ParaProfessional / Clerical civil service tests (state & local) Mathematics & Quantitative Reasoning Syllabus

Mathematics & 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 & Quantitative Reasoning in ParaProfessional / Clerical civil service tests (state & local), not a summary of it.

1. 1

   Arithmetic Computation

   4 topics

   • Whole Number Operations
   • Fractions and Mixed Numbers
   • Decimals and Rounding
   • Order of Operations
2. 2

   Percentages, Ratios & Proportions

   3 topics

   • Percent Calculations and Conversions
     • Percent of a number
     • Percent increase and decrease
   • Ratio and Proportion Problems
   • Averages and Weighted Averages
3. 3

   Practical & Word Problems

   4 topics

   • Money, Wages, and Payroll Computations
   • Discounts, Markups, and Sales Tax
   • Time, Rate, and Distance
   • Unit Conversions and Measurement
4. 4

   Data Interpretation

   4 topics

   • Reading Tables and Charts
   • Bar, Line, and Pie Graphs
   • Drawing Conclusions from Data
   • Estimation and Reasonableness Checks

Mathematics & Quantitative Reasoning flashcards for ParaProfessional / Clerical civil service tests (state & local)

24 of 51 cards from the Mathematics & Quantitative Reasoning deck — real questions with worked answers.

1. What are the four basic whole number operations, and which one is repeated addition?

   Addition, subtraction, multiplication, and division. Multiplication is repeated addition (e.g., 4 x 3 = 3 + 3 + 3 + 3).

2. When adding or subtracting multi-digit whole numbers by hand, how should the numbers be aligned?

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

3. What is the result of dividing any nonzero whole number by itself, and what is any number divided by zero?

   A number divided by itself equals 1. Division by zero is undefined.

4. In the division 47 / 5, what is the quotient and the remainder?

   Quotient 9, remainder 2 (since 5 x 9 = 45, and 47 - 45 = 2).

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

   Divide the numerator by the denominator; the quotient is the whole number, the remainder becomes the new numerator over the same denominator. Example: 17/5 = 3 2/5.

6. What is the rule for adding or subtracting fractions with unlike denominators?

   Find a common denominator (often the least common denominator), rewrite each fraction with it, then add or subtract the numerators and keep the denominator.

7. 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.

8. How do you divide one fraction by another?

   Multiply the first fraction by the reciprocal of the second (invert and multiply). Example: 1/2 / 3/4 = 1/2 x 4/3 = 4/6 = 2/3.

9. How do you convert a mixed number such as 4 3/8 into an improper fraction?

   Multiply the whole number by the denominator, add the numerator, and place over the denominator: (4 x 8 + 3)/8 = 35/8.

10. What does the place value to the right of the decimal point represent in 0.7, 0.07, and 0.007?

    0.7 is seven tenths, 0.07 is seven hundredths, and 0.007 is seven thousandths.

11. How do you round 6.748 to the nearest tenth?

    Look at the hundredths digit (4); since it is less than 5, round down, keeping the tenths digit: 6.7.

12. When multiplying decimals, how do you place the decimal point in the answer?

    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. How do you divide by a decimal, such as 4.5 / 0.5?

    Move the decimal point in the divisor to make it a whole number and move the dividend's decimal the same number of places, then divide: 45 / 5 = 9.

14. State the standard order of operations (PEMDAS).

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

15. Evaluate 8 + 2 x 5 using the order of operations.

    18. Multiply first (2 x 5 = 10), then add 8, giving 18 (not 50).

16. Evaluate (6 + 4) / 2 + 3^2 using the order of operations.

    14. Parentheses: 10/2 = 5; exponent: 3^2 = 9; then 5 + 9 = 14.

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

    Percent to decimal: divide by 100 (move decimal two places left), e.g., 35% = 0.35. Decimal to percent: multiply by 100 (move two places right), e.g., 0.4 = 40%.

18. How do you find a percent of a number, for example 20% of 150?

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

19. 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.

20. A price rises from $40 to $50. What is the percent increase?

    25%. Change is $10; 10/40 = 0.25 = 25%.

21. How do you convert the fraction 3/8 to a percent?

    Divide 3 by 8 to get 0.375, then multiply by 100: 37.5%.

22. What is a ratio, and how is the ratio 12 to 8 simplified?

    A ratio compares two quantities. 12 to 8 simplifies to 3 to 2 by dividing both terms by their greatest common factor (4).

23. What defines a proportion, and how do you solve one using cross multiplication?

    A proportion states two ratios are equal (a/b = c/d). Cross multiply: a x d = b x c, then solve for the unknown.

24. Solve the proportion 3/4 = x/20 for x.

    x = 15. Cross multiply: 4x = 60, so x = 15.

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