GED Math
GED Math Formula Sheet, Explained: Every Formula With Examples
Every formula on the GED formula sheet, explained with a worked example, plus six practice questions on choosing and using the right one.
On the GED Mathematical Reasoning test, you get a formula sheet on paper at the test center and on screen during the test. You don't have to memorize the formulas. You do have to know which one fits the problem and how to put the numbers in correctly, and that is where most points are lost.
This page goes through every group of formulas on the sheet with a worked example, then ends with six practice questions. The official sheet is available from the GED Testing Service on GED.com; the formulas below are written out by us so we can explain them.
Area and perimeter
| Shape | Area | Perimeter |
|---|---|---|
| Square | \(A = s^2\) | \(P = 4s\) |
| Rectangle | \(A = lw\) | \(P = 2l + 2w\) |
| Parallelogram | \(A = bh\) | |
| Triangle | \(A = \tfrac{1}{2}bh\) | \(P = s_1 + s_2 + s_3\) |
| Trapezoid | \(A = \tfrac{1}{2}h(b_1 + b_2)\) | |
| Circle | \(A = \pi r^2\) | \(C = 2\pi r\) or \(C = \pi d\) |
Example: a trapezoid with bases 8 and 12 and height 6 has area \(\tfrac{1}{2}(6)(8 + 12) = 60\). A circle with radius 5 has area \(3.14 \times 5^2 = 78.5\).
The sheet says to use \(\pi \approx 3.14\). Use that value, not the \(\pi\) key, unless the question says otherwise, so your answer matches the choices.
Surface area and volume
| Solid | Surface area | Volume |
|---|---|---|
| Rectangular prism (box) | \(SA = 2lw + 2lh + 2wh\) | \(V = lwh\) |
| Right prism | \(SA = ph + 2B\) | \(V = Bh\) |
| Cylinder | \(SA = 2\pi rh + 2\pi r^2\) | \(V = \pi r^2 h\) |
| Pyramid | \(SA = \tfrac{1}{2}ps + B\) | \(V = \tfrac{1}{3}Bh\) |
| Cone | \(SA = \pi rs + \pi r^2\) | \(V = \tfrac{1}{3}\pi r^2 h\) |
| Sphere | \(SA = 4\pi r^2\) | \(V = \tfrac{4}{3}\pi r^3\) |
Here \(B\) is the area of the base, \(p\) is the perimeter of the base, and \(s\) is the slant height. Two quick examples: a box 4 by 3 by 2 has surface area \(2(12 + 8 + 6) = 52\); a cylinder with radius 2 and height 10 has volume \(3.14 \times 4 \times 10 = 125.6\). A square pyramid with a 6-by-6 base and height 5 has volume \(\tfrac{1}{3}(36)(5) = 60\).
The pattern worth remembering: anything that comes to a point (pyramid, cone) has a \(\tfrac{1}{3}\) in its volume.
Data: mean and median
The sheet defines both in words. The mean is the total of the values divided by how many there are. The median is the middle value once the data is in order, or the mean of the two middle values when there is an even number of them. Sorting first is the step people skip.
Algebra
| Formula | What it's for |
|---|---|
| \(m = \dfrac{y_2 - y_1}{x_2 - x_1}\) | Slope from two points |
| \(y = mx + b\) | Slope-intercept form of a line |
| \(y - y_1 = m(x - x_1)\) | Point-slope form: a line from its slope and one point |
| \(y = ax^2 + bx + c\) | Standard form of a quadratic |
| \(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) | Quadratic formula: solves \(ax^2 + bx + c = 0\) |
| \(a^2 + b^2 = c^2\) | Pythagorean theorem: \(c\) is the longest side |
Example: a right triangle with legs 9 and 12 has hypotenuse \(\sqrt{81 + 144} = \sqrt{225} = 15\). For more on lines, see our lesson on how to find slope.
Money and motion
- Simple interest: \(I = Prt\), with the rate as a decimal and time in years.
- Distance: \(d = rt\). Driving 4 hours at 55 miles per hour covers \(55 \times 4 = 220\) miles.
- Total cost: total cost = number of units × price per unit.
What the sheet doesn't give you
Percents, percent change, exponent rules, probability, and unit conversions are not on the sheet. Our GED math practice test has the full side-by-side list, and our lesson on percent word problems covers the biggest gap.
Practice: using the formula sheet
1.A garden is shaped like a trapezoid. Its parallel sides are 10 feet and 16 feet long, and the distance between them is 7 feet. What is its area?
- A\(182 \text{ ft}^2\)
- B\(91 \text{ ft}^2\)
- C\(112 \text{ ft}^2\)
- D\(13 \text{ ft}^2\)
Show solution
\[\begin{gathered}A = \tfrac{1}{2}h(b_1 + b_2) \\ = \tfrac{1}{2}(7)(10 + 16) \\ = \tfrac{1}{2}(7)(26) = 91\end{gathered}\]Common trap: Forgetting the \(\tfrac{1}{2}\), which gives 182. The trapezoid formula averages the two bases; the \(\tfrac{1}{2}\) is what does the averaging.
Answer: B (\(91 \text{ ft}^2\))
2.A cone-shaped cup has a radius of 3 inches and a height of 8 inches. Using \(\pi \approx 3.14\), what is its volume?
- A\(75.36 \text{ in}^3\)
- B\(226.08 \text{ in}^3\)
- C\(25.12 \text{ in}^3\)
- D\(301.44 \text{ in}^3\)
Show solution
\[\begin{gathered}V = \tfrac{1}{3}\pi r^2 h = \tfrac{1}{3}(3.14)(3^2)(8) \\ = \tfrac{1}{3}(226.08) = 75.36\end{gathered}\]Common trap: Leaving out the \(\tfrac{1}{3}\) and getting 226.08, the volume of a cylinder with the same base and height. Cones and pyramids always have the \(\tfrac{1}{3}\).
Answer: A (\(75.36 \text{ in}^3\))
3.A round table has a diameter of 14 meters. Using \(\pi \approx 3.14\), what is its circumference?
- A87.92 m
- B153.86 m
- C21.98 m
- D43.96 m
Show solution
With the diameter, use \(C = \pi d\).
\[C = 3.14 \times 14 = 43.96\]Common trap: Treating 14 as the radius in \(C = 2\pi r\), which doubles the answer to 87.92. Check whether the problem gives the radius or the diameter before you pick a formula.
Answer: D (43.96 m)
4.A driver travels for 3.5 hours at an average speed of 62 miles per hour. How far does she go?
- A17.71 miles
- B65.5 miles
- C217 miles
- D186 miles
Show solution
\[d = rt = 62 \times 3.5 = 217\]Common trap: Dividing speed by time, which gives about 17.7. Distance is rate times time; the units confirm it: miles per hour times hours is miles.
Answer: C (217 miles)
5.Which equation describes the line with slope \(-2\) that passes through the point \((3, 5)\)?
- A\(y = -2x + 11\)
- B\(y = -2x - 1\)
- C\(y = -2x + 5\)
- D\(y = 2x - 1\)
Show solution
Use point-slope form, \(y - y_1 = m(x - x_1)\), then solve for \(y\).
\[\begin{gathered}y - 5 = -2(x - 3) \\ \Rightarrow\; y - 5 = -2x + 6 \\ \Rightarrow\; y = -2x + 11\end{gathered}\]Common trap: Multiplying \(-2\) by \(-3\) and getting \(-6\), which leads to \(y = -2x - 1\). A negative times a negative is positive.
Answer: A (\(y = -2x + 11\))
6.A ball has a radius of 3 inches. Using \(\pi \approx 3.14\), what is its volume?
- A\(28.26 \text{ in}^3\)
- B\(113.04 \text{ in}^3\)
- C\(84.78 \text{ in}^3\)
- D\(376.8 \text{ in}^3\)
Show solution
\[V = \tfrac{4}{3}\pi r^3 = \tfrac{4}{3}(3.14)(27) = 113.04\]Common trap: Squaring the radius instead of cubing it. Volume is three-dimensional, so the radius is cubed (\(r^3\)); surface area uses \(r^2\).
Answer: B (\(113.04 \text{ in}^3\))
Teacher's note: Having the formula in front of you is only half the job. I ask students to copy the formula onto their scratch paper exactly as it appears, with letters, and only then replace each letter with a number, one at a time. Substituting straight into your head is how the \(\tfrac{1}{3}\) and the \(\tfrac{1}{2}\) disappear.
Keep practicing
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