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Army Clerk Test Mathematics Syllabus

The Mathematics syllabus for Army Clerk Test in full: 7 chapters and 24 topics, every one listed below, plus 50 Mathematics flashcards with answers.

7Chapters
24Topics
50Flashcards

Mathematics syllabus: all 7 chapters

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

  1. Arithmetic

     4 topics
    • Number System
    • HCF and LCM
    • Fractions and Decimals
    • Simplification (BODMAS)

  2. Ratio, Proportion and Percentage

     3 topics
    • Ratio and Proportion
    • Percentage
    • Average

  3. Profit, Loss and Interest

     4 topics
    • Profit and Loss
    • Discount
    • Simple Interest
    • Compound Interest

  4. Time, Work and Distance

     3 topics
    • Time and Work
    • Time, Speed and Distance
    • Pipes and Cisterns

  5. Algebra

     3 topics
    • Algebraic Expressions
    • Linear Equations
    • Factorization

  6. Geometry and Mensuration

     4 topics
    • Lines and Angles
    • Triangles and Quadrilaterals
    • Area and Perimeter
    • Volume and Surface Area

  7. Unitary Method and Partnership

     3 topics
    • Unitary Method
    • Partnership
    • Ages Problems

Army Clerk Test Mathematics flashcards — 50 questions with answers

  1. What is a natural number?

    Counting numbers starting from 1: 1, 2, 3, 4, ... They do not include 0, negatives, or fractions.

  2. What is a whole number?

    All natural numbers together with 0: 0, 1, 2, 3, 4, ... Every natural number is a whole number, but 0 is whole and not natural.

  3. What is a prime number? Give the smallest one.

    A number greater than 1 having exactly two factors, 1 and itself. The smallest prime is 2, which is also the only even prime.

  4. How many prime numbers are there between 1 and 50?

    15 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

  5. What is a composite number?

    A natural number greater than 1 that has more than two factors (i.e., divisible by numbers other than 1 and itself). Example: 4, 6, 8, 9. Note: 1 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. Example: 123 (1+2+3=6, 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. Example: 729 (7+2+9=18, 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 places and the sum of digits in even places 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. What is the HCF (Highest Common Factor) of two numbers?

    The largest number that divides both numbers exactly without leaving a remainder. Also called GCD (Greatest Common Divisor).

  11. What is the LCM (Lowest Common Multiple) of two numbers?

    The smallest number that is exactly divisible by both numbers (the smallest common multiple).

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

    Product of two numbers = HCF x LCM. So one number = (HCF x LCM) / other number.

  13. Find the HCF and LCM of 12 and 18.

    HCF = 6, LCM = 36. Check: 12 x 18 = 216 = 6 x 36.

  14. How do you find the HCF of fractions?

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

  15. How do you find the LCM of fractions?

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

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

    Proper fraction: numerator < denominator (e.g., 3/5). Improper fraction: numerator >= denominator (e.g., 7/4).

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

    Divide the numerator by the denominator. Example: 3/4 = 3 divided by 4 = 0.75.

  18. How do you convert the decimal 0.25 to a fraction?

    Write it as 25/100, then simplify to 1/4.

  19. How do you add or subtract fractions with different denominators?

    Find the LCM of the denominators (common denominator), convert each fraction to that denominator, then add/subtract the numerators.

  20. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal (inverse) of the second. Example: (2/3) / (4/5) = (2/3) x (5/4) = 10/12 = 5/6.

Show the other 30 Mathematics flashcards

  1. What does BODMAS stand for and in what order are operations performed?

    Brackets, Of, Division, Multiplication, Addition, Subtraction. Solve brackets first, then 'of', then division and multiplication (left to right), then addition and subtraction (left to right).

  2. In BODMAS, solve: 8 + 2 x 5.

    18. Multiplication first (2 x 5 = 10), then addition (8 + 10 = 18).

  3. In BODMAS, what is the order of brackets to be removed?

    From innermost to outermost: first ( ) parentheses, then { } curly braces, then [ ] square brackets.

  4. What is a ratio?

    A comparison of two quantities of the same kind by division, written a:b or a/b. It has no units.

  5. What is a proportion?

    A statement that two ratios are equal, written a:b = c:d (or a:b::c:d). Here a and d are extremes, b and c are means.

  6. What is the key rule of proportion (product of means and extremes)?

    In a proportion a:b = c:d, the product of the extremes equals the product of the means: a x d = b x c (cross multiplication).

  7. If a:b = 2:3 and b:c = 4:5, what is a:b:c?

    a:b:c = 8:12:15. (Make b common: 2:3 = 8:12 and 4:5 = 12:15.)

  8. What is the formula to convert a fraction or ratio into a percentage?

    Percentage = (value / total) x 100. Example: 3/4 = (3/4) x 100 = 75%.

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

    Divide the percentage by 100 and simplify. Example: 40% = 40/100 = 2/5.

  10. If a quantity increases from 50 to 60, what is the percentage increase?

    20%. Increase = 10; percentage increase = (10/50) x 100 = 20%.

  11. What is the formula for percentage change (increase or decrease)?

    Percentage change = (Change in value / Original value) x 100.

  12. What is the formula for the average (mean) of a set of numbers?

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

  13. Find the average of 10, 20, 30, 40, 50.

    30. Sum = 150; 150 / 5 = 30.

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

    Average = (n + 1) / 2.

  15. If the average of 5 numbers is 20, what is their total sum?

    100. Sum = Average x Count = 20 x 5 = 100.

  16. What are the formulas for Profit and Loss?

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

  17. What is the formula for Profit Percentage?

    Profit % = (Profit / Cost Price) x 100. Profit percent is always calculated on the cost price.

  18. What is the formula for Loss Percentage?

    Loss % = (Loss / Cost Price) x 100. Loss percent is always calculated on the cost price.

  19. How do you find Selling Price (SP) from Cost Price (CP) and Profit %?

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

  20. An article bought for Rs. 200 is sold for Rs. 250. Find the profit percent.

    25%. Profit = 50; Profit% = (50/200) x 100 = 25%.

  21. What is Discount and on what is it calculated?

    Discount is a reduction given on the Marked Price (MP), also called list price. Discount = MP - SP, and it is calculated on the marked price, not the cost price.

  22. What is the formula for Selling Price after a discount?

    SP = MP x (100 - Discount%) / 100, where MP is the Marked Price.

  23. An item marked at Rs. 500 is sold at a 20% discount. Find the selling price.

    Rs. 400. Discount = 20% of 500 = 100; SP = 500 - 100 = 400.

  24. What is the formula for Simple Interest (SI)?

    SI = (P x R x T) / 100, where P = Principal, R = Rate per annum, T = Time in years.

  25. What is the formula for the Amount in Simple Interest?

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

  26. Find the simple interest on Rs. 1000 at 5% per annum for 2 years.

    Rs. 100. SI = (1000 x 5 x 2) / 100 = 100.

  27. What is the formula for the Amount in Compound Interest (compounded annually)?

    Amount = P(1 + R/100)^T, where P = Principal, R = Rate per annum, T = Time in years. Compound Interest = Amount - P.

  28. What is the key difference between Simple Interest and Compound Interest?

    Simple Interest is calculated only on the original principal each year. Compound Interest is calculated on the principal plus accumulated interest, so it grows faster.

  29. What is the basic relationship between work, time and rate in Time and Work problems?

    If a person completes a work in n days, their one day's work (rate) = 1/n. Total work is taken as 1 unit.

  30. If A can do a work in 10 days and B in 15 days, how long do they take together?

    6 days. Combined one day's work = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so together they finish in 6 days.

Army Clerk Test Mathematics FAQ

What is in the Army Clerk Test Mathematics syllabus?

Army Clerk Test Mathematics is split into 7 chapters: Arithmetic, Ratio, Proportion and Percentage, Profit, Loss and Interest, Time, Work and Distance, Algebra, Geometry and Mensuration and Unitary Method and Partnership. Together they contain 24 topics.

How many chapters are in Army Clerk Test Mathematics?

7 chapters, containing 24 topics. The largest chapter is Arithmetic, with 4 topics.

Are there flashcards for Army Clerk 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.