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

Mathematics and Quantitative Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics and Quantitative Reasoning in Police Officer Selection Test (POST), not a summary of it.

1. 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. 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. 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

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

24 of 50 cards from the Mathematics and Quantitative Reasoning deck — real questions with worked 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.

21. 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.

22. 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).

23. 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.

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

    Addition (+).

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