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Army Soldier Test Mathematics Syllabus

The Mathematics syllabus for Army Soldier Test in full: 7 chapters and 23 topics, every one listed below, plus 50 Mathematics flashcards with answers.

7Chapters
23Topics
50Flashcards

Mathematics syllabus: all 7 chapters

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

  1. Arithmetic

     4 topics
    • Whole Numbers and Operations
    • Fractions and Decimals
    • HCF and LCM
    • Square Roots and Cube Roots

  2. Percentage, Profit and Loss

     3 topics
    • Percentage Calculation
    • Profit and Loss
    • Discount and Markup

  3. Ratio, Proportion and Average

     3 topics
    • Ratio and Proportion
    • Direct and Inverse Proportion
    • Average

  4. Interest and Time

     3 topics
    • Simple Interest
    • Time and Work
    • Time, Speed and Distance

  5. Algebra

     3 topics
    • Algebraic Expressions
    • Linear Equations
    • Factorization

  6. Geometry and Mensuration

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

  7. Number System and Sequences

     3 topics
    • Number Series
    • Divisibility Rules
    • Unitary Method

Army Soldier Test Mathematics flashcards — 50 questions with answers

  1. What is a whole number?

    A whole number is any number from the set {0, 1, 2, 3, 4, ...} — all non-negative integers including zero, with no fractions or decimals.

  2. State the correct order of operations (BODMAS).

    Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — performed left to right within the same level.

  3. What is the identity element for addition and for multiplication of whole numbers?

    The additive identity is 0 (n + 0 = n); the multiplicative identity is 1 (n × 1 = n).

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

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

  5. How do you add two fractions with different denominators?

    Find the LCM of the denominators, convert both fractions to that common denominator, then add the numerators and keep the denominator.

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

    In a proper fraction the numerator is less than the denominator (e.g. 3/5); in an improper fraction the numerator is greater than or equal to the denominator (e.g. 7/5).

  7. How do you multiply two decimals such as 0.3 × 0.2?

    Multiply ignoring decimal points (3 × 2 = 6), then place the decimal point so the result has as many decimal digits as both factors combined: 0.3 × 0.2 = 0.06.

  8. What is the HCF (Highest Common Factor) of two numbers?

    The largest number that divides both numbers exactly without leaving a remainder.

  9. What is the LCM (Least Common Multiple) of two numbers?

    The smallest number that is a multiple of both numbers (i.e. exactly divisible by each).

  10. State the relationship between HCF, LCM and two numbers.

    For two numbers a and b: HCF × LCM = a × b.

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

    HCF = 6 and LCM = 36 (check: 6 × 36 = 216 = 12 × 18).

  12. What is the prime factorization method for finding LCM?

    Write each number as a product of primes, then take each prime to its highest power appearing in any number and multiply them together.

  13. What is a square root?

    The square root of a number x is the value that, when multiplied by itself, gives x. For example, √25 = 5 because 5 × 5 = 25.

  14. What is a cube root?

    The cube root of a number x is the value that, when multiplied by itself three times, gives x. For example, ∛27 = 3 because 3 × 3 × 3 = 27.

  15. What is a perfect square? Give the first six.

    A number that is the square of an integer. The first six are 1, 4, 9, 16, 25, 36.

  16. What is a perfect cube? Give the first five.

    A number that is the cube of an integer. The first five are 1, 8, 27, 64, 125.

  17. What is √144?

    12, because 12 × 12 = 144.

  18. How do you write a percentage as a fraction?

    Place the number over 100 and simplify. For example, 25% = 25/100 = 1/4.

  19. What is the formula to find x% of a number N?

    x% of N = (x/100) × N.

  20. Find 15% of 200.

    (15/100) × 200 = 30.

Show the other 30 Mathematics flashcards

  1. How do you express one quantity as a percentage of another?

    Percentage = (part / whole) × 100. For example, 20 out of 50 is (20/50) × 100 = 40%.

  2. What is the formula for profit?

    Profit = Selling Price (SP) − Cost Price (CP), used when SP is greater than CP.

  3. What is the formula for loss?

    Loss = Cost Price (CP) − Selling Price (SP), used when CP is greater than SP.

  4. What is the formula for profit percentage?

    Profit % = (Profit / Cost Price) × 100.

  5. What is the formula for loss percentage?

    Loss % = (Loss / Cost Price) × 100.

  6. How do you find Selling Price from Cost Price and profit percentage?

    SP = CP × (100 + Profit%) / 100.

  7. How do you find Selling Price from Cost Price and loss percentage?

    SP = CP × (100 − Loss%) / 100.

  8. What is markup?

    Markup is the amount added to the cost price to set the marked (list) price: Marked Price = Cost Price + Markup.

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

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

  10. What is the formula for discount amount and final selling price after discount?

    Discount = (Discount% / 100) × Marked Price; Selling Price = Marked Price − Discount.

  11. An item marked at Rs 500 has a 20% discount. What is the selling price?

    Discount = 20% of 500 = 100, so Selling Price = 500 − 100 = Rs 400.

  12. What is a ratio?

    A ratio is a comparison of two quantities of the same kind by division, written as a:b or a/b.

  13. What is a proportion?

    A proportion is a statement that two ratios are equal, written a:b = c:d (or a/b = c/d).

  14. State the rule of cross-multiplication for a proportion a:b = c:d.

    In a proportion a:b = c:d, the product of the means equals the product of the extremes: b × c = a × d.

  15. In the proportion 3:4 = x:12, find x.

    By cross-multiplication, 4x = 3 × 12 = 36, so x = 9.

  16. What is direct proportion?

    Two quantities are in direct proportion when an increase in one causes a proportional increase in the other; their ratio stays constant (y = kx).

  17. What is inverse proportion?

    Two quantities are in inverse proportion when an increase in one causes a proportional decrease in the other; their product stays constant (xy = k).

  18. Give a real example of inverse proportion.

    Speed and time for a fixed distance: as speed increases, the time taken decreases, since speed × time = distance is constant.

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

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

  20. Find the average of 4, 8, 10, and 14.

    Sum = 36, count = 4, so Average = 36 / 4 = 9.

  21. How do you find the total sum if you know the average and number of items?

    Sum = Average × Number of items.

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

    (n + 1) / 2.

  23. What is simple interest?

    Interest calculated only on the original principal for the entire time period, without compounding.

  24. State the formula for simple interest.

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

  25. What is the formula for the total amount in simple interest?

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

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

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

  27. How do you find the principal if SI, rate and time are known?

    P = (SI × 100) / (R × T).

  28. In Time and Work, if a person completes a job in n days, what is their one-day work?

    Their one-day (one unit time) work is 1/n of the total job.

  29. If A does a job in 'a' days and B in 'b' days, how long do they take working together?

    Together their one-day work is (1/a + 1/b), so time taken = ab / (a + b) days.

  30. A can do a job in 10 days and B in 15 days. How long working together?

    Combined one-day work = 1/10 + 1/15 = 1/6, so together they finish in 6 days.

Army Soldier Test Mathematics FAQ

What is in the Army Soldier Test Mathematics syllabus?

Army Soldier Test Mathematics is split into 7 chapters: Arithmetic, Percentage, Profit and Loss, Ratio, Proportion and Average, Interest and Time, Algebra, Geometry and Mensuration and Number System and Sequences. Together they contain 23 topics.

How many chapters are in Army Soldier Test Mathematics?

7 chapters, containing 23 topics. The largest chapter is Arithmetic, with 4 topics.

Are there flashcards for Army Soldier 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.