The math section of civil service exams does not require algebra, geometry, or statistics. It requires fast, accurate arithmetic applied to realistic workplace scenarios. The same 10 problem types appear on virtually every exam. Learn to recognize and solve them quickly and the math section becomes your highest-scoring section.
All of these must be done without a calculator. Practice them that way from the start.
1. Percentage calculations
The most common math question type. Three variations: finding a percentage of a number (What is 35% of 240?), finding what percentage one number is of another (18 is what percent of 72?), and finding the whole when given a part and percentage (24 is 30% of what?).
Master converting between percentages and decimals instantly. To find 35% of 240: multiply 240 × 0.35 = 84. To find 10% of any number, move the decimal one place left.
2. Percentage change
Formula: (New Value − Old Value) ÷ Old Value × 100. A department's budget increased from $50,000 to $65,000. What is the percentage increase? (65,000 − 50,000) ÷ 50,000 × 100 = 30%.
Watch for "decrease" questions — the formula is the same but the numerator will be negative.
3. Ratio and proportion
Setting up and solving proportions is tested heavily. "If 4 officers can patrol 8 blocks in one hour, how many officers are needed to patrol 20 blocks?" Set up: 4/8 = x/20. Cross-multiply: 8x = 80. Solve: x = 10.
Unit rate problems are a subset: if a supply room stocks 360 pens for 45 employees, how many pens per employee? 360 ÷ 45 = 8 pens per employee.
4. Averages (arithmetic mean)
Sum all values and divide by the count. More challenging average questions give you the average and ask for a missing value. "The average of 5 scores is 82. Four of the scores are 78, 85, 90, and 88. What is the fifth score?" Total must be 82 × 5 = 410. Sum of known scores = 78 + 85 + 90 + 88 = 341. Fifth score = 410 − 341 = 69.
5. Rate, time, and distance
The formula is Distance = Rate × Time (D = RT). "An officer drives 180 miles at 60 mph. How long does the trip take?" T = D ÷ R = 180 ÷ 60 = 3 hours.
Variations include working with different rates for two legs of a trip or two officers traveling toward each other.
6. Work and scheduling problems
"Officer A can complete a task in 4 hours. Officer B can complete the same task in 6 hours. Working together, how long will the task take?" Add their rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of the task per hour. Time = 12/5 = 2.4 hours.
These are rare but high-difficulty questions. Knowing the rate-addition method puts you ahead.
7. Reading tables and charts
Many civil service exams include a table or bar chart followed by 3–5 questions. The math is simple — addition, subtraction, percentage — but the challenge is reading the data correctly under time pressure.
Strategy: read the question first, then find the relevant row/column in the table. Do not read the entire chart first.
8. Fractions and mixed numbers
Adding, subtracting, multiplying, and dividing fractions appear regularly. The most common error is forgetting to find a common denominator before adding or subtracting. Multiplying fractions: multiply numerators and denominators directly. Dividing fractions: multiply by the reciprocal.
9. Unit conversions
"A supply order requires 3.5 gallons of cleaning solution. The solution comes in 32-ounce bottles. How many full bottles are needed?" 3.5 gallons × 128 oz/gallon = 448 oz. 448 ÷ 32 = 14 bottles.
Memorize: 12 inches = 1 foot, 3 feet = 1 yard, 16 ounces = 1 pound, 8 fluid ounces = 1 cup, 4 cups = 1 quart, 4 quarts = 1 gallon.
10. Probability and counting
Basic probability: number of favorable outcomes divided by total possible outcomes. "A bag has 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble?" 3 ÷ 12 = 1/4 = 25%.
These questions are less frequent but straightforward once you recognize the setup. The harder versions involve "and" (multiply probabilities) or "or" (add probabilities) scenarios.