Key Math Concepts Covered in the POST Exam
Arithmetic Fundamentals: Fractions, Decimals, Percentages
The POST math section review begins with a heavy emphasis on the mechanics of rational numbers. Candidates are expected to perform the four basic operations—addition, subtraction, multiplication, and division—on fractions and decimals with high precision. In a law enforcement context, this often translates to calculating the distribution of resources or determining exact measurements in a forensic report. For instance, you might be required to add several decimal-based weights of confiscated substances or determine what fraction of a precinct's fleet is currently out of service.
Understanding the relationship between these formats is vital. You must be able to convert a fraction like 3/8 into its decimal equivalent (0.375) and then into a percentage (37.5%) rapidly. Percentages are particularly prevalent when calculating tax rates on equipment purchases or determining the percentage of a population affected by specific crime trends. A common exam scenario involves finding the "percent of change," which requires the formula: (New Value - Old Value) / Old Value * 100. Precision in decimal placement is the most frequent point of failure; a single misplaced dot can result in an answer that is off by a factor of ten, which is a disqualifying error in both the exam and field reporting.
Ratios, Proportions, and Rates
Ratios and proportions form the backbone of many calculations for police reports, especially those involving scale and comparison. A ratio expresses the relationship between two quantities, such as the number of officers to citizens in a specific district. Proportions are equations where two ratios are set equal to each other, often solved using the cross-multiplication method. For example, if a department knows that 3 patrol cars are required for every 10,000 residents, a candidate must be able to calculate how many cars are needed for a city of 150,000 by setting up the proportion 3/10,000 = x/150,000.
Rates involve a third variable, usually time. The most common rate used in the POST is speed, expressed as distance over time. Candidates must be comfortable manipulating the Rate-Time-Distance formula (R x T = D) to solve for any of the three variables. If a suspect vehicle travels 15 miles in 12 minutes, you must be able to convert that into miles per hour (MPH) by recognizing that 12 minutes is 1/5 of an hour, leading to a speed of 75 MPH. Mastering these conversions is essential because the exam often provides units that do not match, requiring an initial conversion step before the primary calculation can begin.
Basic Algebraic Equations and Problem-Solving
When asking what math is on the police exam, many candidates are surprised to find basic algebra. The POST does not require advanced calculus, but it does demand the ability to solve for an unknown variable (x). These problems are typically presented as linear equations where you must isolate the variable using inverse operations. For example, an equation might represent a departmental budget: 5x + 150 = 500. To solve this, you would subtract 150 from both sides and then divide by 5 to find that x = 70.
Algebraic thinking is also applied to substitution problems, where you are given the values for certain variables and must find the total value of an expression. This mimics real-world scenarios like calculating the total cost of a citation based on a fixed court fee plus a variable fine per mile over the speed limit. If the formula is Total = 100 + 5(m), where m is the miles over the limit, and the driver was going 12 over, the candidate must correctly apply the Order of Operations (PEMDAS) to multiply 5 by 12 before adding the 100. Failure to follow the hierarchy of operations is a primary cause of incorrect answers in the algebra subsection.
Applied Geometry for Law Enforcement Scenarios
Calculating Area and Perimeter at Incident Scenes
Geometry on the POST exam is almost always grounded in the physical realities of a crime or accident scene. Candidates must know the formulas for Perimeter (the distance around an object) and Area (the space inside an object). For a rectangular scene, the perimeter is 2L + 2W, while the area is L x W. These calculations are vital for determining how much police tape is needed to secure a perimeter or for documenting the square footage of a room where evidence was recovered.
Questions may also involve circles, requiring knowledge of Pi (approximated as 3.14), diameter, and radius. To find the circumference (perimeter) of a circular debris field, you use the formula C = πd. To find the area, you use A = πr². A typical exam question might describe a circular skid mark with a diameter of 20 feet and ask for the area of the circle. You must first identify that the radius is 10 feet, square it to get 100, and multiply by 3.14 to arrive at 314 square feet. Accuracy in these geometric applications demonstrates a candidate's ability to provide precise technical data in official documentation.
Understanding Spatial Relationships and Diagrams
Beyond simple formulas, the POST assesses a candidate's ability to interpret spatial data and diagrams. This often involves coordinate geometry or the interpretation of floor plans and maps. You may be presented with a grid representing a neighborhood and asked to determine the shortest distance between two points or to identify the coordinates of a specific building. This tests spatial orientation, a skill used daily when navigating city streets or directing backup to a specific quadrant of a scene.
Another common scenario involves the Pythagorean Theorem (a² + b² = c²), which is used to find the length of the hypotenuse in a right-angled triangle. In a police context, this might be used to calculate the diagonal distance across a vacant lot or the length of a ladder needed to reach a second-story window. Candidates must recognize when a scenario forms a right triangle and apply the theorem correctly. Understanding these spatial relationships is essential for tactical planning and for reconstructing the movements of individuals at a scene based on physical evidence.
Volume Calculations for Evidence and Storage
Volume calculations are less frequent but remain a core part of the POST arithmetic and algebra problems curriculum. Volume measures the amount of three-dimensional space an object occupies, usually calculated as Length x Width x Height for rectangular prisms. In law enforcement, this is relevant for determining the capacity of evidence lockers, the volume of liquid in a container, or the amount of space available in a transport vehicle.
Candidates should also be familiar with the volume of a cylinder (V = πr²h), as this can apply to containers or tanks found at industrial incident sites. The exam may ask you to compare volumes—for example, determining if the contents of a 500-cubic-inch container will fit into a box that is 8 inches by 8 inches by 8 inches. Since 8 cubed is 512, the answer would be yes. These problems often require multiple steps, such as calculating the volume and then converting that volume into a different unit of measurement, such as gallons or liters, using a provided conversion factor.
Mastering Word Problems and Data Interpretation
Deconstructing Police-Related Story Problems
The most challenging aspect of the exam for many is the police test word problem strategies. These questions embed mathematical operations within a narrative, requiring the candidate to filter out irrelevant information (distractors) and identify the core mathematical task. For example, a problem might describe an officer’s shift, mentioning the time they started, the number of coffee breaks taken, and the number of miles driven on three different calls. If the question asks for the average miles per call, the start time and break information are irrelevant data points that must be ignored.
Effective deconstruction involves identifying the key operators—words like "total" or "sum" indicate addition, while "difference" or "leftover" indicate subtraction. "Each" or "per" usually signals multiplication or division. A common strategy is to translate the word problem into a numerical equation before attempting any math. If a problem states that an officer has 50 citations and gives away 5 per day, the equation becomes 50 - 5d. By formalizing the narrative into a mathematical expression, candidates reduce the cognitive load and minimize the risk of making an intuitive but incorrect guess.
Analyzing Graphs, Charts, and Crime Statistics
Data interpretation is a high-level skill tested on the POST, often using bar graphs, line charts, or pie charts to represent crime statistics. Candidates must be able to extract specific values from these visuals and perform secondary calculations. For instance, a bar graph might show the number of burglaries over a six-month period, and the question might ask for the mean (average) number of burglaries per month. This requires summing the values from all bars and dividing by six.
Other questions might focus on the median (the middle value in a sorted list) or the mode (the most frequent value). You may also be asked to identify trends, such as which month saw the greatest percentage increase in reported thefts. This involves comparing the data points between two months and applying the percent of change formula. The ability to read and interpret these visuals is crucial for officers who must review departmental reports or present data to community stakeholders, making it a staple of the selection process.
Sequential Logic and Multi-Step Calculations
Many POST math problems are designed as multi-step puzzles that test sequential logic. These problems cannot be solved in a single operation; instead, the answer to the first part of the problem serves as the input for the second part. Consider a scenario where you must calculate the total cost of a fleet's fuel. You might first need to calculate the total miles driven by all cars, then divide by the average miles per gallon to find the total gallons used, and finally multiply by the price per gallon.
Exam Rule: In multi-step problems, do not round your intermediate answers. Rounding too early in a sequence of calculations can lead to a final result that is slightly off from the multiple-choice options, causing confusion and wasted time.
These questions assess a candidate's ability to maintain focus through a complex process. They mirror the multi-stage nature of police investigations, where one piece of data leads to another. Success requires organized scratchpad work, where each step is clearly labeled to prevent the candidate from losing their place or using the wrong number in the final calculation.
Speed, Distance, and Time Equations
As previously noted, the relationship between speed, distance, and time is a fundamental component of the POST math section review. Beyond the basic D = R x T formula, candidates must be able to manipulate it to solve for time (T = D/R) and speed (R = D/T). In many exam scenarios, you will be given a distance in miles and a speed in miles per hour and asked how long a trip will take in minutes. This requires an extra step: multiplying the resulting fraction of an hour by 60.
For example, if a backup unit is 10 miles away and traveling at 40 MPH, the time taken is 10/40, which is 0.25 hours. To find the minutes, you multiply 0.25 by 60, resulting in 15 minutes. Memorizing these variations and the "60-minute conversion" is vital because time-based questions are a frequent source of errors. Candidates should also be prepared for "closing speed" problems, where two vehicles are moving toward each other, requiring the addition of their speeds to determine how quickly the gap between them will close.
Law enforcement frequently deals with fluctuating statistics, making percentage increase and decrease formulas essential. The standard formula is: |Original - New| / Original. This result is then multiplied by 100 to get the percentage. On the POST, this might appear in the context of a budget cut (percentage decrease) or a rise in the number of calls for service (percentage increase).
It is important to distinguish between "percentage of" and "percentage change." If a question asks what 15% of 200 is, you simply multiply 200 by 0.15. However, if it asks for the percentage increase from 200 to 230, you must find the difference (30), divide by the original (200), which equals 0.15, or 15%. A common pitfall is dividing the difference by the new value instead of the original value. Always remember that the "base" of the change is where the value started, not where it ended.
Standard Measurement Conversions (e.g., feet to miles)
Since the POST is a practical exam, it often requires converting between different units of measurement within the US Customary System. Candidates must memorize key conversion factors, such as:
- 1 mile = 5,280 feet
- 1 yard = 3 feet
- 1 foot = 12 inches
- 1 pound = 16 ounces
- 1 gallon = 4 quarts = 8 pints = 16 cups
In a crime scene scenario, you might be given the length of a room in inches but be asked for the area in square feet. You must convert the inches to feet before multiplying for the area, or convert the final square inches to square feet by dividing by 144 (since a square foot is 12" x 12"). Many candidates fail these questions because they perform the math on the raw numbers provided without checking if the units match the required answer format. Being fluent in these conversions allows you to move through the exam more quickly and with greater confidence.
Common Calculation Pitfalls and How to Avoid Them
Misreading Word Problem Details
The primary reason candidates fail the math section is not a lack of mathematical knowledge, but rather a failure in reading comprehension. The POST uses specific language to trick the unwary. For example, a question might ask how many "full weeks" an officer worked, given a total of 38 days. If the candidate simply divides 38 by 7 and provides the decimal (5.42), they have failed to answer the specific question, which is "5."
Another common trick is the use of "except" or "not." A question might list four types of evidence and their weights, asking for the total weight of all items except the largest one. If you sum all the items, you will likely find that total listed as one of the incorrect multiple-choice options (a distractor). To avoid this, successful candidates use the underline technique, physically marking the specific question being asked and any constraints or units required in the final answer. This forces the brain to focus on the actual objective rather than the first number it calculates.
Errors in Decimal Placement and Unit Conversion
Decimal errors are particularly prevalent in division problems. When dividing by a decimal, you must move the decimal point in both the divisor and the dividend to make the divisor a whole number. For example, in 10 / 0.25, you move the decimal two places to the right in both, changing the problem to 1,000 / 25, which equals 40. Forgetting to move the decimal in the dividend is a classic error that results in an answer of 4 or 0.4.
Unit conversion errors often occur when candidates forget that square and cubic units do not convert the same way as linear units. As mentioned earlier, while there are 12 inches in a foot, there are 144 square inches in a square foot. If a question involves area or volume, you must be extremely careful to apply the conversion factor to each dimension of the object. The safest way to avoid this pitfall is to convert all measurements to the desired final unit before performing any multiplication or division.
Time Management for Complex Problems
The POST is a timed exam, and the math section often creates a bottleneck. Candidates frequently get "stuck" on a single complex word problem, spending five minutes on a question worth the same amount of points as a simple addition problem. This leads to rushing at the end of the section, where simple mistakes become more likely.
To manage time effectively, use the Three-Pass Method. On the first pass, answer all the simple arithmetic and basic formula questions that you can solve in under 30 seconds. On the second pass, tackle the more involved word problems and multi-step calculations. On the third pass, return to the most difficult problems that you initially skipped. This ensures that you have secured all the "easy" points and are not leaving portions of the test blank due to poor pacing. If a problem takes more than two minutes of scratch work, it is usually best to mark it, move on, and return later.
Building a Study Plan for POST Math Mastery
Diagnosing Your Weakest Math Areas
The first step in preparation is an honest assessment of your current skills. Take a diagnostic practice test under timed conditions to identify which of the Police Officer Selection Test math topics cause the most trouble. Are you struggling with the mechanics of long division? Do you find yourself confused by the wording of distance-rate-time problems? Or is geometry your primary hurdle?
Once you have identified your weaknesses, categorize them into "conceptual errors" (not knowing the formula or method) and "execution errors" (knowing the method but making a calculation mistake). Conceptual errors require targeted study of the underlying math rules, while execution errors require more repetitive practice and a focus on neatness and organization. By focusing your study time on your lowest-performing areas rather than reviewing what you already know, you maximize your score improvement per hour of study.
Sourcing Quality Practice Problems
Not all math practice is created equal. To prepare for the POST, you need problems that mimic the specific law enforcement context of the exam. Look for study guides that offer calculations for police reports and situational word problems. Standard GED or SAT prep materials can help with basic arithmetic and algebra, but they will not prepare you for the specific way the POST frames its questions.
Use resources that provide detailed explanations for the correct answers. Simply knowing that "C" is the right answer is not enough; you need to understand the logical path taken to get there. If a practice problem involves a multi-step calculation for crime statistics, follow the explanation step-by-step to see where your own logic may have diverged. This builds the mental framework necessary to tackle unfamiliar scenarios on the actual test day.
Simulating Test-Day Conditions Without a Calculator
The most important part of your study plan is practicing without a calculator. Because the POST requires manual calculation, you must rebuild your "mental math muscles." This includes memorizing multiplication tables up to 12x12, practicing long division on paper, and becoming comfortable with manual square roots for small numbers.
During your final weeks of preparation, take full-length practice math sections using only a pencil and scratch paper. Time yourself strictly to the limits of the actual exam. This simulation helps you develop a sense of pacing and reduces the anxiety associated with the ticking clock. It also highlights the importance of neatness; many candidates lose points simply because they cannot read their own handwriting on their scratchpad. By the time you sit for the actual Police Officer Selection Test, the lack of a calculator should feel like a normal part of your problem-solving process, not a disadvantage.