability and Sample Spaces
$z=\frac{x-\mu}{\sigma}$ ; about $68\%/95\%/99.7\%$ of values fall within $1/2/3$ standard deviations of the mean in a roughly normal distribution	Normal Distributions and Z-Scores
Plausible interval $=$ estimate $\pm$ margin of error; a larger random sample lowers sampling variability, but sample size alone does not fix bias or guarantee representativeness; a claim is rejected when the observed result is unusually rare under simulations built from that claim, and otherwise the decision is to fail to reject it	Introduction to Statistical Inference

Integrating Essential Skills

Integrating Essential Skills
Relationship	Where it was taught
Percent change is always measured against the original value, never the new one	Rates, Percentages, and Proportional Reasoning
An area conversion factor must be squared and a volume conversion factor must be cubed, not applied as a single multiplier	Measurement and Unit Conversion
Average speed is total distance divided by total time, not the simple average of two speeds	Averages and Medians in Context

None of the tables above replaces the teaching in the original units. If a relationship here does not immediately make sense, that is a signal to revisit the unit it came from, not to memorize the row in isolation.