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SSC MTS (Multi-Tasking Staff) Numerical and Mathematical Ability Syllabus

The Numerical and Mathematical Ability syllabus for SSC MTS (Multi-Tasking Staff) in full: 6 chapters, 20 topics and 50 sub-topics, every one listed below, plus 50 Numerical and Mathematical Ability flashcards with answers.

6Chapters
20Topics
50Sub-topics
50Flashcards

Numerical and Mathematical Ability syllabus: all 6 chapters

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

  1. Number System and Arithmetic Fundamentals

     4 topics
    • Whole Numbers and Integers
      • Place value and face value
      • Operations on integers and order of operations (BODMAS)
      • Properties of numbers (even, odd, prime, composite)
    • Fractions and Decimals
      • Conversion between fractions and decimals
      • Comparison and ordering of fractions
      • Operations on decimal numbers
    • LCM and HCF
      • Prime factorisation method
      • Division method
      • Relation between LCM, HCF and product of numbers
    • Divisibility and Simplification
      • Divisibility rules
      • Simplification using BODMAS
      • Approximation

  2. Ratio, Proportion, Percentage and Average

     3 topics
    • Ratio and Proportion
      • Simple and compound ratios
      • Direct and inverse proportion
      • Partnership and division of amounts
    • Percentage
      • Conversion among percentage, fraction and ratio
      • Percentage increase and decrease
      • Successive percentage change
    • Average
      • Average of numbers and quantities
      • Weighted average
      • Change in average on adding or removing data

  3. Commercial Mathematics

     3 topics
    • Profit, Loss and Discount
      • Cost price, selling price and marked price
      • Profit and loss percentage
      • Successive discounts
    • Simple Interest
      • Principal, rate, time and amount
      • Calculation of interest over periods
    • Compound Interest
      • Annual and half-yearly compounding
      • Difference between simple and compound interest

  4. Time, Work, Speed and Distance

     3 topics
    • Time and Work
      • Individual and combined work rates
      • Efficiency and wages distribution
    • Pipes and Cisterns
      • Inlet and outlet pipe rates
      • Combined filling and emptying
    • Time, Speed and Distance
      • Average speed and relative speed
      • Problems on trains
      • Boats and streams

  5. Mensuration, Geometry and Algebra

     4 topics
    • Plane Figures
      • Area and perimeter of triangle, rectangle and square
      • Area and circumference of circle
      • Parallelogram, rhombus and trapezium
    • Solid Figures
      • Volume and surface area of cube and cuboid
      • Cylinder, cone and sphere
    • Basic Geometry
      • Lines, angles and triangles
      • Properties of polygons
    • Elementary Algebra and Powers
      • Linear equations in one variable
      • Squares, cubes and their roots

  6. Data Interpretation

     3 topics
    • Graphical Data
      • Bar graphs
      • Line graphs
    • Pictorial and Tabular Data
      • Pie charts
      • Tables and frequency data
    • Use of Tables and Graphs
      • Reading and interpreting data
      • Calculations based on data sets

SSC MTS (Multi-Tasking Staff) Numerical and Mathematical Ability flashcards — 50 questions with answers

  1. What are whole numbers, and what is the smallest whole number?

    Whole numbers are the set of natural numbers together with zero: {0, 1, 2, 3, ...}. The smallest whole number is 0. There is no largest whole number.

  2. What are integers, and how do they differ from whole numbers?

    Integers are the set {..., -3, -2, -1, 0, 1, 2, 3, ...}, including negative numbers, zero, and positive numbers. Unlike whole numbers, integers include negatives.

  3. State the rules for the sign of a product/quotient of two integers.

    Same signs give a positive result (+×+ = +, -×- = +); different signs give a negative result (+×- = -, -×+ = -). The same rules apply to division.

  4. What is the sum of the first n natural numbers?

    Sum = n(n+1)/2. For example, the sum of 1 to 100 = 100×101/2 = 5050.

  5. What is the sum of the squares and the sum of the cubes of the first n natural numbers?

    Sum of squares = n(n+1)(2n+1)/6. Sum of cubes = [n(n+1)/2]^2 (i.e., the square of the sum of the first n numbers).

  6. How do you convert a fraction to a decimal, and a terminating decimal to a fraction?

    Divide numerator by denominator to get a decimal. To convert a decimal to a fraction, write the decimal over a power of 10 (e.g., 0.75 = 75/100 = 3/4) and simplify.

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

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

  8. How do you compare two fractions like 3/7 and 4/9?

    Cross-multiply: compare 3×9 = 27 with 4×7 = 28. The fraction whose numerator product is larger is greater, so 4/9 > 3/7.

  9. What is the rule for multiplying and dividing decimals?

    To multiply, ignore decimal points, multiply as whole numbers, then place the decimal point so the total decimal places equal the sum of decimal places in the factors. To divide, shift the decimal in divisor and dividend equally to make the divisor whole.

  10. What is the LCM (Least Common Multiple) of two or more numbers?

    The LCM is the smallest positive number that is exactly divisible by each of the given numbers.

  11. What is the HCF (Highest Common Factor / GCD) of two or more numbers?

    The HCF is the largest number that divides each of the given numbers exactly (without remainder).

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

    Product of two numbers = HCF × LCM. So LCM × HCF = a × b, useful for finding one quantity when the others are known.

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

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

  14. State the divisibility rules for 2, 3, 4, and 5.

    Divisible by 2 if last digit is even; by 3 if digit sum is divisible by 3; by 4 if last two digits form a number divisible by 4; by 5 if last digit is 0 or 5.

  15. State the divisibility rules for 6, 8, 9, and 10.

    Divisible by 6 if divisible by both 2 and 3; by 8 if last three digits are divisible by 8; by 9 if digit sum is divisible by 9; by 10 if last digit is 0.

  16. State 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.

  17. State the BODMAS/order of operations rule for simplification.

    Solve in order: Brackets, Of (or Orders/powers), Division, Multiplication, Addition, Subtraction. Within brackets, do ( ), { }, [ ] from innermost outward.

  18. What is a ratio, and what does the ratio a:b mean?

    A ratio compares two quantities of the same kind by division. a:b means a/b, indicating how many times one quantity contains the other. It has no units.

  19. What is a proportion, and what is the key cross-multiplication property?

    A proportion states two ratios are equal: a:b = c:d (or a/b = c/d). Then a×d = b×c. Here a and d are extremes, b and c are means; product of extremes = product of means.

  20. What are mean proportional and third proportional?

    For a:b = b:c, b is the mean proportional, so b = sqrt(a×c). The third proportional to a and b is the value c such that a:b = b:c, giving c = b^2/a.

Show the other 30 Numerical and Mathematical Ability flashcards

  1. Define direct proportion and inverse proportion.

    In direct proportion, as one quantity increases the other increases proportionally (x/y is constant). In inverse proportion, as one increases the other decreases proportionally (x×y is constant).

  2. How do you divide a quantity in a given ratio a:b:c?

    Add the ratio parts (a+b+c), then each share = (its part / total parts) × total quantity. E.g., dividing 600 in 1:2:3 gives 100, 200, 300.

  3. What is percentage, and how do you convert a fraction to a percentage and back?

    Percentage means 'per hundred'. To convert a fraction to percent, multiply by 100 (e.g., 1/4 = 25%). To convert percent to fraction, divide by 100 (e.g., 40% = 40/100 = 2/5).

  4. How do you find x% of a number N, and what percent is A of B?

    x% of N = (x/100) × N. A as a percent of B = (A/B) × 100%.

  5. What is the formula for percentage increase and percentage decrease?

    Percentage increase = (Increase/Original) × 100%. Percentage decrease = (Decrease/Original) × 100%, where the original (initial) value is the base.

  6. 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 successive changes of a% and b%, net % change = a + b + (ab/100), with decreases taken as negative.

  7. What is the average (arithmetic mean) of a set of numbers?

    Average = (Sum of all observations) / (Number of observations). Conversely, Sum = Average × Number of observations.

  8. What is the average of the first n natural numbers, and of n consecutive numbers?

    Average of first n natural numbers = (n+1)/2. The average of any set of consecutive (evenly spaced) numbers equals the average of the first and last terms: (first+last)/2.

  9. How does adding/removing a member change an average (replacement rule)?

    If a new value replaces an old one, the change in total = new value - old value, and change in average = (that difference)/(number of items). New sum = old average × old count ± adjustment.

  10. Define cost price, selling price, profit, and loss.

    Cost Price (CP) is the buying price; Selling Price (SP) is the selling price. If SP > CP, Profit = SP - CP; if SP < CP, Loss = CP - SP.

  11. What are the formulas for profit percent and loss percent?

    Profit% = (Profit/CP) × 100. Loss% = (Loss/CP) × 100. The cost price is always the base for these percentages.

  12. How do you find SP from CP given a profit% or loss%?

    SP = CP × (100 + Profit%)/100 for a profit; SP = CP × (100 - Loss%)/100 for a loss.

  13. How do you find CP from SP given a profit% or loss%?

    CP = SP × 100/(100 + Profit%) for a profit; CP = SP × 100/(100 - Loss%) for a loss.

  14. Define marked price (list price) and discount.

    Marked Price (MP) is the labeled/list price before reduction. Discount is a reduction on the MP. Discount = MP - SP, and Discount% = (Discount/MP) × 100 (MP is the base).

  15. What is the relationship between Marked Price, Discount%, and Selling Price?

    SP = MP × (100 - Discount%)/100. The discount is always calculated on the marked price, not the cost price.

  16. What is the net effect of two successive discounts of x% and y%?

    Equivalent single discount = x + y - (xy/100) percent. The combined discount is always less than the simple sum x + y.

  17. What is the formula for Simple Interest?

    Simple Interest (SI) = (P × R × T)/100, where P = principal, R = rate of interest per annum, T = time in years.

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

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

  19. In simple interest, how do you find the rate or time from SI?

    R = (SI × 100)/(P × T) and T = (SI × 100)/(P × R). Rearrange the formula SI = PRT/100 for the unknown.

  20. At what does money double under simple interest at rate R%?

    Money doubles when SI = P, so PRT/100 = P, giving T = 100/R years. To triple, SI = 2P, so T = 200/R years.

  21. What is the formula for Compound Interest (compounded annually)?

    Amount A = P(1 + R/100)^T, and Compound Interest CI = A - P = P[(1 + R/100)^T - 1], where T is the number of years.

  22. How is the amount formula adjusted for half-yearly and quarterly compounding?

    Half-yearly: A = P(1 + (R/2)/100)^(2T). Quarterly: A = P(1 + (R/4)/100)^(4T). The rate is divided and the number of periods is multiplied accordingly.

  23. For 2 years, what is the difference between Compound Interest and Simple Interest on principal P?

    Difference (CI - SI) for 2 years = P × (R/100)^2. This is the interest on the first year's interest.

  24. Why is compound interest greater than simple interest for the same P, R, and T (T>1)?

    In compound interest, interest is calculated on the accumulated amount (principal plus past interest), so interest earns interest. In simple interest, interest is always on the original principal only.

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

    One day's work = 1/n of the total work. Conversely, if one day's work is 1/n, the whole work takes n days.

  26. If A does a work in 'a' days and B in 'b' days, how long do they take together?

    Combined one-day work = 1/a + 1/b. Time taken together = (a×b)/(a+b) days.

  27. State the work equivalence formula relating men, days, and hours for two work scenarios.

    (M1 × D1 × H1)/W1 = (M2 × D2 × H2)/W2, where M = men, D = days, H = hours/day, W = work done. Used to compare two situations.

  28. How does efficiency relate to time taken in Time and Work problems?

    Efficiency is inversely proportional to time: a more efficient worker takes less time. If A is twice as efficient as B, A takes half the time B takes to do the same work.

  29. In Pipes and Cisterns, how are inlet and outlet pipes represented?

    An inlet pipe fills the tank, so its work is positive (+1/x per hour). An outlet (leak/emptying) pipe drains it, so its work is negative (-1/y per hour).

  30. If an inlet fills a tank in x hours and an outlet empties it in y hours, what is the net time to fill when both are open?

    Net filling rate = 1/x - 1/y per hour. Time to fill = (x×y)/(y - x) hours, valid when y > x (so the tank actually fills).

SSC MTS (Multi-Tasking Staff) Numerical and Mathematical Ability FAQ

What is in the SSC MTS (Multi-Tasking Staff) Numerical and Mathematical Ability syllabus?

SSC MTS (Multi-Tasking Staff) Numerical and Mathematical Ability is split into 6 chapters: Number System and Arithmetic Fundamentals, Ratio, Proportion, Percentage and Average, Commercial Mathematics, Time, Work, Speed and Distance, Mensuration, Geometry and Algebra and Data Interpretation. Together they contain 20 topics and 50 sub-topics.

How many chapters are in SSC MTS (Multi-Tasking Staff) Numerical and Mathematical Ability?

6 chapters, containing 20 topics and 50 sub-topics. The largest chapter is Number System and Arithmetic Fundamentals, with 4 topics.

Are there flashcards for SSC MTS (Multi-Tasking Staff) Numerical and Mathematical Ability?

Yes — a 50-card Numerical and Mathematical Ability 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.