SAT® · Test Mechanics: The Tools and the Traps
What Is on the Math Reference Sheet
The reference sheet printed on the math section gives you area and volume formulas for common shapes plus a few angle facts, but it skips algebra rules like slope, so you still have to memorize those.
The sheet exists because geometry formulas are long and easy to mix up under pressure, while algebra facts like slope or the quadratic formula are short enough to just know cold. So the card hands you area formulas for circles, rectangles, triangles, and parallelograms, then volume formulas for five solids: rectangular box, cylinder, sphere, cone, and pyramid. It also draws two special right triangles, 30-60-90 and 45-45-90, with their side ratios already filled in, and lists 360 degrees in a circle, 180 degrees in a straight line or a triangle, and 2 π radians in a circle.
The trick is reading it as building blocks, not finished answers. A cone volume question hands you the formula directly: one third π r squared h. A sector area question does not hand you anything labeled sector, but it gives you the whole-circle area and the 360 degrees in a full turn, and that is enough to build the sector yourself as a fraction of the circle. The 30-60-90 ratios work the same way: the card gives you sides x, x times the square root of 3, and 2x, and you multiply or divide from there to get area, perimeter, or a missing side.
This connects to the rest of test mechanics because the sheet only covers geometry and a handful of circle facts. Slope, the distance formula, systems of equations, exponent rules, and the quadratic formula are not on it, so those have to live in memory before test day. Knowing exactly what is printed, and what is not, decides how you spend your study time.
Key terms
- Reference sheet
- The printed card of geometry formulas and angle facts available during the math section.
- 30-60-90 triangle
- A right triangle with angles 30, 60, and 90 degrees and side ratios x, x times the square root of 3, and 2x.
- 45-45-90 triangle
- A right triangle with two 45 degree angles and side ratios x, x, and x times the square root of 2.
- Sector
- A pie-slice piece of a circle bounded by two radii and an arc, with area equal to a fraction of the whole circle's area.
Watch it explained
- How it worksHow does one reference card cover circles, rectangles, triangles and five different solids?
- Worked exampleFind the volume of a cone of radius 3 and height 7 using nothing but the SAT reference sheet.
- How it worksWalk me through the 30-60-90 and 45-45-90 side ratios exactly as the reference sheet draws them.
- Going furtherWhat opens up on a hard geometry question once you read 360 degrees, 2 π radians and 180 off the card?
Check yourself
End of topic.