SAT formulas provided vs. formulas to know

The on-screen reference collects selected geometry facts: common area and circumference formulas, several volume formulas, the Pythagorean theorem, and side relationships for special right triangles. Its job is to reduce rote recall for a limited set of relationships. It does not identify which relationship the problem needs, draw missing heights, convert units, or explain whether a dimension is a radius, diameter, slant height, or edge.

Use the reference sheet during Bluebook practice before deciding what you personally need to memorize. A fact can be provided yet still deserve fluency if looking it up repeatedly costs attention. Conversely, avoid spending study time memorizing an elaborate list of obscure formulas. SAT Math rewards flexible use of a smaller network: rates as ratios, slope as change, exponent rules, equivalent quadratic forms, similarity, scale, and the connections between equations and graphs.

Linear work begins with slope as change in output divided by change in input. In y=mx+b, m is the rate of change and b is the output when x=0. Point-slope and standard forms are not separate facts to memorize blindly; they are rearrangements that make different information visible. Systems ask where relationships agree. Inequalities add a direction that can reverse when both sides are multiplied or divided by a negative number.

For quadratics, connect form to feature. Standard form exposes the y-intercept, factored form exposes zeros, and vertex form exposes the vertex. The quadratic formula is a general method, but factoring, completing the square, graphing, or comparing coefficients may be faster. Know exponent rules and what an exponential multiplier means: in a model a(b)^x, a is the value at x=0 and b is the factor for a one-unit increase in x.

Percent problems become reliable when you translate the language into multipliers. An increase of r percent multiplies the original by 1+r/100; a decrease multiplies by 1−r/100. Repeated percentage change repeats the multiplier, so it is exponential rather than a one-time additive adjustment. Percent change compares the difference with the original value, not with the new value. Keep the base visible in your setup.

A rate is a ratio with units. Distance equals rate times time only after units agree, and density equals mass divided by volume only when you track what each number measures. For data, distinguish measures of center from spread. The mean uses every value and can move when an outlier changes; the median depends on order. Standard deviation describes spread around the mean. A line of best fit summarizes an association but does not by itself establish causation.

Area measures a two-dimensional region and uses square units; volume measures three-dimensional space and uses cubic units. Scaling every length by k scales area by k² and volume by k³. That single relationship solves many similarity questions without rebuilding each figure. In right triangles, the Pythagorean theorem connects side lengths, while sine, cosine, and tangent connect an acute angle with ratios of sides. Similar triangles preserve corresponding angle measures and side ratios.

For circles, connect equation and geometry. In (x−h)²+(y−k)²=r², the center is (h,k) and the radius is r. Notice the reversed signs inside the parentheses and the squared radius on the right. Arc length and sector area are the same fraction of the full circumference or area as the central angle is of a full turn. These relationships are more useful than remembering disconnected arc formulas.

Sort formulas into three layers. Layer one is automatic: slope, percent multipliers, exponent rules, key quadratic forms, and basic ratio or rate relationships. Layer two is derivable quickly: midpoint as coordinate averages, arc measures as fractions of a circle, and many surface-area expressions as sums of faces. Layer three is provided: selected geometry references you still need to recognize. Your exact layers may differ, but every item should have a reason for its placement.

Study with two-sided prompts that ask for meaning and use, not just symbols. Instead of ‘What is the slope formula?’ ask ‘What does slope measure, what units does it have, and how can I find it from two points, a table, a graph, or an equation?’ After each practice error, decide whether the problem was recall, recognition, setup, algebra, or arithmetic. Memorizing another formula will not fix a setup error caused by using diameter as radius.