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

Numerical and Mathematical Ability syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Numerical and Mathematical Ability in SSC MTS (Multi-Tasking Staff), not a summary of it.

1. 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. 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. 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. 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. 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. 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

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

23 of 50 cards from the Numerical and Mathematical Ability deck — real questions with worked 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.

21. 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).

22. 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.

23. 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).

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