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Police Officer Selection Test (POST) Mathematics and Quantitative Reasoning Syllabus

The Mathematics and Quantitative Reasoning syllabus for Police Officer Selection Test (POST) in full: 3 chapters, 10 topics and 21 sub-topics, every one listed below, plus 50 Mathematics and Quantitative Reasoning flashcards with answers.

3Chapters
10Topics
21Sub-topics
50Flashcards

Mathematics and Quantitative Reasoning syllabus: all 3 chapters

Expand any chapter to see its topics and sub-topics.

  1. Arithmetic Foundations

     4 topics
    • Whole Number Operations
      • Addition, subtraction, multiplication, division
      • Order of operations
    • Fractions and Decimals
      • Converting between fractions, decimals, and percents
      • Operations with mixed numbers
    • Percentages
      • Finding percent of a number
      • Percent increase and decrease
    • Ratios and Proportions
      • Setting up proportions
      • Rate problems (speed, distance, time)

  2. Applied Word Problems

     3 topics
    • Translating Words into Equations
      • Identifying knowns and unknowns
      • Selecting the correct operation
    • Multi-Step Problem Solving
      • Breaking problems into sequential steps
      • Checking reasonableness of answers
    • Police-Context Calculations
      • Computing speed, stopping distance, and travel time
      • Calculating blood alcohol estimates and dosages
      • Counting and reconciling evidence or cash

  3. Measurement and Data

     3 topics
    • Units and Conversions
      • Length, weight, volume, and time conversions
      • Distance and area measurement
    • Interpreting Charts and Graphs
      • Bar, line, and pie graphs
      • Reading crime-statistics tables
    • Basic Statistics
      • Mean, median, mode, and range
      • Interpreting trends over time

Police Officer Selection Test (POST) Mathematics and Quantitative Reasoning flashcards — 50 questions with answers

  1. What is the correct order of operations for evaluating an arithmetic expression?

    PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).

  2. When subtracting a larger digit from a smaller one within a column, what process do you use?

    Borrowing (regrouping): take 1 from the next column to the left (worth 10 in the current place value) and add it to the current digit before subtracting.

  3. What is the result of 7 x 0, and what general rule does it illustrate?

    0. Any number multiplied by 0 equals 0 (the zero property of multiplication).

  4. In a division problem, what are the names for the number being divided, the number you divide by, and the answer?

    Dividend (number being divided), divisor (number you divide by), and quotient (the answer). Any leftover is the remainder.

  5. How do you round a whole number to the nearest hundred?

    Look at the tens digit: if it is 5 or more, round the hundreds digit up; if 4 or less, keep it the same. Then replace the tens and units with zeros.

  6. What is a prime number, and give the smallest example?

    A whole number greater than 1 with exactly two factors—1 and itself. The smallest prime is 2 (and the only even prime).

  7. How do you add two fractions with different denominators?

    Find a common denominator (often the least common denominator), convert each fraction to it, add the numerators, keep the denominator, then simplify.

  8. How do you multiply two fractions?

    Multiply the numerators together and the denominators together, then simplify. Example: 2/3 x 3/4 = 6/12 = 1/2.

  9. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second (flip the divisor). Example: 1/2 ÷ 1/4 = 1/2 x 4/1 = 2.

  10. How do you convert the fraction 3/4 to a decimal?

    Divide the numerator by the denominator: 3 ÷ 4 = 0.75.

  11. How do you convert the decimal 0.6 to a fraction in lowest terms?

    Write it as 6/10 (tenths place), then simplify by dividing by 2 to get 3/5.

  12. What is the rule for placing the decimal point when multiplying two decimals?

    Multiply as whole numbers, then count the total number of decimal places in both factors and place the decimal that many places from the right in the product.

  13. When dividing decimals, how do you handle a decimal in the divisor?

    Move the decimal point in the divisor to make it a whole number, move the dividend's decimal the same number of places, then divide normally.

  14. What does 'percent' mean literally, and what is its fractional/decimal equivalent?

    'Percent' means 'per hundred.' So x% = x/100, and to convert to a decimal divide by 100 (e.g., 45% = 0.45).

  15. How do you find a percentage of a number, e.g., 20% of 150?

    Convert the percent to a decimal and multiply: 0.20 x 150 = 30.

  16. What is the formula for percent increase or decrease?

    Percent change = (new value − original value) / original value x 100. A positive result is an increase; negative is a decrease.

  17. How do you find what percent one number is of another, e.g., 'What percent is 18 of 72?'

    Divide the part by the whole and multiply by 100: 18/72 = 0.25 = 25%.

  18. If an item is 30% off and the discount equals $24, what was the original price?

    The part is the whole times the percent: 24 = 0.30 x original, so original = 24 / 0.30 = $80.

  19. What is a ratio, and how is the ratio 'three to five' written?

    A ratio compares two quantities by division. 'Three to five' is written 3:5, 3 to 5, or 3/5.

  20. What is a proportion, and how do you solve one?

    A proportion states two ratios are equal (a/b = c/d). Solve by cross-multiplication: a x d = b x c, then isolate the unknown.

Show the other 30 Mathematics and Quantitative Reasoning flashcards

  1. If 4 patrol cars cover 6 zones, how many cars are needed for 15 zones at the same rate?

    Set up 4/6 = x/15, cross-multiply: 6x = 60, so x = 10 cars.

  2. What is a unit rate, and give an example?

    A rate with a denominator of 1. Example: 120 miles in 2 hours = 60 miles per hour (the unit rate).

  3. How do you scale a recipe or mixture given as a ratio when one quantity is known?

    Set the known ratio equal to the new ratio with the unknown, then cross-multiply to solve. The ratio between parts stays constant.

  4. In word problems, what operation do the phrases 'sum,' 'total,' 'increased by,' and 'more than' usually signal?

    Addition (+).

  5. In word problems, what do 'difference,' 'less than,' 'decreased by,' and 'fewer' usually signal?

    Subtraction (−). Note 'less than' reverses order: '5 less than x' is x − 5.

  6. What words typically signal multiplication and division in word problems?

    Multiplication: 'product,' 'of,' 'times,' 'twice.' Division: 'quotient,' 'per,' 'divided by,' 'each,' 'ratio.'

  7. How would you translate 'twice a number increased by 7 equals 19' into an equation?

    2n + 7 = 19.

  8. In an equation, what does the word 'is' (or 'equals,' 'yields,' 'results in') translate to?

    The equals sign (=).

  9. What is the basic step for isolating a variable in a one-step equation like x + 8 = 20?

    Perform the inverse operation on both sides. Here, subtract 8 from both sides: x = 12.

  10. What is a recommended general strategy for solving multi-step word problems?

    Read carefully, identify what is asked, list given values, choose operations/equations, solve step by step, then check that the answer is reasonable and answers the question.

  11. When a multi-step problem has multiple operations, how do you decide the sequence?

    Work in logical real-world order, respecting order of operations; compute intermediate quantities first, then combine them to reach the final answer.

  12. Why should you estimate before computing a multi-step problem?

    Estimation gives a ballpark check so you can catch unreasonable answers caused by calculation or setup errors.

  13. A suspect travels at 45 mph for 20 minutes. How far does the suspect travel?

    Convert 20 min to 1/3 hour. Distance = rate x time = 45 x 1/3 = 15 miles.

  14. What is the distance-rate-time formula and its two rearrangements?

    Distance = rate x time (d = rt). Rearranged: rate = distance/time, and time = distance/rate.

  15. An officer works an 8-hour shift and issues 12 citations evenly. What is the rate per hour, and how many in a 10-hour shift at that rate?

    Rate = 12/8 = 1.5 citations per hour. In 10 hours: 1.5 x 10 = 15 citations.

  16. If a report shows 3 of 25 stops resulted in arrests, what percentage is that?

    3/25 = 0.12 = 12%.

  17. How many feet are in one mile?

    5,280 feet.

  18. How do you convert minutes to hours and vice versa?

    Divide minutes by 60 to get hours; multiply hours by 60 to get minutes (1 hour = 60 minutes).

  19. How many inches are in a foot, and feet in a yard?

    12 inches in a foot; 3 feet in a yard (so 36 inches in a yard).

  20. What is the general method for converting units using a conversion factor?

    Multiply by a fraction equal to 1 (the conversion factor) arranged so the unwanted unit cancels and the desired unit remains. Example: 2 mi x 5280 ft/1 mi = 10,560 ft.

  21. How many ounces are in a pound, and how do you convert pounds to ounces?

    16 ounces in a pound. Multiply pounds by 16 to get ounces (e.g., 3 lb = 48 oz).

  22. On a bar graph, what does each axis typically represent and how do you read a value?

    One axis lists categories, the other a numeric scale. Read a bar's value by tracing its top across to the numeric scale.

  23. What does a line graph best show, and how do you interpret a rising versus falling line?

    It shows change over time/trends. A rising line means an increase; a falling line means a decrease; a flat line means no change.

  24. In a pie (circle) chart, what do the slices represent and what must they total?

    Each slice is a part's proportion of the whole; all slices together represent 100% (or the full data set).

  25. How do you find the actual quantity a pie-chart percentage represents?

    Multiply the slice's percentage (as a decimal) by the total amount the whole chart represents.

  26. What is the mean (average), and how is it calculated?

    The arithmetic average: add all the values and divide by the number of values. Mean = sum / count.

  27. What is the median, and how do you find it?

    The middle value when data is ordered. With an odd count it's the center value; with an even count it's the average of the two middle values.

  28. What is the mode of a data set?

    The value that appears most frequently. A set can have no mode, one mode, or multiple modes.

  29. What is the range of a data set, and how is it computed?

    A measure of spread equal to the largest value minus the smallest value.

  30. For the data set 4, 8, 8, 10, 20, what are the mean, median, and mode?

    Mean = (4+8+8+10+20)/5 = 50/5 = 10; median = 8 (middle value); mode = 8 (most frequent).

Police Officer Selection Test (POST) Mathematics and Quantitative Reasoning FAQ

What is in the Police Officer Selection Test (POST) Mathematics and Quantitative Reasoning syllabus?

Police Officer Selection Test (POST) Mathematics and Quantitative Reasoning is split into 3 chapters: Arithmetic Foundations, Applied Word Problems and Measurement and Data. Together they contain 10 topics and 21 sub-topics.

How many chapters are in Police Officer Selection Test (POST) Mathematics and Quantitative Reasoning?

3 chapters, containing 10 topics and 21 sub-topics. The largest chapter is Arithmetic Foundations, with 4 topics.

Are there flashcards for Police Officer Selection Test (POST) Mathematics and Quantitative Reasoning?

Yes — a 50-card Mathematics and Quantitative Reasoning deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.