National Police Officer Selection Test (NPOST / Stanard & Associates POST) Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

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

1. 1

   Whole Numbers and Basic Operations

   4 topics

   • Addition and Subtraction
     • Multi-digit addition with carrying
     • Subtraction with borrowing
     • Checking answers by reverse operation
   • Multiplication and Division
     • Multi-digit multiplication
     • Long division with remainders
     • Divisibility and factors
   • Order of Operations
     • PEMDAS sequence
     • Grouping symbols in mixed expressions
   • Rounding and Estimation
     • Rounding to nearest ten, hundred, thousand
     • Estimating sums and products for quick checks
2. 2

   Fractions, Decimals, and Percentages

   4 topics

   • Working with Fractions
     • Simplifying and finding common denominators
     • Adding, subtracting, multiplying, dividing fractions
     • Mixed numbers and improper fractions
   • Decimal Operations
     • Place value and aligning decimal points
     • Decimal multiplication and division
   • Converting Between Forms
     • Fraction to decimal to percent conversions
   • Percentage Calculations
     • Finding a percent of a number
     • Percent increase and decrease
     • Determining the whole from a part and percent
3. 3

   Word Problems and Applied Reasoning

   4 topics

   • Translating Words into Equations
     • Identifying keywords for operations
     • Setting up one-step and two-step equations
   • Rate, Time, and Distance
     • Speed and travel-time calculations
     • Response and patrol scenario problems
   • Ratios and Proportions
     • Scaling quantities
     • Unit rate problems
   • Money and Measurement Problems
     • Cash handling and change calculations
     • Unit conversions for length, weight, time
4. 4

   Data Interpretation and Basic Statistics

   3 topics

   • Reading Tables and Charts
     • Extracting values from incident logs
     • Comparing rows and columns
   • Graphs and Visual Data
     • Bar and line graph interpretation
     • Pie chart proportions
   • Averages and Central Measures
     • Mean, median, and mode
     • Weighted averages

Mathematics flashcards for National Police Officer Selection Test (NPOST / Stanard & Associates POST)

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. When adding or subtracting multi-digit whole numbers, how should the numbers be arranged?

   Align them vertically by place value (ones under ones, tens under tens, etc.), then add or subtract column by column from right to left, carrying or borrowing as needed.

2. What is 'borrowing' (regrouping) in subtraction?

   When a top digit is smaller than the digit below it, you take 1 from the next-higher place value (worth 10 in the current column) so the subtraction can be completed.

3. What is the commutative property of addition, and does it also apply to subtraction?

   Addition is commutative: a + b = b + a (order doesn't matter). Subtraction is NOT commutative: a - b ≠ b - a in general.

4. How can you check the answer to a subtraction problem (difference) using addition?

   Add the difference to the number you subtracted (the subtrahend); the result should equal the original number (the minuend). E.g., 50 - 18 = 32, and 32 + 18 = 50.

5. What does multiplication represent, and what are the parts of a multiplication problem called?

   Multiplication is repeated addition of equal groups. The numbers multiplied are factors, and the result is the product.

6. In division, what are the dividend, divisor, quotient, and remainder?

   Dividend ÷ divisor = quotient. The dividend is the number being divided, the divisor is what you divide by, the quotient is the result, and the remainder is what is left over.

7. Is multiplication commutative? Is division?

   Multiplication is commutative (a × b = b × a). Division is NOT commutative (a ÷ b ≠ b ÷ a in general).

8. How do you check the answer to a division problem?

   Multiply the quotient by the divisor and add any remainder; the result should equal the dividend. (quotient × divisor) + remainder = dividend.

9. What is the standard order of operations and a common mnemonic for it?

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

10. In order of operations, how do you handle multiplication and division that appear together (and addition and subtraction together)?

    They have equal priority within their pair, so you perform them left to right in the order they appear, not multiplication before division or addition before subtraction.

11. Using order of operations, evaluate 2 + 3 × 4.

    14. Multiplication first (3 × 4 = 12), then add 2, giving 14 — not 20.

12. Using order of operations, evaluate (6 + 2) × 3 - 5.

    19. Parentheses first (8), then 8 × 3 = 24, then 24 - 5 = 19.

13. What is the general rule for rounding a number to a given place value?

    Look at the digit immediately to the right of the rounding place: if it is 5 or more, round the place-value digit up by 1; if it is 4 or less, leave it the same. Replace all digits to the right with zeros.

14. Round 3,847 to the nearest hundred.

    3,800. The digit in the tens place is 4 (less than 5), so the hundreds digit stays 8 and the rest become zeros.

15. What is estimation, and why is it useful on a math test?

    Estimation is finding an approximate answer by rounding numbers to convenient values before calculating. It lets you quickly check if a computed answer is reasonable and eliminate unlikely multiple-choice options.

16. Estimate 297 × 41 by rounding.

    About 12,000. Round to 300 × 40 = 12,000 (the exact answer is 12,177).

17. In a fraction, what do the numerator and denominator represent?

    The denominator (bottom) is the number of equal parts the whole is divided into; the numerator (top) is how many of those parts are being counted.

18. How do you add or subtract fractions?

    Convert them to a common denominator, add or subtract the numerators only, keep the common denominator, then simplify.

19. How do you multiply two fractions?

    Multiply the numerators together and the denominators together (no common denominator needed), then simplify. E.g., 2/3 × 3/4 = 6/12 = 1/2.

20. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal (flip) of the second fraction. E.g., 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.

21. How do you convert an improper fraction to a mixed number?

    Divide the numerator by the denominator; the whole-number quotient is the whole part, the remainder becomes the new numerator over the same denominator. E.g., 11/4 = 2 3/4.

See more Mathematics flashcards →

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