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Police Constable Test Mathematics Syllabus

The Mathematics syllabus for Police Constable Test in full: 5 chapters and 21 topics, every one listed below, plus 50 Mathematics flashcards with answers.

5Chapters
21Topics
50Flashcards

Mathematics syllabus: all 5 chapters

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

  1. Arithmetic

     5 topics
    • Number System
    • HCF and LCM
    • Fractions and Decimals
    • Simplification
    • Square Roots and Cube Roots

  2. Commercial Mathematics

     6 topics
    • Percentage
    • Profit and Loss
    • Ratio and Proportion
    • Average
    • Simple Interest
    • Discount

  3. Time, Distance and Work

     3 topics
    • Time and Work
    • Time, Speed and Distance
    • Trains and Boats

  4. Basic Algebra and Geometry

     4 topics
    • Linear Equations
    • Perimeter and Area
    • Volume and Surface Area
    • Angles and Triangles

  5. Data Interpretation

     3 topics
    • Tables
    • Bar Graphs and Pie Charts
    • Basic Statistics

Police Constable Test Mathematics flashcards — 50 questions with answers

  1. What is a natural number?

    A counting number starting from 1: 1, 2, 3, 4, ... (positive integers). The set is denoted N.

  2. What is the difference between whole numbers and natural numbers?

    Whole numbers include 0 along with all natural numbers (0, 1, 2, 3, ...), whereas natural numbers begin at 1.

  3. Define a prime number and give the smallest prime.

    A prime number has exactly two distinct factors: 1 and itself. The smallest prime is 2, which is also the only even prime.

  4. What is a composite number?

    A natural number greater than 1 that has more than two factors (i.e., it is divisible by numbers other than 1 and itself), e.g., 4, 6, 8, 9.

  5. Is 1 prime, composite, or neither?

    Neither. 1 has only one factor (itself), so it is neither prime nor composite.

  6. What is the divisibility rule for 3?

    A number is divisible by 3 if the sum of its digits is divisible by 3.

  7. What is the divisibility rule for 9?

    A number is divisible by 9 if the sum of its digits is divisible by 9.

  8. What is the divisibility rule for 11?

    A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.

  9. What is the divisibility rule for 4 and for 8?

    Divisible by 4 if the last two digits form a number divisible by 4; divisible by 8 if the last three digits form a number divisible by 8.

  10. Define HCF (Highest Common Factor).

    The HCF (or GCD) of two or more numbers is the largest number that divides each of them exactly without leaving a remainder.

  11. Define LCM (Least Common Multiple).

    The LCM of two or more numbers is the smallest number that is exactly divisible by each of them.

  12. What is the relationship between HCF, LCM and two numbers?

    Product of two numbers = HCF x LCM. So for numbers a and b: a x b = HCF(a,b) x LCM(a,b).

  13. How do you find HCF and LCM of fractions?

    HCF of fractions = HCF of numerators / LCM of denominators. LCM of fractions = LCM of numerators / HCF of denominators.

  14. For two co-prime numbers, what is their HCF and LCM?

    Co-prime numbers have HCF = 1, and their LCM equals the product of the two numbers.

  15. What is a proper fraction versus an improper fraction?

    A proper fraction has numerator less than denominator (e.g., 3/4); an improper fraction has numerator greater than or equal to denominator (e.g., 5/3).

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

    Divide the numerator by the denominator. For example, 3/4 = 3 divided by 4 = 0.75.

  17. How do you convert a recurring decimal like 0.333... to a fraction?

    For a single repeating digit, the fraction is that digit over 9. So 0.333... = 3/9 = 1/3.

  18. How do you compare two fractions such as 3/5 and 4/7?

    Cross-multiply: compare 3x7=21 with 4x5=20. Since 21 > 20, 3/5 > 4/7.

  19. What is the BODMAS / order of operations rule?

    Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

  20. In BODMAS, how are multiplication and division handled?

    They have equal priority and are performed from left to right in the order they appear, not multiplication always before division.

Show the other 30 Mathematics flashcards

  1. What is a perfect square? Give examples.

    A number that is the square of an integer, e.g., 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

  2. What is the square root of 144 and of 169?

    The square root of 144 is 12; the square root of 169 is 13.

  3. What is a perfect cube? Give examples.

    A number that is the cube of an integer, e.g., 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.

  4. What is the cube root of 343 and of 512?

    The cube root of 343 is 7; the cube root of 512 is 8.

  5. How do you simplify the square root of a product, e.g., sqrt(50)?

    Factor out the largest perfect square: sqrt(50) = sqrt(25 x 2) = 5 x sqrt(2).

  6. What does 'percent' mean and how is x% written as a fraction?

    Percent means 'per hundred'. x% = x/100. For example, 25% = 25/100 = 1/4.

  7. How do you convert a fraction to a percentage?

    Multiply the fraction by 100. For example, 3/4 = (3/4) x 100 = 75%.

  8. What is the formula for percentage increase?

    Percentage increase = (Increase / Original value) x 100.

  9. If a value increases by x% then decreases by x%, what is the net change?

    There is a net decrease of (x^2/100)%. For example, +20% then -20% gives a net 4% decrease.

  10. What is the formula for Profit and for Loss?

    Profit = Selling Price (SP) - Cost Price (CP), when SP > CP. Loss = CP - SP, when CP > SP.

  11. What is the formula for Profit percent and Loss percent?

    Profit% = (Profit / CP) x 100; Loss% = (Loss / CP) x 100. Both are always calculated on the Cost Price.

  12. How do you find SP from CP and profit percent?

    SP = CP x (100 + Profit%) / 100. For a loss, SP = CP x (100 - Loss%) / 100.

  13. How do you find CP from SP and profit percent?

    CP = SP x 100 / (100 + Profit%). For a loss, CP = SP x 100 / (100 - Loss%).

  14. What is a ratio?

    A ratio is a comparison of two quantities of the same kind by division, written a : b, indicating how many times one is of the other.

  15. What is a proportion?

    A proportion is an equality of two ratios: a : b = c : d, meaning a/b = c/d. Here a and d are extremes, b and c are means.

  16. In a proportion a : b = c : d, what is the key property?

    Product of extremes = product of means, i.e., a x d = b x c (cross-multiplication).

  17. How do you divide a quantity in the ratio a : b?

    Total parts = a + b. First share = (a / (a+b)) x Total; second share = (b / (a+b)) x Total.

  18. What is the mean proportional between two numbers a and b?

    The mean proportional is sqrt(a x b), the square root of their product.

  19. What is the formula for average (arithmetic mean)?

    Average = (Sum of all observations) / (Number of observations).

  20. How do you find the total from average and number of items?

    Sum = Average x Number of items.

  21. What is the average of the first n natural numbers?

    Average = (n + 1) / 2.

  22. What is the formula for Simple Interest?

    SI = (P x R x T) / 100, where P = principal, R = rate percent per annum, T = time in years.

  23. What is the formula for Amount in simple interest?

    Amount = Principal + Simple Interest = P + (P x R x T)/100 = P(1 + RT/100).

  24. How do you find the rate R in simple interest?

    R = (SI x 100) / (P x T).

  25. In simple interest, how many years does it take a sum to double at rate R%?

    Time to double = 100 / R years (since SI must equal the principal).

  26. What is discount and on what is it calculated?

    Discount is a reduction given on the Marked Price (MP). It is calculated as a percentage of the Marked Price, not the cost price.

  27. What is the formula relating Selling Price, Marked Price and Discount?

    SP = MP - Discount, and Discount% = (Discount / MP) x 100. So SP = MP x (100 - Discount%)/100.

  28. If a person can do a work in n days, how much work is done in one day?

    One day's work = 1/n of the total work.

  29. If A does a work in x days and B in y days, in how many days do they finish together?

    Together they take (x x y) / (x + y) days, since combined one-day work = 1/x + 1/y.

  30. State the Work = Rate x Time relationship and the M.D.H formula for work.

    Work done is proportional to (Men x Days x Hours). If work is equal: (M1 x D1 x H1)/W1 = (M2 x D2 x H2)/W2.

Police Constable Test Mathematics FAQ

What is in the Police Constable Test Mathematics syllabus?

Police Constable Test Mathematics is split into 5 chapters: Arithmetic, Commercial Mathematics, Time, Distance and Work, Basic Algebra and Geometry and Data Interpretation. Together they contain 21 topics.

How many chapters are in Police Constable Test Mathematics?

5 chapters, containing 21 topics. The largest chapter is Commercial Mathematics, with 6 topics.

Are there flashcards for Police Constable Test 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.