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🇵🇰 NED Admission Test · subject
NED Admission Test Mathematics Syllabus
Every chapter and topic of Mathematics examined in NED Admission Test — 12 chapters, 49 topics, plus 69 flashcards written against it.
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 NED Admission Test, not a summary of it.
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Algebra and Quadratic Equations
4 topics- Polynomials and Factorization
- Quadratic Equations
- Partial Fractions
- Equations Reducible to Quadratic Form
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Matrices and Determinants
4 topics- Types and Algebra of Matrices
- Determinants and their Properties
- Inverse of a Matrix
- Solution of Linear Systems
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Sequences and Series
5 topics- Arithmetic Progression
- Geometric Progression
- Harmonic Progression
- Arithmetic, Geometric and Harmonic Means
- Sum to Infinity of Geometric Series
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Permutations, Combinations and Probability
4 topics- Factorial Notation
- Permutations
- Combinations
- Probability
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Binomial Theorem and Mathematical Induction
4 topics- Principle of Mathematical Induction
- Binomial Theorem for Positive Index
- General and Middle Terms
- Binomial Series for Negative and Fractional Index
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Trigonometry
5 topics- Measurement of Angles and Radian Measure
- Trigonometric Identities
- Trigonometric Equations
- Solution of Triangles
- Inverse Trigonometric Functions
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Functions and Limits
4 topics- Domain and Range of Functions
- Types of Functions
- Limits of Functions
- Continuity
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Differentiation
5 topics- Derivative from First Principles
- Rules of Differentiation
- Derivatives of Trigonometric, Exponential and Logarithmic Functions
- Maxima and Minima
- Rate of Change and Tangents
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Integration
4 topics- Indefinite Integrals
- Methods of Integration
- Definite Integrals
- Area Under a Curve
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Analytic Geometry
3 topics- The Straight Line
- The Circle
- Conic Sections
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Vectors
4 topics- Vectors in Two and Three Dimensions
- Scalar (Dot) Product
- Vector (Cross) Product
- Scalar Triple Product
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Complex Numbers
3 topics- Algebra of Complex Numbers
- Argand Diagram and Modulus
- Polar Form and De Moivre's Theorem
Mathematics flashcards for NED Admission Test
21 of 69 cards from the Mathematics deck — real questions with worked answers.
What is a polynomial in one variable x?
An algebraic expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀, where the coefficients aᵢ are constants, n is a non-negative integer, and aₙ ≠ 0.
How is the degree of a polynomial defined?
The degree is the highest power of the variable that appears in the polynomial with a non-zero coefficient.
State the Remainder Theorem.
When a polynomial p(x) is divided by (x − a), the remainder equals p(a).
State the Factor Theorem.
(x − a) is a factor of polynomial p(x) if and only if p(a) = 0.
Factorize a² − b² (difference of two squares).
a² − b² = (a − b)(a + b).
Give the factorization of a³ + b³ (sum of cubes).
a³ + b³ = (a + b)(a² − ab + b²).
Give the factorization of a³ − b³ (difference of cubes).
a³ − b³ = (a − b)(a² + ab + b²).
Expand (a + b)³.
(a + b)³ = a³ + 3a²b + 3ab² + b³.
What is the general (standard) form of a quadratic equation?
ax² + bx + c = 0, where a, b, c are real constants and a ≠ 0.
State the quadratic formula for solving ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a).
What is the discriminant of a quadratic equation and its symbol?
The discriminant is D = b² − 4ac. It determines the nature of the roots of ax² + bx + c = 0.
How does the discriminant determine the nature of the roots of a quadratic?
If D > 0: two distinct real roots; if D = 0: two equal (real, repeated) roots; if D < 0: two complex conjugate (no real) roots.
For ax² + bx + c = 0, what is the sum of the roots?
Sum of roots = −b/a.
For ax² + bx + c = 0, what is the product of the roots?
Product of roots = c/a.
How do you form a quadratic equation given its roots α and β?
x² − (α + β)x + αβ = 0, i.e. x² − (sum of roots)x + (product of roots) = 0.
When are the roots of a quadratic equation rational (assuming rational coefficients)?
When the discriminant b² − 4ac is a perfect square (and ≥ 0).
What is a partial fraction decomposition used for?
It expresses a proper rational function as a sum of simpler fractions whose denominators are the factors of the original denominator.
What is the difference between a proper and an improper rational fraction?
In a proper fraction the degree of the numerator is less than the degree of the denominator; in an improper fraction it is greater than or equal to it (and must first be reduced by division before partial fractions).
For a linear (non-repeated) factor (x − a) in the denominator, what form does its partial fraction take?
A constant over the factor: A / (x − a).
For a repeated linear factor (x − a)² in the denominator, what partial fractions are written?
A/(x − a) + B/(x − a)², i.e. one term for each power up to the highest.
For an irreducible quadratic factor (ax² + bx + c) in the denominator, what form does its partial fraction take?
A linear numerator over the factor: (Ax + B)/(ax² + bx + c).
Planning Mathematics for NED Admission Test
Mathematics is about 33% of the NED Admission Test syllabus by topic count — 49 of 150 topics, spread over 12 chapters. At roughly 45 minutes per topic plus 12 minutes per sub-topic, a first pass runs to about 35 hours.
The heaviest chapters are Sequences and Series (5 topics), Trigonometry (5 topics), Differentiation (5 topics) . Front-load those while your energy is high; the short chapters are better revision filler later.
Work top-down: read the chapter, then tick topics off individually rather than marking the whole chapter done. Sub-topics are where silent gaps hide.
Mathematics (NED Admission Test) FAQ
What is in the NED Admission Test Mathematics syllabus?
Mathematics is split into 12 chapters — Algebra and Quadratic Equations, Matrices and Determinants, Sequences and Series, Permutations, Combinations and Probability, Binomial Theorem and Mathematical Induction and Trigonometry, and 6 more, containing 49 topics and 0 sub-topics in total.
How many chapters are there in Mathematics for NED Admission Test?
12 chapters. Mathematics accounts for about 33% of the topics in the whole NED Admission Test syllabus (49 of 150).
How long should I spend on Mathematics for NED Admission Test?
Budget around 35 hours for a first pass through Mathematics — about 45 minutes per topic plus 12 minutes per sub-topic across its 49 topics. Add revision cycles on top.
Are there flashcards for NED Admission Test Mathematics?
Yes — a 69-card Mathematics deck. Sample cards are printed on this page, and the full deck is free in the Examius app with spaced repetition scheduling.