NTS NAT-IGS Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in NTS NAT-IGS, not a summary of it.

1. 1

   Sets, Functions and Groups

   3 topics

   • Sets and Set Operations
   • Relations and Functions
   • Types of Functions
2. 2

   Algebra and Matrices

   6 topics

   • Matrices and Determinants
   • Quadratic Equations and Roots
   • Partial Fractions
   • Sequences and Series
   • Permutations and Combinations
   • Binomial Theorem
3. 3

   Trigonometry

   4 topics

   • Trigonometric Ratios and Identities
   • Angles and Their Measurement
   • Trigonometric Functions and Graphs
   • Solution of Triangles
4. 4

   Analytic Geometry

   3 topics

   • Straight Lines
   • Circle and Conic Sections
   • Distance and Section Formula
5. 5

   Calculus

   4 topics

   • Limits and Continuity
   • Differentiation
   • Applications of Derivatives
   • Integration
6. 6

   Vectors

   2 topics

   • Vector Algebra
   • Dot and Cross Product

Mathematics flashcards for NTS NAT-IGS

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. What is a set?

   A well-defined collection of distinct objects, called its elements or members.

2. Define the union of two sets A and B (A ∪ B).

   The set of all elements that belong to A, to B, or to both: A ∪ B = {x : x ∈ A or x ∈ B}.

3. Define the intersection of two sets A and B (A ∩ B).

   The set of all elements common to both A and B: A ∩ B = {x : x ∈ A and x ∈ B}.

4. What is the difference of sets A − B?

   The set of elements that are in A but not in B: A − B = {x : x ∈ A and x ∉ B}.

5. State De Morgan's laws for sets.

   (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.

6. If a set has n elements, how many subsets does it have?

   2^n subsets (including the empty set and the set itself).

7. What is a relation from set A to set B?

   Any subset of the Cartesian product A × B; a set of ordered pairs (a, b) with a ∈ A and b ∈ B.

8. When is a relation called a function?

   When every element of the domain is associated with exactly one element of the codomain (no input maps to two outputs).

9. What are the domain and range of a function?

   The domain is the set of all input (first) values; the range is the set of all actual output (second) values produced.

10. Define a reflexive relation.

    A relation R on set A is reflexive if (a, a) ∈ R for every a ∈ A.

11. Define a symmetric relation.

    A relation R is symmetric if whenever (a, b) ∈ R, then (b, a) ∈ R.

12. Define a transitive relation.

    A relation R is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.

13. What is a one-to-one (injective) function?

    A function in which distinct elements of the domain map to distinct elements of the codomain: f(a) = f(b) implies a = b.

14. What is an onto (surjective) function?

    A function whose range equals its codomain; every element of the codomain is the image of at least one element of the domain.

15. What is a bijective function?

    A function that is both one-to-one (injective) and onto (surjective); it has an inverse.

16. What is an even function and a property of its graph?

    A function with f(−x) = f(x); its graph is symmetric about the y-axis.

17. What is an odd function and a property of its graph?

    A function with f(−x) = −f(x); its graph is symmetric about the origin.

18. What is the order of a matrix?

    Its size expressed as (number of rows) × (number of columns), e.g., a 2 × 3 matrix has 2 rows and 3 columns.

19. What is an identity matrix?

    A square matrix with 1's on the main diagonal and 0's elsewhere; it satisfies AI = IA = A.

20. What is the transpose of a matrix?

    The matrix obtained by interchanging its rows and columns, denoted A^T.

21. How is the determinant of a 2×2 matrix [[a, b], [c, d]] calculated?

    det = ad − bc.

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