Why this has a page of its own. The formula sheet is the second thing they hand you, after the calculator, and like the calculator it belongs to no single family. Knowing what is on it changes what you have to study. Knowing what is not on it changes it more.
On the Mathematical Reasoning test, a button on the screen opens a sheet of formulas, and it is there for the whole 115 minutes. You are not asked to remember the area of a circle or the quadratic formula. You are asked to know which one a question wants, and to put the right numbers into it.
That is worth saying twice, because it changes what studying means. Time spent memorizing what is printed below is time wasted. Time spent recognizing shapes and situations is not.
What follows is everything on the sheet, grouped by the family it belongs to rather than in the order the sheet prints it, so you can see which part of your studying it covers.
Area
Family 7, geometry- squareA = s2
- rectangleA = lw
- parallelogramA = bh
- triangleA = ½bh
- trapezoidA = ½h(b1 + b2)
- circleA = πr2
Perimeter, and around a circle
Family 7, geometry- squareP = 4s
- rectangleP = 2l + 2w
- triangleP = s1 + s2 + s3
- circle (circumference)C = 2πr or C = πd
- and the value it tells you to useπ ≈ 3.14
Surface area and volume
Family 7, geometry — here p is the perimeter of the base and B is its area- rectangular prism (a box)SA = 2lw + 2lh + 2wh · V = lwh
- right prismSA = ph + 2B · V = Bh
- cylinderSA = 2πrh + 2πr2 · V = πr2h
- pyramidSA = ½ps + B · V = 1⁄3Bh
- coneSA = πrs + πr2 · V = 1⁄3πr2h
- sphereSA = 4πr2 · V = 4⁄3πr3
Lines, and quadratics
Families 12 and 13- slope of a linem = y2 − y1x2 − x1
- slope-intercept form of a liney = mx + b
- point-slope form of a liney − y1 = m(x − x1)
- standard form of a quadratic equationy = ax2 + bx + c
- the quadratic formulax = −b ± √b2 − 4ac2a
- the Pythagorean theorema2 + b2 = c2
Money, rates, and time
Family 5, and the rate work in family 2- simple interestI = Prt
- distance, as rate times timed = rt
- total costtotal cost = (number of units) × (price per unit)
Two definitions, written out in words
Family 8, dataThe sheet does not give a formula for these. It gives a sentence for each. The mean is the total of the values divided by how many values there are. The median is the middle value once they are sorted — or, when there is an even number of them, the mean of the middle two.
This is the more useful list, because everything on it you have to carry in yourself. The test asks about all of these.
- Mode and range · the sheet defines the mean and the median and stops. Family 8
- The distance between two points on a grid, and the midpoint · neither is there. Family 14
- Standard form of a line, Ax + By = C · the “standard form” on the sheet is the one for a quadratic. Family 13
- Which way round the coordinates go · that a point is written (x, y). Family 14
- Anything about percent · no percent formula at all, and no way to set up a proportion. Family 5
- Unit conversions · not one of them. Family 6
- The rules of exponents, and scientific notation. Family 10
- Anything about probability or counting. Family 9
- How to solve an equation, or what to do with an inequality. Family 12
- The rules for fractions · adding, multiplying, dividing, none of it. Family 3
- How to read a graph · no sheet can give you that. Family 8
Read that list as a study plan. The sheet carries geometry for you, and almost nothing else.
The sheet has a line labelled distance formula, and it says d = rt. That is distance as rate times time — a car, a walk, a rate question.
It is not the distance between two points on a grid. That one has a square root in it, it is a different piece of mathematics altogether, and it is not on the sheet at all. If a question shows you two points and asks how far apart they are, the sheet will not help you, and the line that looks as though it should is about something else. Family 14 is where that lives, and Lines on the Grid teaches it.
Name the thing before you go looking. Say it to yourself first: this is a cylinder, and it wants the volume. Then open the sheet and find that line. Opening it first and reading down hoping something fits is how five minutes disappear.
Write the formula out before you put numbers in it. On the scratch paper, in full. Substituting straight from the screen into your head is where the mistakes happen, and they are not mistakes you catch.
Check what the units did. An area comes out in square units and a volume in cubic ones. If you worked out an area and the answer is in plain feet, something went in the wrong slot.
Practice with it open. Same rule as the calculator: you do not study a reference sheet, you use one until you know where things are. Keep it beside you while you work through the quizzes on this site, and by test day finding a formula will cost you seconds instead of minutes.
The sheet is published by GED Testing Service, the people who make the test, and it is theirs — so it is not reproduced here as a file. Their own copy is the one to print, and it is on GED.com among the test resources.
Ask in class and you will be given one.