NUST NET 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 NUST NET, not a summary of it.

1. 1

   Number Systems and Complex Numbers

   4 topics

   • Real Numbers and Properties
   • Complex Numbers and Operations
   • Argand Diagram and Modulus
   • De Moivre's Theorem
2. 2

   Matrices and Determinants

   4 topics

   • Types of Matrices and Operations
   • Determinants and Properties
   • Inverse of a Matrix
   • Systems of Linear Equations
3. 3

   Quadratic Equations

   4 topics

   • Methods of Solving Quadratics
   • Nature of Roots and Discriminant
   • Sum and Product of Roots
   • Equations Reducible to Quadratic Form
4. 4

   Sequences and Series

   4 topics

   • Arithmetic Progression
   • Geometric Progression
   • Harmonic Progression
   • Means and Sum Formulas
5. 5

   Permutations, Combinations and Probability

   4 topics

   • Fundamental Counting Principle
   • Permutations (nPr)
   • Combinations (nCr)
   • Probability Theorems
6. 6

   Mathematical Induction and Binomial Theorem

   4 topics

   • Principle of Mathematical Induction
   • Binomial Expansion
   • General and Middle Term
   • Binomial Series for Rational Index
7. 7

   Trigonometry

   5 topics

   • Trigonometric Functions and Identities
   • Sum, Difference and Multiple Angle Formulas
   • Trigonometric Equations
   • Inverse Trigonometric Functions
   • Solution of Triangles
8. 8

   Functions and Graphs

   4 topics

   • Domain and Range
   • Types of Functions
   • Composition and Inverse Functions
   • Graphical Transformations
9. 9

   Differential Calculus

   5 topics

   • Limits and Continuity
   • Differentiation Rules
   • Derivatives of Trigonometric, Logarithmic and Exponential Functions
   • Applications: Maxima and Minima
   • Rate of Change and Tangents
10. 10

    Integral Calculus

    4 topics

    • Indefinite Integrals
    • Techniques of Integration
    • Definite Integrals
    • Area Under Curves
11. 11

    Analytic Geometry

    3 topics

    • Straight Lines
    • Circles
    • Conic Sections
12. 12

    Vectors

    5 topics

    • Vectors in 2D and 3D
    • Addition and Subtraction of Vectors
    • Scalar (Dot) Product
    • Vector (Cross) Product
    • Geometric Applications of Vectors

Mathematics flashcards for NUST NET

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

1. What is the definition of a rational number?

   A number that can be expressed as p/q where p and q are integers and q ≠ 0. Its decimal expansion is either terminating or recurring.

2. What is an irrational number, and give two examples.

   A real number that cannot be written as p/q (q ≠ 0); its decimal is non-terminating and non-recurring. Examples: √2 and π.

3. State the closure, commutative, associative, and distributive properties of real numbers under addition/multiplication.

   Closure: a+b and a·b are real. Commutative: a+b=b+a, ab=ba. Associative: (a+b)+c=a+(b+c), (ab)c=a(bc). Distributive: a(b+c)=ab+ac.

4. What are the additive identity, multiplicative identity, additive inverse, and multiplicative inverse for real numbers?

   Additive identity: 0. Multiplicative identity: 1. Additive inverse of a: −a. Multiplicative inverse of a (a≠0): 1/a.

5. State the trichotomy property of real numbers.

   For any two real numbers a and b, exactly one of these holds: a < b, a = b, or a > b.

6. Define the imaginary unit i and give the values of i², i³, and i⁴.

   i = √(−1). Then i² = −1, i³ = −i, and i⁴ = 1. Powers of i cycle with period 4.

7. What is the standard (rectangular) form of a complex number, and what are its real and imaginary parts?

   z = a + bi, where a = Re(z) is the real part and b = Im(z) is the imaginary part (a, b real).

8. How do you add and subtract two complex numbers (a+bi) and (c+di)?

   Add/subtract real and imaginary parts separately: (a+bi)±(c+di) = (a±c) + (b±d)i.

9. How do you multiply two complex numbers (a+bi)(c+di)?

   (a+bi)(c+di) = (ac − bd) + (ad + bc)i, using i² = −1.

10. What is the complex conjugate of z = a + bi, and what is z·z̄?

    The conjugate is z̄ = a − bi. Their product z·z̄ = a² + b² = |z|², a real non-negative number.

11. How do you divide complex numbers (a+bi)/(c+di)?

    Multiply numerator and denominator by the conjugate of the denominator: (a+bi)(c−di) / (c²+d²).

12. On the Argand diagram, how is a complex number z = a + bi represented?

    As the point (a, b) in the plane, with the horizontal axis as the real axis and the vertical axis as the imaginary axis.

13. What is the modulus of a complex number z = a + bi?

    |z| = √(a² + b²), the distance from the origin to the point (a, b) on the Argand diagram.

14. What is the argument (amplitude) of a complex number z = a + bi?

    arg(z) = θ where tan θ = b/a; it is the angle the line from origin to (a,b) makes with the positive real axis (adjusting for the correct quadrant).

15. What is the polar (trigonometric) form of a complex number?

    z = r(cos θ + i sin θ), where r = |z| is the modulus and θ = arg(z) is the argument.

16. State the property of the modulus of a product and a quotient of complex numbers.

    |z₁z₂| = |z₁||z₂| and |z₁/z₂| = |z₁|/|z₂| (z₂ ≠ 0).

17. State De Moivre's Theorem.

    For any integer n: [r(cos θ + i sin θ)]ⁿ = rⁿ(cos nθ + i sin nθ).

18. Using De Moivre's Theorem, what is the formula for the n-th roots of a complex number r(cos θ + i sin θ)?

    r^(1/n)[cos((θ+2kπ)/n) + i sin((θ+2kπ)/n)] for k = 0, 1, …, n−1, giving n distinct roots.

19. What are the cube roots of unity, and what is their key property?

    1, ω, ω², where ω = (−1+i√3)/2. They satisfy 1 + ω + ω² = 0 and ω³ = 1.

20. How is De Moivre's Theorem used to express cos(nθ) and sin(nθ)?

    Expand (cos θ + i sin θ)ⁿ via the binomial theorem and equate real and imaginary parts to (cos nθ + i sin nθ).

21. Define a row matrix and a column matrix.

    A row matrix has a single row (order 1×n); a column matrix has a single column (order m×1).

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