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Struggling to remember key ASVAB math formulas under pressure? You’re not alone. Many test-takers blank when confronted with fractions, percentages, and geometry during the ASVAB. That’s why we've crafted this ultimate ASVAB math formulas guide. In the next few minutes, you'll gain clarity on essential formulas, organized by topic group, so you can confidently crack every question, without scrambling mid-test. We’ll go beyond regurgitated lists and show you how and when to apply each formula. By the end, you'll have an actionable formula toolbox and the confidence to maximize your ASVAB score.
ASVAB math formulas
ASVAB math formulas
Divisibility, prime numbers, GCF & LCM
Understanding divisibility rules, prime numbers, GCF (Greatest Common Factor), and LCM (Least Common Multiple) is essential for solving many arithmetic problems. To help you quickly recall and apply these concepts, refer to the summary table of key ASVAB formulas below.
Divisibility rules:
Divisibility Rule
Condition
Divisible by 2
The number ends in an even digit (0, 2, 4, 6, 8)
Divisible by 3
The sum of its digits is divisible by 3
Divisible by 5
The number ends in 0 or 5
Divisible by 9
The sum of its digits is divisible by 9
Greatest common factor (GCF)
\[\text{GCF}(a, b) = \text{GCF}(b, \ a \bmod b)\]
Least common multiple (LCM):
\[\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCF}(a, b)}\]
Fractions, decimals & ratios
Mastering conversions between fractions, decimals, and ratios is crucial for understanding relationships and solving comparison problems. Use the formula table below to refresh your skills quickly.
These problems test your ability to apply math in real-world scenarios. Use the key ASVAB formulas in the table to break down and solve complex word problems more efficiently.
Concept
Formula
Meaning
Distance, rate, time
\[d = r \times t\]
d: distance, r: rate (speed), t: time
Simple interest
\[I = Prt\]
I: interest, P: principal (starting amount), r: rate (annual interest rate), t: time (years)
Compound interest
\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]
A: final amount, P: principal, r: annual rate, n: compounding periods per year, t: years
Work together
\[\frac{1}{T} = \frac{1}{A} + \frac{1}{B}\quad \text{where } T = \text{total time working together}\]
T: total time working together, A: time for person A alone, B: time for person B alone
Simple relationship between present, past, and future age
Algebra essentials
Algebra involves working with variables, expressions, and equations. Refer to the formula table below for quick access to foundational rules and techniques.
Concept
Formula
Meaning
Distributive property
\[a(b + c) = ab + ac\]
Slope and line equations
\[y - y_1 = m(x - x_1)\]
Line through point \[x_1, y_1\] with slope m
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
m: slope between two points \[x_1, y_1\] and \[x_2, y_2\]
\[y = mx + b\]
A slope-intercept form where m is the slope and b is the y-intercept
Quadratics & factoring
\[ax^2 + bx + c = 0\]
Standard quadratic form
\[(x + a)(x + b) = x^2 + (a + b)x + ab\]
FOIL method (First, Outer, Inner, Last) for factoring quadratics
\[\text{If } a < b \text{ and you multiply both sides by } -1, \text{ then: } -a > -b\]
Flip the inequality sign when multiplying/dividing by a negative number
Exponent rules
\[a^m \cdot a^n = a^{m+n}\]
Add exponents when multiplying the same base
\[(a^m)^n = a^{mn}\]
Multiply exponents when raising a power to another power
\[a^{-n} = \frac{1}{a^n}\]
A negative exponent means reciprocal
\[\sqrt{a^2} = |a|\]
Scientific notation
\[a \times 10^n\]
Used to express large/small numbers in powers of 10, \[1≤ a<10\], n is an integer
Systems of equations
Systems of equations involve finding values that satisfy multiple equations at once.
Elimination: Add or subtract to eliminate one variable.
Substitution: Solve one equation for a variable, and plug it into the other.
Geometry & measurement
Geometry covers shapes, sizes, angles, and measurement concepts. Use the summary table to recall essential formulas for area, perimeter, volume, and more.
Shape
Perimeter / Area
Volume
Surface Area
Meaning
Rectangle
\[P = 2(l + w)\]
\[A = lw\]
l: length, w: width
Triangle
\[P = a + b + c\]
\[A = \frac{1}{2} \times b \times h\]
a,b,c: sides, b: base, h: height
Circle
\[C = \pi d = 2 \pi r\]
\[A = \pi r^2\]
d: diameter, r: radius
Trapezoid
\[P = a + b + c + d\]
\[A = \frac{1}{2} (b_1 + b_2) h\]
Distance between 3D points: \[\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\]
Sum of angles in triangle: Sum of \[\text{Sum of angles} = 180^\circ\]
Volume of prism (general): \[\text{Base Area} \times \text{Height}\]
Exponents, scientific notation & factorials
These topics help simplify large or small numbers and repeated multiplication. Check the table for key rules and shortcuts to handle them quickly and accurately.
\[\log_b(xy) = \log_b x + \log_b y\]
\[\log_b \left(\frac{x}{y}\right) = \log_b x - \log_b y\]
\[\log_b \left(x^a\right) = a \log_b x\]
Logarithm properties that convert multiplication, division, and exponents into sums, differences, and products respectively
Ratios & proportions
Ratios and proportions are used to compare quantities and solve scaling problems. Use the formulas in the table to solve them confidently and correctly.
Concept
Formula
Notes
Ratio
\[\frac{a}{b}\] or a : b
Comparison between two quantities
Proportion
\[\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc\]
Cross multiplication
Part-to-whole ratio
\[\frac{\text{Part}}{\text{Total}}\]
Fraction of total
Scale ratio
\[\frac{\text{Model}}{\text{Real}}\] or vice versa
This section deals with data interpretation and chance. Refer to the table for important formulas on mean, median, mode, range, and basic probability calculations.
Concept
Formula
Meaning
Mean (average)
\[\text{Mean} = \frac{\text{Sum of terms}}{\text{Number of terms}}\]
Mastering the ASVAB math formulas is essential for boosting your confidence and scoring high on the test. This formula guide is designed to give you quick access to the most important equations across topics like algebra, geometry, ratios, and probability. By understanding these key formulas and applying them through regular practice, you’ll be able to tackle a wide range of math problems more efficiently. Remember, success on the ASVAB isn’t just about memorization; it’s about knowing when and how to use the right formula. Stay focused, keep practicing, and let this guide support your journey to a better score.
