SSC CHSL (Combined Higher Secondary Level) Quantitative Aptitude Syllabus

Quantitative Aptitude syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Aptitude in SSC CHSL (Combined Higher Secondary Level), not a summary of it.

1. 1

   Number System and Arithmetic Operations

   4 topics

   • Number System
     • Types of numbers and divisibility
     • HCF and LCM
     • Surds and indices
     • Simplification and BODMAS
   • Fractions and Decimals
   • Square Roots and Cube Roots
   • Average
     • Average of numbers and groups
     • Weighted average and replacement
2. 2

   Commercial and Applied Arithmetic

   7 topics

   • Percentage
     • Conversions and applications
     • Successive and net change
   • Ratio and Proportion
     • Simple and compound ratio
     • Partnership
   • Profit, Loss and Discount
     • Cost, marked and selling price
     • Successive discount
   • Simple and Compound Interest
   • Mixture and Alligation
   • Time, Speed and Distance
     • Relative speed
     • Trains, boats and streams
   • Time and Work
     • Work efficiency
     • Pipes and cisterns
3. 3

   Algebra and Elementary Functions

   4 topics

   • Basic Algebraic Identities
     • School-level algebra of polynomials
     • Standard identities and their application
   • Linear Equations
     • Graphs of linear equations in two variables
   • Quadratic Equations
     • Roots and relations
   • Componendo and Dividendo
4. 4

   Geometry and Mensuration

   5 topics

   • Lines, Angles and Triangles
     • Congruence and similarity
     • Centres of a triangle
   • Circles
     • Tangents and chords
     • Cyclic properties
   • Polygons and Quadrilaterals
   • 2D Mensuration
     • Area and perimeter of plane figures
   • 3D Mensuration
     • Cube, cuboid and cylinder
     • Cone, sphere and hemisphere
5. 5

   Trigonometry and Data Interpretation

   4 topics

   • Trigonometric Ratios and Identities
     • Standard angles
     • Complementary angles
   • Heights and Distances
   • Degree and Radian Measures
   • Data Interpretation
     • Bar graphs and histograms
     • Pie charts and line graphs
     • Tables and frequency polygon

Quantitative Aptitude flashcards for SSC CHSL (Combined Higher Secondary Level)

21 of 51 cards from the Quantitative Aptitude deck — real questions with worked answers.

1. What is the place value vs. face value of a digit in a number? Give the rule.

   Face value is the digit itself, regardless of position. Place value $=$ digit $\times$ its positional value. E.g. in $4528$, face value of $5$ is $5$, but its place value is $5 \times 100 = 500$.

2. Define natural numbers, whole numbers, and integers.

   Natural numbers: $1, 2, 3, \dots$ (counting numbers). Whole numbers: $0, 1, 2, 3, \dots$ (naturals plus $0$). Integers: $\dots, -2, -1, 0, 1, 2, \dots$ (whole numbers plus negatives).

3. Distinguish rational and irrational numbers.

   A rational number can be written as $\frac{p}{q}$ with integers $p, q$ and $q \neq 0$ (terminating or recurring decimal). An irrational number cannot, and has a non-terminating, non-repeating decimal, e.g. $\sqrt{2}, \pi$.

4. What is a prime number, and how many even primes exist?

   A prime has exactly two distinct factors: $1$ and itself. The only even prime is $2$; all other primes are odd. ($1$ is neither prime nor composite.)

5. How many prime numbers are there below $100$, and how do you test if $n$ is prime?

   There are $25$ primes below $100$. To test $n$, check divisibility by all primes $\leq \sqrt{n}$; if none divide $n$, it is prime.

6. State the divisibility rules for $2$, $4$, and $8$.

   Divisible by $2$ if last digit is even; by $4$ if the last two digits form a number divisible by $4$; by $8$ if the last three digits form a number divisible by $8$.

7. State the divisibility rules for $3$ and $9$.

   A number is divisible by $3$ if the sum of its digits is divisible by $3$, and by $9$ if the digit sum is divisible by $9$.

8. State 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. State the divisibility rules for $6$, $12$, and $15$.

   Divisible by $6$ if divisible by both $2$ and $3$; by $12$ if divisible by both $3$ and $4$; by $15$ if divisible by both $3$ and $5$ (i.e. divisible by co-prime factors).

10. What does the division algorithm state?

    For dividend $D$, divisor $d$, quotient $q$, remainder $r$: $$D = d \times q + r, \quad 0 \leq r < d.$$

11. Define HCF (GCD) and LCM of two numbers.

    HCF (Highest Common Factor) is the largest number dividing both exactly. LCM (Lowest Common Multiple) is the smallest number that is a multiple of both.

12. State the relationship between HCF and LCM of two numbers $a$ and $b$.

    $$\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b.$$ This holds only for two numbers.

13. How do you find HCF and LCM using prime factorization?

    HCF $=$ product of common prime factors raised to their lowest powers. LCM $=$ product of all prime factors raised to their highest powers.

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

    $$\text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}}, \quad \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}.$$

15. A number leaves the same remainder $r$ when dividing $a$, $b$, $c$. How do you find the largest such divisor?

    Take the HCF of the differences: $$\text{HCF}(a-b,\ b-c,\ c-a).$$ This gives the greatest number leaving the same remainder.

16. Define a surd, and write the general form of an $n$-th order surd.

    A surd is an irrational root of a rational number that cannot be simplified to remove the root, e.g. $\sqrt{2}$. General form: $\sqrt[n]{a}$ where $a$ is rational and $\sqrt[n]{a}$ is irrational.

17. What is the rationalizing factor of $\sqrt{a} + \sqrt{b}$?

    Its conjugate $\sqrt{a} - \sqrt{b}$, because $(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) = a - b$, which is rational.

18. State the laws of indices for multiplication, division, and power of a power.

    $$a^{m} \cdot a^{n} = a^{m+n}, \quad \frac{a^{m}}{a^{n}} = a^{m-n}, \quad (a^{m})^{n} = a^{mn}.$$

19. Evaluate $a^{0}$ and $a^{-n}$ for $a \neq 0$.

    $$a^{0} = 1, \qquad a^{-n} = \frac{1}{a^{n}}.$$

20. Express a fractional exponent $a^{m/n}$ as a radical.

    $$a^{m/n} = \sqrt[n]{a^{m}} = \left(\sqrt[n]{a}\right)^{m}.$$

21. What is the full form of BODMAS and the order of operations it dictates?

    Brackets, Of, Division, Multiplication, Addition, Subtraction. Solve in that order: brackets first (in order $(), \{\}, []$), then 'of', then $\times$ and $\div$ left to right, then $+$ and $-$.

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