A student opens the Bluebook testing app, taps into the math section, and finds a blue link near the corner of the screen labeled Reference. Tapping it reveals a small panel of shapes and equations. Relief washes over the unprepared candidate: the formulas are right there, so memorizing them was never necessary. That relief is the single most expensive feeling in the math section, because the supplied panel is a trap of false security. It hands you the area of a circle and the volume of a cone, then stays silent on the slope of a line, the coordinates of a parabola’s vertex, the distance between two points, and roughly a dozen other relationships that appear far more often than any solid the panel bothers to define. The candidate who relies only on the provided list walks into Module 2 missing the exact tools the harder items demand.
This is the complete SAT math formulas reference, built to be the page you keep open during your final review and the one you print and tape above your desk. It is organized the way the digital section actually behaves, by domain, with a one-line usage note attached to every relationship so the page reads as a working tool rather than a memory dump. You will see clearly which items the official panel already supplies, so you never waste a single minute memorizing the area of a triangle, and which high-frequency relationships the panel omits, so you never lose a question because you forgot the vertex form or the rule for an inequality sign. The governing idea of this guide is plain: knowing which relationships the supplied panel leaves out, and knowing precisely when each one applies, converts directly into speed and into points. A relationship you can recall in two seconds is a relationship you can deploy while a slower candidate is still scrolling to the corner of the screen.
The digital format rewards fluency in a way the old paper exam never did. With the built-in graphing calculator one tap away and the clock pacing roughly two questions every three minutes, the candidate who pauses to derive the discriminant or to re-reason the multiplier for a percent decrease is bleeding the one resource that cannot be replaced. Recall is speed. Speed is margin. Margin is the difference between finishing the module with time to flag and recheck, and arriving at the last two items with the timer in single digits. Everything below is engineered around that arithmetic of time. Treat it as a reference you return to, not an essay you read once, and pair it with the deliberate drilling described in the process of elimination and backsolving guide, because a memorized relationship is only worth what you can do with it under pressure.
What the Provided Panel Gives You, and Why That Is the Wrong Question
The instinct most candidates bring to the digital exam is to ask what the reference panel contains. That is the wrong question, and the framing quietly costs points. The useful question is the inverse: what does the panel leave out, and how often do the omitted relationships appear? Answer that, and your memorization effort goes exactly where the points live instead of being scattered across material the screen already hands you for free.
Start with what the panel supplies, because you should never spend a second of study time on any of it. As of the current Digital SAT, and you should always confirm this against the latest official College Board materials since panels are revised over time, the supplied reference contains a tidy set of geometric facts. It gives the area and circumference of a circle. It gives the area of a rectangle and the area of a triangle. It states the Pythagorean theorem. It supplies the side relationships for the two special right triangles, the 30-60-90 and the 45-45-90. It provides volume relationships for a rectangular box, a cylinder, a sphere, a cone, and a pyramid. It states three plain facts as well: a circle contains 360 degrees, a circle contains 2 pi radians, and the angles of a triangle sum to 180 degrees. That is essentially the whole panel. Notice what it is: almost entirely geometry and solid volumes, with a thin sliver of angle facts.
Now notice the silence. The panel says nothing about lines. It offers no slope relationship, no slope-intercept form, no point-slope form, no standard form. It offers nothing about quadratics beyond the bare Pythagorean fact: no quadratic formula, no vertex coordinates, no discriminant rule, no factored form. It offers nothing about exponents, nothing about radicals, nothing about the distance between two points, nothing about the midpoint of a segment, nothing about the equation of a circle in the coordinate plane. On the statistics side it is equally bare: no mean relationship, no probability definition, no counting principle, no conditional probability. The panel is a geometry cheat sheet wearing the costume of a complete reference, and the costume fools thousands of candidates every administration.
Where the Omitted Relationships Actually Live
Here is the part that should reorganize your study plan. The relationships the panel supplies cluster in the lowest-frequency corner of the section. Solid volume questions, the ones for which the screen hands you the cone and the sphere, appear sparingly, often only once across both modules, and they reward application rather than recall because the relationship is right there. Meanwhile the relationships the panel omits, lines and slope and quadratics and exponents and basic statistics, saturate the section. Linear relationships are the connective tissue of the algebra domain. Quadratic and exponential behavior anchors the advanced material. Percent reasoning and data interpretation run through the problem-solving and data-analysis content. The candidate who memorized the supplied volumes and skipped the slope-intercept form prepared for the rarest item and neglected the most common one.
Frame the frequencies as observed tendencies rather than fixed counts, because the exam never publishes a guaranteed distribution and the digital format adapts question by question. The durable pattern, verified across recent official practice material and worth re-checking against the current released tests, is that linear and function content dominates, data and statistics content has grown since the digital launch, and pure geometry, the panel’s specialty, occupies a smaller share than students expect. So the relationships you most need to own from memory are precisely the ones the screen refuses to give you. This guide front-loads those. The deeper treatment of each topic lives in the domain guides, and you will find the linear material developed fully in the algebra domain complete guide and the quadratic and exponential material in the advanced math domain complete guide.
The Recall-Versus-Reference Tradeoff
A subtle point separates a high scorer from a middling one. Even for relationships the panel supplies, the strongest candidates memorize the high-frequency ones anyway, because the tap-and-scroll to the corner of the screen costs time that compounds across a module. The special right triangle ratios are on the panel, yet a top scorer recognizes a 30-60-90 the instant it appears and writes the sides without opening anything. The same logic applies to the Pythagorean triples, which are not on the panel at all and which turn a multi-step computation into a single act of recognition. The principle generalizes: memorize anything you will use more than a couple of times per module, regardless of whether the screen offers it, because the panel is a safety net for the rare item, not a substitute for fluency on the common one. The right triangles and unit circle guide develops this recognition habit in full.
This guide therefore flags every relationship in two ways. It tells you whether the official panel already supplies it, so you know what is optional to memorize, and it gives you a usage note, the short statement of when you actually reach for the relationship. Read the usage notes as carefully as the relationships themselves, because a relationship you can state but cannot recognize the moment for is inert. The whole section that follows is the working reference, domain by domain.
How to Read the Reference Tables That Follow
Before the relationships themselves, a word on how the tables are built, because the structure is the point. Each domain gets a table. Every row carries three things: the relationship written in plain notation, a short note on when you use it, and a flag stating whether the official panel supplies it. The flag matters for your study plan. A row flagged as supplied is one you may safely leave to the screen if your memory is crowded, though the high-frequency supplied relationships are worth owning anyway for speed. A row flagged as omitted is non-negotiable: the screen will not help you, so the relationship must live in your memory or you will lose the item.
Because the absolute formatting rules of this series forbid bullet lists in the body, the tables are the one place the material is allowed to compress into rows, and they are the findable artifact of this page: the domain-organized reference with usage notes and supplied-versus-omitted flags. Everything outside the tables is prose, including the worked demonstrations, because narration teaches the reasoning that a bare row cannot. Read the table to find the relationship, then read the surrounding prose to learn the move.
One more orientation point. The relationships are grouped by the College Board’s own domain structure where it helps, but the grouping here is pragmatic rather than official. Algebra comes first because linear and quadratic relationships are the highest-frequency omitted material. Geometry and trigonometry come second, blending what the panel supplies with the recognition shortcuts it does not. Statistics and probability come third. A short final group collects the rules that are not relationships in the usual sense but behave like ones, the sign flip on an inequality, the meaning of absolute value as distance, the cycle of the imaginary unit, and the complementary trig identity. Each group is followed by worked micro-demonstrations, because this is a reference, and a reference earns trust by showing the relationship doing its job.
The Algebra Domain Reference
Algebra is where the supplied panel is most silent and where the points are most concentrated. The relationships below are the spine of the section. Linear behavior alone touches more items than any solid the panel defines, and the candidate who owns these cold has a recall advantage that pays off on item after item. Study this group first.
Linear Relationships, Every Form
A line can be written four ways, and each way is the right way for a particular question. The exam exploits this by phrasing items so that one form is fast and the others are slow. Knowing which form to reach for is half the skill.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Slope | m = (y2 - y1) / (x2 - x1) | You have two points and need the rate of change | Omitted |
| Slope-intercept form | y = mx + b | You know slope and y-intercept, or you want to read them off | Omitted |
| Point-slope form | y - y1 = m(x - x1) | You know one point and the slope | Omitted |
| Standard form | Ax + By = C | The item gives a line this way, or asks for integer coefficients | Omitted |
| Parallel lines | slopes equal | Two lines never meet | Omitted |
| Perpendicular lines | slopes are negative reciprocals | Two lines meet at a right angle | Omitted |
| x-intercept | set y = 0, solve for x | You need where the line crosses the horizontal axis | Omitted |
| y-intercept | set x = 0, solve for y, or read b in y = mx + b | You need where the line crosses the vertical axis | Omitted |
Every row in that table is omitted from the screen, which tells you how badly the panel underserves the most common content. The slope relationship is the workhorse. When a question gives you a table of values and asks for the rate, you compute slope between two rows and you are done. When a question describes a real situation, a phone plan with a flat fee plus a per-minute charge, a tank draining at a steady rate, the slope is the per-unit rate and the y-intercept is the starting amount. Reading those two numbers straight out of the words is the move that the interpreting coefficients and constants guide develops in depth, and it is one of the highest-frequency skills in the section.
The four forms are not redundant. Point-slope is fastest when you have a point and a slope and the question wants the equation, because you plug in and you are finished without solving for the intercept. Standard form matters when the item gives you a line that way and asks you to find an intercept quickly, since setting one variable to zero is instant in standard form. Slope-intercept is the default for reading behavior off a graph. The candidate who can move fluidly among the forms answers a linear item in seconds; the candidate who only knows one form spends those seconds converting.
Quadratic Relationships
Quadratics are the heart of the advanced material, and the panel supplies none of what you need. Memorize this group with care, because the questions here carry weight and several of them route to the harder difficulty band where the points are scarce and valuable.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Standard form | y = ax^2 + bx + c | The default form; c is the y-intercept | Omitted |
| Quadratic formula | x = (-b plus or minus the square root of (b^2 - 4ac)) / (2a) | You cannot factor and need the roots | Omitted |
| Discriminant | b^2 - 4ac | You need the number and type of real solutions | Omitted |
| Vertex form | y = a(x - h)^2 + k, vertex at (h, k) | The question asks for the maximum, minimum, or vertex | Omitted |
| Axis of symmetry | x = -b / (2a) | You need the x-coordinate of the vertex from standard form | Omitted |
| Factored form | y = a(x - r1)(x - r2) | You need the roots, which are r1 and r2 | Omitted |
| Sum of roots | r1 + r2 = -b / a | You need the roots’ sum without solving | Omitted |
| Product of roots | r1 times r2 = c / a | You need the roots’ product without solving | Omitted |
The discriminant deserves a separate mention because the exam tests it directly and the question type is fast points for anyone who has the rule memorized. The expression under the radical, b squared minus 4ac, decides everything about the real roots. If it is positive, there are two distinct real solutions. If it is exactly zero, there is one repeated real solution, which graphically means the parabola is tangent to the horizontal axis. If it is negative, there are no real solutions, only a complex conjugate pair. A question that asks for the value of a parameter that makes a quadratic have exactly one solution is really asking you to set the discriminant to zero and solve, and a candidate who recognizes that finishes in well under a minute.
The vertex form is the other recall that converts directly to points. Whenever a word problem asks for a maximum height, a minimum cost, or the moment a thrown object reaches its peak, the answer is the vertex, and vertex form reads it off without calculus. If the quadratic is in standard form, the axis of symmetry gives the x-coordinate of the vertex as negative b over 2a, and substituting that value back gives the y-coordinate. These are not on the screen, and the questions that need them are common. The hardest question types guide catalogs several disguised quadratic items where this recall is the unlock.
Exponents, Radicals, and Their Conversions
Exponent rules are pure recall with zero support from the screen, and they appear constantly inside larger problems rather than as standalone items, which makes forgetting one quietly fatal. You rarely lose a whole question to a forgotten exponent rule and notice it; you lose the question because a simplification stalled and you never reached the answer.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Product rule | x^a times x^b = x^(a+b) | Multiplying like bases | Omitted |
| Quotient rule | x^a / x^b = x^(a-b) | Dividing like bases | Omitted |
| Power rule | (x^a)^b = x^(ab) | Raising a power to a power | Omitted |
| Negative exponent | x^(-a) = 1 / x^a | Moving a factor across the fraction bar | Omitted |
| Zero exponent | x^0 = 1, for x not 0 | Any nonzero base to the zero | Omitted |
| Fractional exponent | x^(a/b) = the b-th root of x^a | Converting between radical and exponent notation | Omitted |
| Square root as exponent | the square root of x = x^(1/2) | Rewriting a radical so exponent rules apply | Omitted |
| Rationalizing | multiply by the conjugate or the matching radical | A radical sits in a denominator | Omitted |
The fractional exponent conversion is the single most useful row here, because the exam loves to write the same quantity two ways and ask which expressions are equivalent. The cube root of x squared and x to the two-thirds are the same object; recognizing that instantly collapses a question that looks hard into one that is trivial. The negative exponent rule is the second most useful, because it lets you clear a variable out of a denominator and combine terms that otherwise sit on opposite sides of a fraction bar. None of this is on the screen, and all of it is constant connective tissue. Treat the exponent group as vocabulary: you must read it without translating.
Worked Demonstrations, Algebra
A reference proves itself by showing a relationship at work, so here are three short demonstrations, narrated rather than listed.
Consider the discriminant in action. A question states that the equation 2x squared plus kx plus 8 equals 0 has exactly one real solution, and asks for the possible values of k. The single-solution condition means the discriminant equals zero. Here a is 2, b is k, and c is 8, so the discriminant is k squared minus 4 times 2 times 8, which is k squared minus 64. Setting that to zero gives k squared equals 64, so k is 8 or negative 8. The whole solution took one rule and one line of arithmetic. A candidate without the discriminant memorized would try to factor, fail, and burn ninety seconds. The principle generalizes: whenever a question constrains the number of solutions of a quadratic, the discriminant is the lever.
Consider the distance relationship, which is omitted from the panel and which the next domain table also lists because it bridges algebra and geometry. A question gives two points, (1, 2) and (4, 6), and asks for the distance between them. The relationship is the square root of the sum of the squared differences: the horizontal difference is 4 minus 1, which is 3, and the vertical difference is 6 minus 2, which is 4. Squaring and summing gives 9 plus 16, which is 25, and the square root of 25 is 5. The points form the legs of a 3-4-5 right triangle, which is exactly why the distance relationship is the Pythagorean theorem in disguise. A candidate who memorized the triples sees the answer before computing.
Consider an equivalent-expression item that turns on exponent fluency. A question asks which expression equals the square root of (16 x to the sixth). The square root of 16 is 4, and the square root of x to the sixth is x to the sixth times one-half, which is x cubed. So the expression simplifies to 4 x cubed. The move was the fractional exponent rule applied to the radical, and the candidate who reads radicals as exponents did it in one step. For drilling sets that rehearse exactly these moves under timed conditions, ReportMedic’s SAT math practice questions give you unlimited items with full worked solutions, which is the natural next action after you have the relationships in memory.
The Functions and Systems Reference
Functions and systems sit inside the algebra domain in the official structure, but they deserve their own group here because the relationships govern a question family that the supplied panel ignores entirely and that the digital format leans on heavily. A candidate who owns this group reads graph-behavior items and system-condition items at a glance rather than reasoning them out from scratch.
Function Notation, Transformations, and Graph Behavior
Function questions reward a small set of moves applied to a graph or an equation. The transformations especially are pure recall with zero support from the screen, and the exam tests them by showing a base graph and asking what happens when the equation changes.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Evaluating a function | f(a) substitutes a for the variable | A function is evaluated at a number or expression | Omitted |
| Vertical shift | f(x) + k moves the graph up by k | A constant is added outside the function | Omitted |
| Horizontal shift | f(x - h) moves the graph right by h | A constant is subtracted inside the function | Omitted |
| Vertical reflection | -f(x) flips the graph over the horizontal axis | A negative sits outside the function | Omitted |
| Horizontal reflection | f(-x) flips the graph over the vertical axis | The variable inside is negated | Omitted |
| Vertical stretch | a times f(x) stretches by factor a | A coefficient multiplies the whole function | Omitted |
| Zeros from a graph | the x-values where the graph crosses the horizontal axis | The roots, solutions, or x-intercepts are asked for | Omitted |
| Maximum or minimum from a graph | the y-value at the highest or lowest point | The extreme value of a function is asked for | Omitted |
The horizontal shift is the transformation that trips candidates most, because the direction feels backward: f of the quantity x minus 3 moves the graph to the right by 3, not to the left, even though the sign inside is negative. The cure is to ask what input value makes the inside zero, since that input is where the shifted graph sits. For f of the quantity x minus 3, the inside is zero when x is 3, so the feature that was at the origin is now at 3, confirming a rightward shift. The vertical shift behaves intuitively: adding outside moves up, subtracting outside moves down. Reflections flip across the axis named by where the negative sits, outside for the horizontal axis and inside for the vertical. These relationships are entirely omitted from the screen, and a graph-transformation item is fast points for anyone who has them automatic. The deeper development, including combined transformations, lives in the broader function material referenced throughout the advanced math domain complete guide.
The reading of zeros from a graph connects to the factored form you saw in the quadratic group. A zero of a function is an x-value where the output is zero, which graphically is a crossing of the horizontal axis, and algebraically is a root or a solution. The exam treats “zero,” “root,” “solution,” and “x-intercept” as the same idea wearing four names, and a candidate who recognizes the synonyms reads a question that switches vocabulary without losing a step. When a polynomial is given in factored form, its zeros are the values that make each factor zero, so the factored form hands you the zeros directly, which is exactly why the factored form is worth memorizing alongside vertex and standard form.
Systems, Sequences, and Variation
The conditions under which a system of equations has no solution or infinitely many solutions are a recurring high-value item, and the relationships are omitted from the panel.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| System with one solution | the lines have different slopes | Two equations cross at a single point | Omitted |
| System with no solution | same slope, different intercepts | The lines are parallel and never meet | Omitted |
| System with infinite solutions | same slope and same intercept | The two equations describe the same line | Omitted |
| Arithmetic sequence | each term adds a common difference d | Terms grow by a fixed amount | Omitted |
| Geometric sequence | each term multiplies by a common ratio r | Terms grow by a fixed factor | Omitted |
| Direct variation | y = kx, y proportional to x | Doubling x doubles y | Omitted |
| Inverse variation | y = k/x, y inversely proportional to x | Doubling x halves y | Omitted |
| Average rate of change | (change in output) / (change in input) | The average slope over an interval is asked for | Omitted |
The no-solution and infinite-solution conditions are the system items the exam favors, because they look like ordinary systems but turn on a single recognition. A system has no solution when the two equations have the same slope but different intercepts, meaning the lines are parallel, and it has infinitely many solutions when the equations have the same slope and the same intercept, meaning they are secretly the same line. A question that asks for the value of a coefficient that makes a system have no solution is asking you to match the slopes while keeping the intercepts different, and recognizing that converts a frightening item into a slope comparison. The full treatment is in the systems with no solution and infinite solutions guide, which works through the algebra step by step.
The distinction between arithmetic and geometric sequences mirrors the distinction between linear and exponential models, which is itself a tested comparison developed in the linear versus exponential models guide. An arithmetic sequence adds the same amount each step, which is linear behavior, while a geometric sequence multiplies by the same factor each step, which is exponential behavior. Direct and inverse variation are the proportional relationships behind a class of word problems: direct variation means the ratio of y to x stays constant, so the two quantities rise and fall together, while inverse variation means their product stays constant, so one rises as the other falls. None of these is on the screen, and the variation problems in particular catch candidates who assume every relationship between two quantities is direct.
Worked Demonstrations, Functions and Systems
A transformation demonstration shows the backward-feeling shift. Suppose the graph of f(x) passes through the origin, and the question asks where the graph of f of the quantity x minus 4, plus 2 passes. The inside subtraction of 4 shifts the graph right by 4, and the outside addition of 2 shifts it up by 2, so the point that was at the origin lands at (4, 2). The candidate who read the inside subtraction as a leftward move would place it at (negative 4, 2) and select a distractor. The principle: inside the function affects the horizontal direction and runs opposite to the sign, while outside affects the vertical direction and runs with the sign.
A system demonstration shows the no-solution recognition. A question gives the system 2x plus 3y equals 6 and 4x plus 6y equals 15, asking how many solutions it has. Rewriting both in slope-intercept form, or simply noticing that the second equation’s left side is exactly twice the first’s while the right sides are not in that same ratio, reveals that the lines have the same slope but different intercepts, so they are parallel and the system has no solution. A candidate who tried to solve by elimination would eliminate both variables and reach a false statement like 0 equals 3, which is the algebraic signature of no solution, but recognizing the parallel condition first is faster.
A variation demonstration shows the inverse trap. A question states that y varies inversely with x, and that y is 12 when x is 2, then asks for y when x is 8. Inverse variation means the product xy stays constant, so the constant is 12 times 2, which is 24, and when x is 8 the value of y is 24 divided by 8, which is 3. A candidate who assumed direct variation would have scaled y up with x and landed far from the answer. The principle: read the word “inversely” as a signal that the product, not the ratio, is fixed.
The Polynomial and Unit-Reasoning Reference
Two more groups round out the omitted material the section leans on. Polynomial factoring patterns turn a hard-looking expression into a solved one, and unit reasoning underlies a quiet but steady share of the problem-solving content. Neither is on the supplied panel, and both reward the same instinct: recognize the pattern, then apply a single move.
Factoring Patterns and the Factor Relationship
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Greatest common factor | pull the shared factor out front | Every term shares a common factor | Omitted |
| Difference of squares | a^2 - b^2 = (a + b)(a - b) | A subtraction of two perfect squares | Omitted |
| Perfect square trinomial | a^2 + 2ab + b^2 = (a + b)^2 | A trinomial that is a square | Omitted |
| Factoring a basic trinomial | find two numbers that multiply to c and add to b | A quadratic x^2 + bx + c must be split | Omitted |
| Factor and root link | (x - a) is a factor exactly when a is a root | You convert between factors and solutions | Omitted |
The difference of squares is the pattern the exam reuses most, because it lets a candidate collapse an expression in one step. The quantity x squared minus 9 factors instantly into the quantity x plus 3 times the quantity x minus 3, and the same pattern handles less obvious cases like x to the fourth minus 1, which is the quantity x squared plus 1 times the quantity x squared minus 1, and the second factor is itself a difference of squares. Recognizing the pattern twice in one expression is the kind of move the harder routing rewards. The factor-and-root link is the conceptual glue: a value is a root of a polynomial exactly when the corresponding linear factor divides it evenly, so a question that tells you 2 is a solution is also telling you that the quantity x minus 2 is a factor, and that equivalence lets you move between the factored picture and the solution picture without recomputing. The polynomial behavior, including zeros of higher-degree expressions, is developed in the polynomial zeros and factors guide, and the equivalent-expression rewriting that factoring supports is covered in the equivalent expressions guide.
Unit Rate, Conversion, and Proportional Reasoning
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Unit rate | divide to get the amount per single unit | A per-unit price or speed is asked for | Omitted |
| Unit conversion | multiply by a fraction equal to 1 | A quantity must change units | Omitted |
| Proportion | set two ratios equal and cross-multiply | Two quantities scale together | Omitted |
| Combined rate | add rates that act together | Two agents work or fill at the same time | Omitted |
Unit conversion is the relationship students underrate, because it looks like arithmetic rather than a technique. The reliable method is to multiply by a fraction that equals 1, arranged so the unwanted unit cancels. Converting 90 kilometers per hour into meters per second means multiplying by 1000 meters per kilometer and by 1 hour per 3600 seconds, so the kilometers and hours cancel and the meters and seconds remain, giving 25 meters per second. Setting the conversion up as canceling fractions rather than as a remembered factor protects you from inverting the conversion, which is the error the exam baits with multi-step unit problems. Proportional reasoning, the cross-multiplication of equal ratios, threads through the problem-solving content and connects to the percent material already covered, and the problem solving and data analysis guide develops the full set of rate and ratio techniques.
Worked Demonstrations, Polynomials and Units
A factoring demonstration shows the difference-of-squares collapse. A question asks for the value of the quantity 102 squared minus 98 squared without a calculator-friendly setup, and the difference-of-squares pattern turns it into the quantity 102 plus 98 times the quantity 102 minus 98, which is 200 times 4, or 800. A candidate who squared both numbers and subtracted would reach the same answer slower and with more chance of an arithmetic slip. The principle: a difference of two squares is always a product of the sum and the difference, and spotting the pattern replaces heavy computation with light computation.
A unit-conversion demonstration shows the canceling-fractions method. A question states that a printer runs at 30 pages per minute and asks how many pages it produces in 2 hours. Converting 2 hours to minutes by multiplying by 60 minutes per hour gives 120 minutes, and 30 pages per minute times 120 minutes gives 3600 pages, with the minutes canceling cleanly. A candidate who multiplied 30 by 2 directly, forgetting the hour-to-minute conversion, would land on 60 and a wrong answer. The principle: when a rate and a time use different units, convert one so the units match before multiplying, and let the canceling units confirm the setup is right.
How Adaptive Routing Changes Which Relationships Matter
The digital exam is section-adaptive, which has a direct consequence for how you weight the relationships above. The math section delivers two modules, and your performance on the first module routes you into an easier or harder second module. The relationships you most need shift between the two, and understanding the shift sharpens your priorities. The mechanics of the routing are developed in the Module 1 versus Module 2 guide, but the formula-recall consequence is worth stating here.
The first module mixes difficulty and leans on the high-frequency foundational relationships: the slope and forms of a line, basic function evaluation, percent reasoning, mean and median, and the straightforward applications of the supplied geometry. A candidate who has the first-tier algebra automatic moves through the first module quickly and accurately, which earns the harder second module where the high scores live. The relationships that carry the first module are precisely the omitted high-frequency ones this reference front-loads, which is another reason to memorize them first: they are the gate to the scoring opportunity.
The harder second module concentrates the second-tier and key-rule relationships. The disguised quadratics that need the discriminant or the vertex, the circle equations that need completing the square, the conditional probability items with a careful denominator, the absolute-value inequalities that split into compound form, the imaginary-unit powers, and the system-condition items all skew toward the harder routing. A candidate aiming above the middle band cannot rely on the supplied panel here, because the panel offers nothing for any of these. The recall that wins the second module is the second-tier and key-rule material, owned cold. This is the structural reason the supplied-versus-omitted flagging matters so much: the harder the module gets, the more it leans on relationships the screen does not provide, so the candidate’s memory is the only resource, and the hardest question types guide shows item after item where this holds.
The practical takeaway is to build recall in the order the routing rewards. Lock the first-tier algebra to automatic speed so the first module is fast and accurate, which earns the harder second module. Then own the second-tier and key-rule relationships so the harder module’s disguised items yield rather than stall. A candidate who inverts this, drilling the rare supplied volumes while shaky on slope, prepares for a module they may never see while neglecting the one that decides their score.
The Geometry and Trigonometry Domain Reference
Geometry is where the supplied panel is generous, so your job shifts. For this domain you are not memorizing everything; you are memorizing the high-frequency recognition shortcuts the panel omits and confirming you can apply the relationships it supplies. The single most valuable items here, the Pythagorean triples and the complementary trig identity, are not on the screen at all, and they are the ones that turn a slow computation into instant recall.
Coordinate Geometry, Lines and Circles in the Plane
The coordinate relationships bridge algebra and geometry, and almost all of them are omitted from the panel even though they appear regularly.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Distance between two points | the square root of ((x2 - x1)^2 + (y2 - y1)^2) | You need the length of a segment in the plane | Omitted |
| Midpoint of a segment | ((x1 + x2)/2, (y1 + y2)/2) | You need the point halfway between two points | Omitted |
| Circle, standard form | (x - h)^2 + (y - k)^2 = r^2, center (h, k), radius r | You need a circle’s center and radius and the equation is in standard form | Omitted |
| Circle, general form | x^2 + y^2 + Dx + Ey + F = 0 | The equation must be completed to the square to find center and radius | Omitted |
| Recognizing a circle | equal coefficients on x^2 and y^2 | You must identify that an equation is a circle at all | Omitted |
The distance and midpoint relationships are high-frequency and entirely absent from the screen, so memorize both. The circle equation is the more dangerous omission, because the exam often disguises a circle in general form, with the squared terms expanded, and the candidate who does not recognize the disguise stares at it as though it were something exotic. The recognition cue is simple and worth stating as a citable rule: when an equation has an x-squared term and a y-squared term with the same coefficient, it is a circle, and you complete the square in both variables to recover the center and radius. The full treatment, including the completing-the-square steps, lives in the circles, arcs, sectors, and radians guide.
Right Triangles, the Triples, and the Special Triangles
This is the highest-leverage geometry recall in the section, and the panel supplies only part of it.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Pythagorean theorem | a^2 + b^2 = c^2 | Any right triangle, finding a third side | Supplied |
| Common triples | 3-4-5, 5-12-13, 8-15-17, 7-24-25 and their multiples | A right triangle’s sides match a triple; recognize instead of computing | Omitted |
| 30-60-90 ratio | sides in ratio 1 to the square root of 3 to 2 | The triangle has a 30 and a 60 degree angle | Supplied |
| 45-45-90 ratio | sides in ratio 1 to 1 to the square root of 2 | The triangle is right and isosceles | Supplied |
| Similar triangles | corresponding sides in equal ratio | Two triangles share all three angle measures | Omitted |
The triples are the prize, and they are not on the screen. A right triangle with legs 6 and 8 has a hypotenuse of 10, because 6-8-10 is the 3-4-5 triple doubled, and recognizing that takes a second while applying the Pythagorean theorem takes thirty. Memorize the four common triples and the fact that any multiple of a triple is also a triple. The special triangle ratios are supplied by the panel, which means they are optional to memorize, but the same time argument applies: a candidate who recognizes a 45-45-90 the instant the figure shows two equal legs writes the hypotenuse without scrolling. Similar triangles, omitted from the screen, underlie a whole class of problems where a smaller triangle sits inside a larger one and proportions of corresponding sides solve for an unknown.
Trigonometry, the Compact Set the Exam Actually Uses
The trig the exam tests is narrow, and one identity inside it is the most reliably tested trig fact on the whole section.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| SOH CAH TOA | sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent | A right triangle and you need a side or an angle ratio | Omitted |
| Complementary identity | sin(x) = cos(90 - x) | The question pairs the sine of one acute angle with the cosine of the other | Omitted |
| Radian-degree conversion | multiply by pi/180 for degrees to radians; by 180/pi for the reverse | The item mixes radian and degree measure | Omitted |
| Common angle values | the sine and cosine of 0, 30, 45, 60, 90 degrees | A unit-circle value is needed for a standard angle | Omitted |
The complementary identity is the trig fact to own absolutely. In a right triangle the two acute angles sum to 90 degrees, so the sine of one equals the cosine of the other, written as the sine of x equals the cosine of 90 minus x. The exam tests this directly with items like “if the sine of A is four-fifths, find the cosine of B” where A and B are the two acute angles of a right triangle, and the answer is simply four-fifths because B is the complement of A. A candidate who has the identity answers instantly; a candidate without it tries to reconstruct the triangle and may not finish. The full development, including the unit-circle angle values, is in the right triangles and unit circle guide.
Angles, Parallel Lines, and Polygons
Angle reasoning rewards a compact rule set applied in sequence, and the panel supplies only the triangle sum.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Triangle angle sum | three angles sum to 180 degrees | Any triangle | Supplied |
| Straight angle | adjacent angles on a line sum to 180 degrees | Angles share a vertex on a straight line | Omitted |
| Vertical angles | opposite angles at an intersection are equal | Two lines cross | Omitted |
| Transversal, corresponding and alternate | corresponding equal, alternate interior equal, same-side interior supplementary | A line crosses two parallel lines | Omitted |
| Polygon interior sum | (n - 2) times 180 degrees | You need the sum of a polygon’s interior angles | Omitted |
| Regular polygon interior angle | (n - 2) times 180, divided by n | Each angle of a regular n-sided polygon | Omitted |
| Exterior angle sum | always 360 degrees | The exterior angles of any polygon | Omitted |
The transversal relationships are the workhorse, since the parallel-lines-cut-by-a-line setup appears on nearly every administration. The trap the exam plants is the confusion between alternate interior angles, which are equal, and same-side interior angles, which are supplementary, and the angles, parallel lines, and polygons guide contrasts the two on a single figure so the distinction sticks.
Worked Demonstrations, Geometry
A demonstration of the complementary identity makes the recall concrete. A question states that in right triangle ABC the right angle is at C, and the sine of A is 0.6, then asks for the cosine of B. Because A and B are the two acute angles, they are complementary, so the cosine of B equals the sine of A, which is 0.6. No triangle needs to be drawn. The principle: in a right triangle, a sine and the cosine of the other acute angle are always equal, so the question is testing whether you know the relationship, not whether you can compute.
A demonstration of the disguised circle shows the recognition cue at work. A question gives x squared plus y squared minus 6x plus 8y plus 9 equals 0 and asks for the radius. The equal coefficients on the squared terms flag a circle. Completing the square on the x terms turns x squared minus 6x into the quantity x minus 3, squared, minus 9, and completing the square on the y terms turns y squared plus 8y into the quantity y plus 4, squared, minus 16. Substituting back and moving constants gives the quantity x minus 3 squared plus the quantity y plus 4 squared equals 16, so the radius is the square root of 16, which is 4. The recognition that the equation was a circle at all was the entire difficulty; the algebra after that is routine.
A demonstration of the triple shows the time dividend. A figure shows a right triangle with one leg 9 and a hypotenuse 15, asking for the other leg. Rather than computing 15 squared minus 9 squared, recognize 9-15 as three times 3-5, so the triangle is the 3-4-5 triple scaled by 3, making the missing leg 12. Recognition replaced computation, and across a full module those saved seconds accumulate into the buffer that lets you recheck flagged items.
The Statistics and Probability Domain Reference
The data and statistics content has grown since the digital exam launched, and the panel supplies none of the relationships you need. This domain rewards careful reading as much as recall, but the core relationships still have to live in memory.
Center, Spread, and the Reading of Data
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Mean | sum of values, divided by the count | The arithmetic average is asked for | Omitted |
| Median | the middle value when ordered | The center is asked for and outliers may distort the mean | Omitted |
| Mode | the most frequent value | The most common value is asked for | Omitted |
| Range | largest value minus smallest value | A simple measure of spread is asked for | Omitted |
| Weighted mean | sum of (value times weight), divided by sum of weights | Groups of different sizes are combined | Omitted |
| Effect of an added value | recompute the mean with the new sum and count | A value is added or removed and the mean changes | Omitted |
The exam tests the relationship between mean and median more than it tests either in isolation. When a data set is skewed, the mean is pulled toward the long tail while the median holds steady, so a question that adds a large outlier is really asking you to predict that the mean rises while the median barely moves. The standard-deviation comparison, treated fully in the standard deviation, mean, and median guide, is conceptual rather than computational: you compare which of two sets has values clustered more tightly around the center, since the more spread-out set has the larger standard deviation. You will never compute a standard deviation by hand on this exam, but you must reason about it.
Probability and Counting
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Simple probability | favorable outcomes, divided by total outcomes | A single event with equally likely outcomes | Omitted |
| Probability from a two-way table | the cell count, divided by the relevant row or column total | A frequency table and a probability question | Omitted |
| Conditional probability | probability of A given B = outcomes in both, divided by outcomes in B | The question restricts attention to a subgroup | Omitted |
| Counting principle | multiply the number of choices at each independent stage | The total number of arrangements or selections is asked for | Omitted |
| Complement | probability of not A = 1 minus the probability of A | It is easier to count the unwanted outcomes | Omitted |
Conditional probability from a two-way table is the form the exam favors, and it is where careless candidates lose points by dividing by the wrong total. The phrase “given that” is the signal: it tells you to restrict the denominator to the subgroup named after it, not the whole population. A worked demonstration follows below. The full treatment of frequency tables is in the two-way tables and probability guide.
Percent, the Multiplier, and Change
Percent reasoning runs through the entire problem-solving and data-analysis content, and the multiplier method, while not a single panel relationship, is the recall that converts the most arithmetic into the least effort.
| Relationship | Notation | Use this when | On the panel |
|---|---|---|---|
| Percent of a number | the percent as a decimal, times the number | A part of a whole is asked for | Omitted |
| Percent increase multiplier | multiply by (1 + r) | A quantity grows by rate r | Omitted |
| Percent decrease multiplier | multiply by (1 - r) | A quantity shrinks by rate r | Omitted |
| Percent change | (new minus old), divided by old, times 100 | The percent by which a value changed | Omitted |
| Successive percent change | multiply the multipliers in sequence | Two or more changes apply one after another | Omitted |
The multiplier method is the rule worth internalizing. A 20 percent increase is multiplication by 1.2, and a 20 percent decrease is multiplication by 0.8. Successive changes multiply: a 20 percent rise followed by a 20 percent fall is 1.2 times 0.8, which is 0.96, a net 4 percent loss, not a return to the start. The exam plants exactly that trap, expecting candidates to assume the changes cancel. The candidate who reasons with multipliers avoids it automatically.
Worked Demonstrations, Statistics and Probability
A conditional probability demonstration makes the denominator trap vivid. Suppose a two-way table sorts 100 students by whether they take a language class and whether they play a sport. Say 40 students play a sport, and of those 40, 30 take a language. The question asks for the probability that a randomly chosen student takes a language, given that the student plays a sport. The phrase “given that the student plays a sport” restricts the universe to the 40 athletes, so the denominator is 40, not 100. The answer is 30 over 40, which is three-quarters. A candidate who divides 30 by 100 has answered a different question and lost the point. The principle: the condition sets the denominator.
A percent demonstration shows the multiplier saving time. A price rises 10 percent, then the higher price is discounted 30 percent, and the question asks the net percent change from the original. Multiplying the multipliers, 1.10 times 0.70 gives 0.77, which is a net 23 percent decrease. The candidate who tried to add the percents, treating a 10 percent rise and a 30 percent fall as a net 20 percent fall, lands on the wrong answer the exam offers as a distractor. Percent reasoning, developed further in the problem solving and data analysis guide, rewards the multiplier habit on item after item.
A mean demonstration shows the added-value reasoning. A set of five numbers has a mean of 12, so the sum is 60. A sixth number, 24, is added. The new sum is 84 across six values, so the new mean is 14. The relationship you used was that the mean times the count equals the sum, run in both directions, and that two-way fluency is what separates a quick solve from a stall.
A weighted-mean demonstration shows why a plain average sometimes misleads. Suppose one class of 30 students averages 80 on a test and another class of 20 students averages 90, and the question asks for the combined average across all 50 students. A candidate who averages 80 and 90 to get 85 has ignored the different class sizes and chosen a distractor. The correct move multiplies each average by its group size, giving 30 times 80, which is 2400, and 20 times 90, which is 1800, then divides the combined total of 4200 by the 50 students, landing on 84. The larger class pulls the combined average toward its own value, which is the entire point of a weighted mean. The principle: when groups of different sizes are combined, weight each average by its size before dividing, because a simple average of averages silently assumes the groups are equal.
The Key Rules That Behave Like Relationships
A handful of facts are not relationships in the sense of an equation you plug into, but they govern whole question types and the exam tests them as if they were relationships. None is on the panel, and forgetting any one of them produces a specific, predictable error.
| Rule | Statement | Use this when | On the panel |
|---|---|---|---|
| Inequality sign flip | reverse the inequality when multiplying or dividing by a negative | You solve an inequality and a negative coefficient appears | Omitted |
| Absolute value as distance | the absolute value of x is the distance of x from zero | An equation or inequality involves an absolute value | Omitted |
| Absolute value to compound | the absolute value of an expression less than k becomes a double inequality | You must split an absolute-value inequality | Omitted |
| Imaginary unit cycle | i, then negative 1, then negative i, then 1, repeating every four powers | A power of the imaginary unit must be simplified | Omitted |
| Complex conjugate | multiply by the conjugate to clear i from a denominator | A complex number sits in a denominator | Omitted |
| Function notation | f(a) means substitute a for the variable | A function is evaluated at a value or another function | Omitted |
| Composition | f(g(x)) means evaluate g first, then f | Two functions are nested | Omitted |
The inequality sign flip is the most common silent error in the entire section, because the algebra looks identical to solving an equation right up to the moment a negative coefficient demands the reversal, and a candidate in a hurry forgets it and inverts the whole answer set. The absolute-value-to-compound conversion is the rule that unlocks a question type some candidates never crack: the absolute value of an expression being less than a constant becomes a sandwiched double inequality, while the absolute value being greater than a constant splits into two separate inequalities joined by “or.” The imaginary unit cycle reduces any power of i to one of four values by taking the exponent’s remainder when divided by 4, which turns a frightening-looking power into a one-step lookup. Function notation and composition are not difficult, but they are tested constantly, and the only error candidates make is evaluating the outer function first instead of the inner one. Work the inner function, then feed its output to the outer.
Worked Demonstrations, Key Rules
An inequality demonstration shows the flip. Solving negative 3x plus 5 greater than 11, subtract 5 to get negative 3x greater than 6, then divide both sides by negative 3, and the sign reverses, giving x less than negative 2. A candidate who forgot to flip writes x greater than negative 2 and selects the wrong half of the number line. The rule is mechanical, but only if it is automatic.
An imaginary unit demonstration shows the cycle. To simplify i to the 23rd power, divide 23 by 4 to get a remainder of 3, and i to the third power is negative i. The full power collapsed to a single value because the cycle repeats every four steps. The complex-number material, including division by the conjugate, is developed in the broader treatment of advanced topics, and the advanced math domain complete guide carries it further.
A composition demonstration shows the order. If f(x) is 2x plus 1 and g(x) is x squared, then f(g(3)) means evaluate g at 3 first, getting 9, then evaluate f at 9, getting 19. A candidate who reversed the order would compute f(3) first and land on the wrong result. Inside out is the rule.
Which Relationships to Memorize First, and Why
Owning every relationship above is the goal, but a study plan needs an order, because limited time spent on the rarest item is time stolen from the most common one. The priority is set by frequency and by whether the screen helps, and the logic runs straight from the supplied-versus-omitted flags you have been reading.
The first tier is the omitted, high-frequency algebra: the slope relationship and the four forms of a line, the quadratic formula and the discriminant and the vertex, and the full exponent rule set. These appear in the largest share of items, the screen supplies none of them, and a gap here costs points across the whole section rather than on one isolated question. If your review time is short, this tier is where it goes, and the broader SAT math preparation section guide sequences a full plan around exactly this priority.
The second tier is the omitted geometry and statistics recall that the panel ignores: the Pythagorean triples, the complementary trig identity, the distance and midpoint relationships, the circle equation and its recognition cue, the conditional probability denominator rule, and the percent multipliers. These are individually high-value, because each one converts a slow computation or a careless error into instant recall, and the questions that need them are common enough that the payoff is reliable.
The third tier is the supplied geometry you may safely lean on the screen for if your memory is full: the solid volumes, the area relationships, the special triangle ratios. Memorizing these still buys speed, and a candidate aiming above the middle band should, but if you are triaging, this is the tier the panel covers, so it is the tier you can defer. The score 1500 plus guide makes the case that top scorers memorize even the supplied relationships for the time advantage, while a candidate fighting for a mid-band score gets more return from the first two tiers.
The fourth and final consideration is the key rules group, which sits outside the frequency tiering because it is small and because each rule governs a whole question type. The inequality sign flip, the absolute-value conversions, the imaginary unit cycle, and function composition are quick to learn and disproportionately costly to forget, so fold them into your first review pass regardless of where the topics fall in the frequency picture.
How to Use This Reference in Your Final Two Weeks
A reference earns its keep in the last stretch before the exam, when new learning has mostly stopped and consolidation is the work. The relationships above are not meant to be read once; they are meant to be tested against your own recall until the recall is automatic. The most effective final-review use is active rather than passive: cover the notation column, read only the usage note, and produce the relationship from memory, then check. The relationships you miss become your short list, and you cycle that short list daily until it shrinks to nothing.
Pair the recall drilling with applied practice, because a relationship you can recite is not yet a relationship you can deploy under a running clock. After a recall pass, work a timed set so the relationships fire inside real items rather than in isolation, and the immediate worked-solution feedback from ReportMedic’s math practice tool turns each missed item into a diagnosis: did you not know the relationship, or did you know it and apply it wrong. Those are different failures with different fixes, and the practice tool’s full solutions let you tell them apart. The structured countdown for this period, day by day, is laid out in the last two weeks review checklist, which slots formula recall into a taper that leaves you sharp rather than exhausted on exam morning.
One caution about the final stretch: do not try to add the supplied panel relationships to your memory in the last days if they are not already there, because the screen has them and your scarce review time is better spent locking down the omitted high-frequency tier. The whole point of the supplied-versus-omitted flagging is to let you spend the final hours where they matter. A candidate who, on the night before, drills the cone volume the screen already provides while shaky on the slope relationship has inverted the priorities this reference exists to correct.
A final note on the digital interface itself. The relationships live in your memory, but the built-in graphing tool can verify many of them, and the strongest candidates use the tool as a check rather than a crutch. Graphing a quadratic confirms the vertex you computed; graphing a circle from its equation confirms the center and radius you found by completing the square. The Desmos calculator strategy guide develops this verification habit, and the pairing of memorized recall with on-screen confirmation is how a careful candidate guards against the arithmetic slips catalogued in the careless mistakes guide. For US candidates weighing the two main admissions tests, the relationship coverage here maps closely onto the math content of the other exam, and the ACT versus SAT comparison lays out where the formula demands diverge.
Common Formula-Recall Errors and the Cure for Each
Knowing a relationship and deploying it correctly under a clock are different skills, and the gap between them is where a predictable set of recall errors lives. Each error below is specific, each is common, and each has a concrete cure that costs nothing but attention. Folding these cures into your practice is often worth more than learning a new relationship, because they recover points you are already losing on material you already know.
The first error is trusting the supplied panel to be complete, which this entire reference exists to correct. The cure is the supplied-versus-omitted flagging: before the exam, you should be able to state without hesitation which high-frequency relationships the screen omits, because that knowledge tells you exactly what your memory must carry. A candidate who walks in believing the panel has the slope relationship will waste seconds discovering it does not, at the worst possible moment.
The second error is the inequality sign that does not get flipped. The algebra of solving an inequality looks identical to solving an equation right up to the step where a negative coefficient is divided out, and a candidate moving fast forgets to reverse the sign and inverts the entire answer set. The cure is a mechanical habit: the instant you divide or multiply an inequality by a negative, flip the sign before writing the next line, every time, with no exception, so the action becomes automatic rather than a thing you must remember to check.
The third error is the horizontal transformation read in the wrong direction. The function f of the quantity x minus 3 shifts right, not left, and the negative sign inside misleads candidates into the opposite move. The cure is the zero test described earlier: ask what input makes the inside zero, and that input is where the shifted feature sits, which resolves the direction without relying on a half-remembered rule.
The fourth error is the conditional probability denominator. A question that says “given that” restricts the universe to the named subgroup, so the denominator is the subgroup total, not the whole population, and a candidate who divides by the population total answers a different question. The cure is to underline the “given that” phrase and write the subgroup total as the denominator before doing anything else, so the restriction is locked in before the arithmetic begins.
The fifth error is treating successive percent changes as additive. A 20 percent rise followed by a 20 percent fall is not a wash; it is a 4 percent net loss, because the multipliers 1.2 and 0.8 give 0.96. The cure is the multiplier habit: convert every percent change to a multiplier and multiply them in sequence, never adding or subtracting the percentages, so the compounding is handled correctly by the arithmetic itself.
The sixth error is evaluating a composition from the outside in. The notation f of g of x means evaluate g first and feed its output to f, but the left-to-right reading of the symbols tempts candidates to start with f. The cure is to read composition as a pipeline that flows from the innermost function outward, working the inside completely before touching the outside.
The seventh error is missing the disguised circle. An equation with expanded squared terms is still a circle if the x-squared and y-squared coefficients match, but a candidate who does not recognize the disguise stalls. The cure is the recognition cue stated as a habit: whenever you see both a squared x term and a squared y term, check whether their coefficients match, and if they do, prepare to complete the square. These error cures, together with the broader catalog of slips in the careless mistakes guide, are the difference between a candidate’s potential score and the score they actually post, and the unlimited timed sets at ReportMedic are where you rehearse the cures until they hold under pressure.
The Most Overlooked Relationship, and the Misconception Behind It
The misconception this guide exists to correct is the belief that the supplied panel is enough. It is the most common formula-related error candidates make, and it is not a small one, because the panel is generous in a low-frequency domain and silent in the high-frequency ones, so trusting it inverts the candidate’s priorities without their noticing. The fix is the flagging you now have: memorize the omitted high-frequency relationships, lean on the screen for the supplied low-frequency ones, and never confuse the two. A useful way to test whether you have internalized this is to try, from memory, to list the relationships the screen omits, because a candidate who can produce that list on demand has already organized their preparation around the right priorities, while a candidate who cannot is likely still studying the wrong tier. The list is long and the omissions are the common ones, which is the whole uncomfortable truth of the supplied panel.
If a single overlooked relationship had to be named, it would be the vertex form of a quadratic, with the discriminant a close second. The vertex form is overlooked because students assume the quadratic formula covers all quadratic needs, when in fact a large share of quadratic questions ask not for the roots but for the maximum or minimum, which is the vertex, and the quadratic formula does not give you that directly while vertex form does. The discriminant is overlooked because it never appears as a relationship students are told to memorize, only as a quantity buried inside the quadratic formula, so the question type that asks for the number of solutions catches them flat. Both are omitted from the screen. Both are high-frequency. Both convert a hard-looking item into a one-line solve. If your final review fixes nothing else, fix those two, and then widen out to the rest of the first-tier algebra. The verdict of this reference is unambiguous: study the omitted relationships first, in the order this guide tiers them, because that order is where your points actually are.
Frequently Asked Questions
Which math formulas are not on the SAT reference sheet?
The supplied panel leaves out far more than it includes, and the omissions are the high-frequency relationships. It gives you no slope relationship and none of the four forms of a line, no quadratic formula, no discriminant, no vertex form, no exponent or radical rules, no distance or midpoint relationship, and no coordinate-plane circle equation. On the statistics side it omits the mean, simple and conditional probability, the counting principle, and the percent multipliers. It also omits the key rules that govern whole question types, such as the inequality sign flip and the imaginary unit cycle. Because these omitted relationships appear in the largest share of items while the panel’s supplied content clusters in low-frequency geometry, the practical takeaway is that the things you most need to memorize are precisely the things the screen refuses to give you. Build your memorization plan around the omissions, not the inclusions.
What formulas does the SAT reference sheet already provide?
As of the current Digital SAT, and you should confirm against the latest official materials since the panel is occasionally revised, the supplied reference is almost entirely geometry. It provides the area and circumference of a circle, the area of a rectangle and a triangle, the Pythagorean theorem, the side ratios for the 30-60-90 and 45-45-90 special triangles, and volume relationships for a rectangular box, a cylinder, a sphere, a cone, and a pyramid. It also states three facts: a circle has 360 degrees, a circle has 2 pi radians, and a triangle’s angles sum to 180 degrees. Notice the pattern. Everything supplied is geometry or a solid volume, and those topics occupy a smaller share of the section than students expect. You should never spend study time memorizing the supplied content, though the highest-frequency supplied items, the special triangles especially, are worth owning anyway for the speed of instant recognition.
What is the vertex formula and when do I use it?
A quadratic in vertex form is written as y equals a times the quantity x minus h, squared, plus k, and the vertex sits at the point (h, k). You use it whenever a question asks for a maximum, a minimum, or the turning point of a parabola, which is a common request disguised as a word problem about peak height, minimum cost, or maximum profit. If the quadratic is given in standard form instead, the x-coordinate of the vertex is negative b divided by 2a, the axis of symmetry, and substituting that value back gives the y-coordinate. The vertex form is not on the supplied panel, and it is one of the most overlooked high-value relationships in the section, because students assume the quadratic formula handles every quadratic need when in fact the quadratic formula gives roots, not the vertex. Memorize both vertex form and the axis-of-symmetry shortcut, because together they answer the maximum-and-minimum questions the exam asks repeatedly.
What is the distance formula on the SAT?
The distance between two points is the square root of the sum of the squared differences in their coordinates: the square root of the quantity x2 minus x1, squared, plus the quantity y2 minus y1, squared. It is not on the supplied panel, yet it appears regularly, so memorize it. The relationship is really the Pythagorean theorem applied to the horizontal and vertical legs between the two points, which is why a candidate who knows the common triples can often skip the computation entirely. If the horizontal difference is 3 and the vertical difference is 4, the distance is 5 without any arithmetic, because 3-4-5 is the most common triple. Use the distance relationship whenever a question asks for the length of a segment drawn in the coordinate plane, the perimeter of a figure with plotted vertices, or whether a point lies inside or outside a circle, since that last question compares a point’s distance from the center against the radius.
What is the midpoint formula and when is it tested?
The midpoint of a segment is the average of the endpoints’ coordinates, written as the point with x-coordinate equal to the average of the two x-values and y-coordinate equal to the average of the two y-values. The supplied panel omits it. You reach for it whenever a question asks for the point halfway between two given points, the center of a circle whose diameter’s endpoints are given, since the center is the midpoint of any diameter, or a missing endpoint when the midpoint and one endpoint are known. That last variant is the one the exam favors as a slightly harder item: it gives you the midpoint and one endpoint and asks for the other, which you solve by reversing the averaging, doubling the midpoint coordinate and subtracting the known endpoint. Memorize the midpoint relationship alongside the distance relationship, because the two appear together often and neither is on the screen.
What are the exponent rules I need for the SAT?
You need the full standard set, and none of it is on the supplied panel. Multiplying like bases adds the exponents, dividing like bases subtracts them, and raising a power to a power multiplies them. A negative exponent moves the factor across the fraction bar, so x to the negative a equals one over x to the a. Any nonzero base to the zero power is 1. The most useful rule for this exam is the fractional exponent: x to the a over b equals the b-th root of x to the a, which lets you convert any radical into exponent notation so the other rules apply. The square root of x is x to the one-half. Exponent rules rarely form a standalone question; they appear inside larger problems as the connective tissue that lets a simplification go through, so a forgotten rule does not cost one question, it stalls the simplification and costs whatever question depended on it. Treat them as automatic vocabulary.
How do I read the discriminant to classify roots?
The discriminant is the expression b squared minus 4ac, the part of the quadratic formula that sits under the radical, and its sign tells you everything about the real roots without solving. If the discriminant is positive, the quadratic has two distinct real solutions and its graph crosses the horizontal axis twice. If the discriminant is exactly zero, there is one repeated real solution and the graph is tangent to the axis, touching it at a single point. If the discriminant is negative, there are no real solutions, only a conjugate pair of complex ones, and the graph never touches the axis. The exam tests this directly with questions that ask for the value of a parameter making a quadratic have exactly one solution, which means setting the discriminant to zero and solving. The discriminant is omitted from the supplied panel and is one of the most overlooked high-value relationships, so memorize the three-case rule and recognize the question type on sight.
Which formulas should I memorize for speed even if provided?
The supplied panel is a safety net for rare items, not a substitute for fluency on common ones, so the strongest candidates memorize the high-frequency supplied relationships anyway. The clearest examples are the two special right triangles. The 30-60-90 and 45-45-90 ratios are on the screen, but a top scorer recognizes them instantly from a figure and writes the sides without tapping into the panel, saving the seconds that compound across a module. The Pythagorean theorem is supplied, yet the triples built on it, 3-4-5 and its relatives, are not, and memorizing those triples turns the theorem into instant recognition. The triangle angle sum is supplied and worth owning because angle-chasing items use it repeatedly. The rule is simple: memorize anything you will use more than a couple of times per module, regardless of whether the screen offers it, because reaching for the panel costs time you would rather spend on the harder items at the end.
What is the counting principle on the SAT?
The fundamental counting principle says that if a process happens in independent stages, the total number of outcomes is the product of the number of choices at each stage. If you choose a shirt from 4 options and a pair of pants from 3, you have 4 times 3, which is 12 outfits. The exam uses this for arrangement and selection questions, sometimes dressed up as a menu with several courses, a license plate with several positions, or a committee chosen in steps. The principle is not on the supplied panel. The trap to watch is whether the stages are truly independent and whether order matters or repetition is allowed, since those conditions change the count. For most exam items the straightforward multiplication applies, but read carefully for phrases like “without repetition,” which reduce the choices available at later stages. Memorize the multiply-the-stages rule and slow down just enough to confirm the stages are independent before applying it.
How do I convert between point-slope and slope-intercept form?
The two forms describe the same line, and converting is a matter of algebra rather than a separate relationship to memorize. Point-slope form is y minus y1 equals m times the quantity x minus x1, which you write directly when you have one point and the slope. To convert it to slope-intercept form, y equals mx plus b, distribute the slope across the parenthesis and then move the constant to isolate y. For example, starting from y minus 2 equals 3 times the quantity x minus 1, distribute to get y minus 2 equals 3x minus 3, then add 2 to both sides to get y equals 3x minus 1, which is slope-intercept form with a y-intercept of negative 1. The reverse conversion is rarely needed, since slope-intercept is usually the destination. Knowing both forms lets you start from whatever the question gives you, a point and a slope or two points, and arrive at the form the answer choices use without wasted steps.
Is the quadratic formula on the SAT reference sheet?
No, the quadratic formula is not on the supplied panel, which surprises many candidates because it is the single most famous relationship in school algebra. You must memorize it: x equals negative b, plus or minus the square root of the quantity b squared minus 4ac, all divided by 2a. You use it to find the roots of any quadratic written as ax squared plus bx plus c equals 0 when factoring is not obvious. Because it is omitted from the screen and because quadratics are high-frequency on this exam, the quadratic formula belongs in your first tier of memorization. A useful companion fact is that the expression under the radical is the discriminant, so once the formula is memorized you get the root-classification rule for free. On the digital exam you can often confirm a root by graphing, but you cannot graph your way out of a question that gives the quadratic only symbolically, so the formula has to be in memory.
What is the standard form of a line on the SAT?
Standard form of a line is Ax plus By equals C, where A, B, and C are typically integers. It is omitted from the supplied panel. Its advantage shows up on intercept questions, because setting y to zero and solving for x gives the x-intercept in one step, and setting x to zero gives the y-intercept just as fast, which is quicker in standard form than rearranging into slope-intercept first. The exam sometimes gives a line in standard form and asks for a coefficient that produces a particular slope or a particular intercept, in which case you either rearrange to slope-intercept, where the slope is negative A over B, or work directly. Knowing standard form alongside slope-intercept and point-slope means you can read or build a line in whatever shape the question presents, rather than committing to one form and converting everything into it, which wastes the time the digital clock does not give you.
Which formulas matter most for a final review?
Concentrate your final review on the omitted, high-frequency relationships, because those are where the screen does not help and where most points live. The top priority is the algebra: the slope relationship and the four forms of a line, the quadratic formula, the discriminant, the vertex form, and the full exponent rule set. The second priority is the high-value omitted geometry and statistics recall: the Pythagorean triples, the complementary trig identity, the distance and midpoint relationships, the circle equation and its recognition cue, the conditional probability denominator rule, and the percent multipliers. Fold in the key rules that govern whole question types, especially the inequality sign flip and the absolute-value conversions, since they are quick to learn and costly to forget. Do not spend final-review hours on the supplied panel content, the solid volumes and area relationships, because the screen has those and your scarce time is better spent locking the omissions into automatic recall.
How should I use a formula sheet during the last week?
Use it actively, not passively, because reading a reference and recalling from it are different skills and only the second one helps on exam day. Cover the notation and read only the usage note, then produce the relationship from memory and check yourself. The ones you miss become a short list you cycle daily until it shrinks to nothing. Pair each recall pass with a timed practice set so the relationships fire inside real items under a clock rather than in isolation, since a relationship you can recite calmly may still desert you under pressure. After practice, separate two kinds of failure: not knowing a relationship, which recall drilling fixes, and knowing it but applying it wrong, which careful worked-solution review fixes. Avoid cramming the supplied panel content in the last week, because the screen provides it. Taper the volume as exam day approaches so you arrive sharp rather than depleted, and trust that automatic recall, not last-minute additions, is what carries you through the section.
What is the most overlooked formula on the SAT?
The vertex form of a quadratic is the most overlooked, with the discriminant close behind. Vertex form, y equals a times the quantity x minus h squared plus k with the vertex at (h, k), is overlooked because students assume the quadratic formula covers every quadratic need, when in fact a large share of quadratic questions ask for a maximum or minimum, which is the vertex, and the quadratic formula gives roots rather than the turning point. The discriminant is overlooked because it is never presented as a relationship to memorize on its own, only as a piece buried inside the quadratic formula, so the question type asking for the number of solutions catches unprepared candidates. Both are omitted from the supplied panel, both are high-frequency, and both turn a hard-looking item into a one-line solve. If your review fixes only two relationships, fix these, then widen out to the rest of the first-tier algebra where the bulk of your points wait.
