SAT Last-minute CRAM SheetSAT Last-minute CRAM Sheet

LINES & SYSTEMS

Slope m = (y2−y1)/(x2−x1) · y = mx + b · ax + by = c has slope −a/b

Parallel = same slope. Perpendicular = negative reciprocal (m2 = −1/m1).

No solution: same slope, different intercept. Infinite solutions: identical equations (all coefficients proportional). "Rate of change," "per," "each" → that's the slope. Starting value / flat fee → that's b.

QUADRATICS

Standard ax2+bx+c · Vertex a(x−h)2+k → vertex (h,k) · Factored a(x−r1)(x−r2) → roots

Vertex/axis of symmetry: x = −b/2a

x = [−b ± √(b2−4ac)] / 2a

Discriminant b2−4ac: >0 → 2 real solutions, =0 → 1, <0 → none

Sum of roots = −b/a | Product of roots = c/a

Zeros = roots = solutions = x-intercepts = factors. Same thing, five names.

EXPONENTS & RADICALS

xa·xb = xa+b · xa/xb = xa−b · (xa)b = xab

x−a = 1/xa · x0 = 1 · x1/n = the n-th root of x · xm/n = (n-th root of x)m

Same base on both sides → set the exponents equal.

PERCENT, RATIO, GROWTH

% change = (new − old) / old × 100 (always divide by the original)

Up p% → multiply by (1 + p/100). Down p% → multiply by (1 − p/100).

Exponential: y = a(1 ± r)t. Doubling/halving every k periods: y = a·bt/k.

Linear adds the same amount each time; exponential multiplies by the same factor.

Ratios: set up a proportion and cross-multiply. Keep units in the same spot on both sides.

FUNCTIONS & GRAPHS

f(x)+k → up k | f(x)−k → down k

f(x+k) → LEFT k | f(x−k) → RIGHT k (inside the parentheses is backwards)

−f(x) flips over the x-axis; f(−x) flips over the y-axis. f(a) = b just means the point (a, b) is on the graph.

GEOMETRY & TRIG

45-45-90: x, x, x√2 | 30-60-90: x, x√3, 2x

Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25 (and multiples)

Circle: (x−h)2 + (y−k)2 = r2. If it's not in this form, complete the square.

Arc length = (θ/360)·2πr | Sector area = (θ/360)·πr2 | radians = degrees × π/180

Similar figures: sides scale by k, areas by k2, volumes by k3. SOH CAH TOA. Also: sin(x°) = cos(90°−x°).

Triangle angles = 180°; polygon interior sum = (n−2)·180°. Volume/area formulas are on the reference sheet — don't memorize, just look.

STATISTICS & DATA

Sum = mean × count. Most "find the missing value" problems are this.

Outliers drag the mean; the median barely moves. Standard deviation = spread. Tighter cluster → smaller SD. Larger sample → smaller margin of error → narrower confidence interval.

Random selection lets you generalize to the population. Random assignment lets you claim cause and effect. Correlation alone never does.

Line of best fit questions: read the line, not the individual dots.

DESMOS QUICK WINS

Systems: type both equations, click the intersection point. Quadratics: graph it and click the vertex or the x-intercepts. No algebra needed.

"How many solutions?": graph and count intersections. Inequalities/regions: graph and test a point.

Stats: type the list, then use mean(L), median(L), stdev(L).

WHEN YOU'RE STUCK

Backsolve: plug the answer choices into the problem. Start with B or C.

Pick numbers when the answers have variables in them. Use 100 for percent problems, 2 and 3 for general numbers (avoid 0 and 1).

Translate word problems one phrase at a time: "is" = =, "of" = ×, "per" = ÷.

Guess something and move on — there is no penalty and every question is worth the same.

TRAPS THAT COST REAL POINTS

Solving for x when the question wants 2x, x+3, or y. Re-read the last line.

Unit switches: minutes vs. hours, cm vs. m, per week vs. per year.

Grid-ins: no commas, no % or $ signs; fractions are fine; don't round early.

Negative signs lost while distributing.

Module 2 gets harder if you did well in Module 1 — that's normal, not a disaster.

SAT MATH — LAST-MINUTE CHEAT SHEET

Page 1 of 2 — Math

PUNCTUATION & BOUNDARIES

Two complete sentences must be joined by: a period, a semicolon, a comma + FANBOYS (for, and, nor, but, or, yet, so), or a colon/dash.

Semicolon = period. If a period works there, so does the semicolon — and vice versa.

Colon needs a full sentence before it. What follows can be a list, an example, or an explanation.

Dashes can act like a colon (one dash) or like a pair of commas (two dashes). Openers and closers must match: comma…comma, dash…dash.

However, therefore, moreover, furthermore, nevertheless are not conjunctions. They need a semicolon or period before them, not a comma.

Never put a single comma between a subject and its verb, or between a verb and its object.

Nonessential info gets commas on both sides; essential info gets none.

Its = belongs to it. It's = it is. Also: their / they're / there, whose / who's, your / you're.

dogs (plural) · dog's (one dog owns it) · dogs' (many dogs own it)

GRAMMAR RULES ACTUALLY TESTED

Subject–verb agreement: cross out prepositional phrases in between. "The box of old letters is…"

Verb tense: match the timeline the passage already established. Don't switch without a reason.

Pronouns: singular antecedent → singular pronoun; the reference must be unambiguous.

Modifiers: whatever comes right after an opening phrase must be the thing that phrase describes. "Running late, Maria grabbed her keys."

Parallel structure in lists and comparisons: hiking, swimming, and biking.

Comparisons must compare like things: "Unlike Smith's novels, Jones's novels…" not "unlike Smith."

TRANSITIONS

Contrast: however, but, nevertheless, conversely, on the other hand, still

Cause / result: therefore, thus, consequently, as a result, so Addition: moreover, furthermore, in addition, also, similarly Example: for example, for instance, namely, specifically Emphasis / restatement: indeed, in fact, in other words Method: cover the answer choices. Read the sentence before and after, decide the relationship in your own words, then pick.

WORDS IN CONTEXT

Cover the blank. Predict your own word from the clues in the sentence. Then find the closest match.

Signal words tell you the direction: but, although, however, despite flip it; because, since, and, similarly keep it. The fanciest word is usually not the answer. Pick by meaning, not difficulty.