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

The Mathematics syllabus for National Police Officer Selection Test (NPOST / Stanard & Associates POST) in full: 4 chapters, 15 topics and 33 sub-topics, every one listed below, plus 50 Mathematics flashcards with answers.

4Chapters
15Topics
33Sub-topics
50Flashcards

Mathematics syllabus: all 4 chapters

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

  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. 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. 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. 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

National Police Officer Selection Test (NPOST / Stanard & Associates POST) Mathematics flashcards — 50 questions with 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.

Show the other 30 Mathematics flashcards

  1. 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.

  2. How do you simplify (reduce) a fraction to lowest terms?

    Divide both the numerator and denominator by their greatest common factor. E.g., 8/12 ÷ 4/4 = 2/3.

  3. How do you align numbers when adding or subtracting decimals?

    Line up the decimal points vertically (so matching place values align), fill in zeros if needed, then add or subtract and bring the decimal point straight down into the answer.

  4. How do you place the decimal point when multiplying two decimals?

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

  5. How do you divide by a decimal divisor?

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

  6. How do you convert a fraction to a decimal?

    Divide the numerator by the denominator. E.g., 3/4 = 3 ÷ 4 = 0.75.

  7. How do you convert a decimal to a percent, and a percent to a decimal?

    To convert a decimal to a percent, multiply by 100 (move the decimal 2 places right) and add %. To convert a percent to a decimal, divide by 100 (move the decimal 2 places left). E.g., 0.35 = 35%; 35% = 0.35.

  8. How do you convert a percent to a fraction?

    Write the percent over 100 and simplify. E.g., 40% = 40/100 = 2/5.

  9. What is the decimal and fraction equivalent of 50%, 25%, and 75%?

    50% = 0.5 = 1/2; 25% = 0.25 = 1/4; 75% = 0.75 = 3/4.

  10. How do you find a percent of a number (e.g., 'What is 20% of 80')?

    Convert the percent to a decimal and multiply: 0.20 × 80 = 16.

  11. How do you calculate a percent increase or decrease?

    Percent change = (amount of change ÷ original amount) × 100. Use 'increase' if the value went up and 'decrease' if it went down.

  12. A $50 item is discounted 30%. What is the sale price?

    $35. The discount is 0.30 × 50 = $15, so 50 - 15 = $35 (or directly 0.70 × 50 = $35).

  13. How do you find what percent one number is of another (e.g., '15 is what percent of 60')?

    Divide the part by the whole and multiply by 100: (15 ÷ 60) × 100 = 25%.

  14. In word problems, what operations do the keywords 'sum', 'difference', 'product', and 'quotient' indicate?

    Sum = addition, difference = subtraction, product = multiplication, quotient = division.

  15. When translating words to equations, what do 'is', 'of', and 'per' usually indicate?

    'Is' usually means equals (=), 'of' usually means multiply (×), and 'per' usually means divide (÷).

  16. Translate into an equation: 'Five less than twice a number is 11.'

    2n - 5 = 11. ('Twice a number' = 2n, 'five less than' subtracts 5, 'is' = equals.)

  17. What is the distance formula relating rate, time, and distance?

    Distance = Rate × Time (d = r × t).

  18. How do you solve for rate or time given the distance formula?

    Rate = Distance ÷ Time (r = d/t); Time = Distance ÷ Rate (t = d/r).

  19. A car travels 150 miles in 3 hours. What is its average speed?

    50 miles per hour. Rate = distance ÷ time = 150 ÷ 3 = 50 mph.

  20. What is a ratio, and what are common ways to write one?

    A ratio compares two quantities. It can be written as a to b, a:b, or as the fraction a/b.

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

    A proportion states that two ratios are equal (a/b = c/d). Solve it by cross-multiplying: a × d = b × c, then solve for the unknown.

  22. If 3 apples cost $1.50, how much do 7 apples cost (set up and solve the proportion)?

    $3.50. Set 3/1.50 = 7/x, cross-multiply: 3x = 10.50, so x = $3.50.

  23. How many inches are in a foot, feet in a yard, and ounces in a pound?

    12 inches = 1 foot; 3 feet = 1 yard; 16 ounces = 1 pound.

  24. How do you make change correctly (e.g., $20 paid for a $13.45 purchase)?

    Subtract the cost from the amount paid: $20.00 - $13.45 = $6.55 in change.

  25. When reading a data table to answer a question, what should you do first?

    Identify the correct row and column headings (labels and units) so you locate the exact cell where the needed value intersects, and note units before calculating.

  26. On a bar graph, how do you read the value of a given bar?

    Trace from the top of the bar horizontally to the value axis (usually the y-axis) and read the number where it lands, accounting for the scale/interval between gridlines.

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

    A line graph shows change or trends over time. A rising line means the value is increasing; a falling line means it is decreasing; a flat line means no change.

  28. What does a pie (circle) chart represent, and what do all its slices add up to?

    A pie chart shows parts of a whole as proportional slices; all slices together represent 100% (or the full total).

  29. How do you calculate the mean (average) of a set of numbers?

    Add all the values together and divide by how many values there are. Mean = sum of values ÷ number of values.

  30. How do you find the median, mode, and range of a data set?

    Median: order the values and take the middle one (average the two middle values if the count is even). Mode: the value that appears most often. Range: the largest value minus the smallest value.

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

What is in the National Police Officer Selection Test (NPOST / Stanard & Associates POST) Mathematics syllabus?

National Police Officer Selection Test (NPOST / Stanard & Associates POST) Mathematics is split into 4 chapters: Whole Numbers and Basic Operations, Fractions, Decimals, and Percentages, Word Problems and Applied Reasoning and Data Interpretation and Basic Statistics. Together they contain 15 topics and 33 sub-topics.

How many chapters are in National Police Officer Selection Test (NPOST / Stanard & Associates POST) Mathematics?

4 chapters, containing 15 topics and 33 sub-topics. The largest chapter is Whole Numbers and Basic Operations, with 4 topics.

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

Yes — a 50-card Mathematics 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.