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NED Admission Test Mathematics Syllabus
The Mathematics syllabus for NED Admission Test in full: 12 chapters and 49 topics, every one listed below, plus 69 Mathematics flashcards with answers.
Mathematics syllabus: all 12 chapters
Expand any chapter to see its topics and sub-topics.
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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
NED Admission Test Mathematics flashcards — 69 questions with 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.
Show the other 49 Mathematics flashcards
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).
What is the first step in resolving an improper rational fraction into partial fractions?
Divide the numerator by the denominator to write it as a polynomial plus a proper fraction, then decompose the proper fraction.
What does it mean for an equation to be 'reducible to quadratic form'?
It is a higher-degree or non-quadratic equation that, by a suitable substitution, can be rewritten as a quadratic equation in a new variable.
How do you solve a biquadratic equation such as ax⁴ + bx² + c = 0?
Substitute y = x², giving ay² + by + c = 0; solve for y, then find x from x = ±√y.
What substitution reduces aˣ-type or exponential equations like a^(2x) + b·aˣ + c = 0 to quadratic form?
Let y = aˣ, giving ay² + by + c = 0; solve for y, then solve aˣ = y for x.
When solving radical equations by squaring, what must always be checked?
All solutions must be checked in the original equation to discard extraneous roots introduced by squaring.
What is a matrix?
A rectangular array of numbers (or elements) arranged in rows and columns, enclosed in brackets, of order m × n (m rows, n columns).
Define a square matrix.
A matrix in which the number of rows equals the number of columns (order n × n).
What is a diagonal matrix?
A square matrix in which all elements off the main diagonal are zero (only diagonal entries may be non-zero).
What is an identity (unit) matrix?
A diagonal matrix in which every main-diagonal element is 1; denoted I, it satisfies AI = IA = A.
Define the transpose of a matrix.
The transpose Aᵀ is obtained by interchanging the rows and columns of A; the (i, j) element of A becomes the (j, i) element of Aᵀ.
What is a symmetric matrix?
A square matrix A for which Aᵀ = A (i.e. aᵢⱼ = aⱼᵢ).
What is a skew-symmetric matrix?
A square matrix A for which Aᵀ = −A; its main-diagonal elements are all zero.
What is the condition for two matrices A and B to be multipliable (AB defined)?
The number of columns of A must equal the number of rows of B. If A is m × n and B is n × p, then AB is m × p.
Is matrix multiplication commutative?
No. In general AB ≠ BA; matrix multiplication is not commutative.
What is the condition for two matrices to be added?
They must have the same order (same number of rows and the same number of columns).
What is a determinant?
A scalar value associated with a square matrix, computed from its elements, denoted det(A) or |A|.
How is the determinant of a 2×2 matrix [[a, b],[c, d]] computed?
|A| = ad − bc.
How is the value of a determinant affected if two rows (or columns) are interchanged?
The sign of the determinant changes (it is multiplied by −1).
What is the determinant of a matrix that has two identical rows or columns?
Zero.
What happens to a determinant if every element of one row (or column) is multiplied by a constant k?
The value of the determinant is multiplied by k.
How is det(Aᵀ) related to det(A)?
They are equal: det(Aᵀ) = det(A).
What is the property of det(AB) for square matrices A and B?
det(AB) = det(A) · det(B).
When is a square matrix called singular?
When its determinant is zero (|A| = 0); such a matrix has no inverse.
What is the formula for the inverse of a non-singular square matrix A?
A⁻¹ = (1/|A|) · adj(A), where adj(A) is the adjoint of A and |A| ≠ 0.
What is the adjoint (adjugate) of a matrix?
The transpose of the matrix of cofactors of A.
Give the inverse of a 2×2 matrix A = [[a, b],[c, d]].
A⁻¹ = (1/(ad − bc)) · [[d, −b],[−c, a]], provided ad − bc ≠ 0.
What is the defining property of the inverse A⁻¹ of a matrix A?
AA⁻¹ = A⁻¹A = I, the identity matrix.
State Cramer's Rule condition for a unique solution of a linear system AX = B.
A unique solution exists if and only if the coefficient determinant |A| ≠ 0, and then xᵢ = |Aᵢ| / |A|.
In the matrix method, how is the solution of the system AX = B found?
By X = A⁻¹B, provided A is non-singular (|A| ≠ 0).
What is an arithmetic progression (A.P.)?
A sequence in which each term after the first is obtained by adding a fixed number (the common difference d) to the preceding term.
What is the formula for the nth term of an A.P. with first term a and common difference d?
aₙ = a + (n − 1)d.
What is the sum of the first n terms of an A.P.?
Sₙ = (n/2)[2a + (n − 1)d] = (n/2)(a + l), where l is the last term.
What is a geometric progression (G.P.)?
A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed non-zero number (the common ratio r).
What is the formula for the nth term of a G.P. with first term a and common ratio r?
aₙ = a·rⁿ⁻¹.
What is the sum of the first n terms of a G.P. (r ≠ 1)?
Sₙ = a(rⁿ − 1)/(r − 1) = a(1 − rⁿ)/(1 − r).
What is the sum to infinity of a G.P., and when does it exist?
S∞ = a/(1 − r), valid only when |r| < 1.
What is a harmonic progression (H.P.)?
A sequence whose reciprocals form an arithmetic progression; e.g. 1/a, 1/(a+d), 1/(a+2d), ...
How do you find the nth term of a harmonic progression?
Take the corresponding A.P. of the reciprocals, find its nth term using a + (n−1)d, then take the reciprocal of that result.
What is the arithmetic mean (A.M.) of two numbers a and b?
A.M. = (a + b)/2.
What is the geometric mean (G.M.) of two positive numbers a and b?
G.M. = √(ab).
What is the harmonic mean (H.M.) of two non-zero numbers a and b?
H.M. = 2ab/(a + b).
State the relationship between A.M., G.M. and H.M. of two positive numbers.
G.M.² = A.M. × H.M., and they satisfy A.M. ≥ G.M. ≥ H.M. (equality when the numbers are equal).
How do you insert n arithmetic means between two numbers a and b?
Form an A.P. with a as first term and b as the (n+2)th term; the common difference is d = (b − a)/(n + 1), giving the means a + d, a + 2d, ..., a + nd.
How do you insert a single geometric mean G between two positive numbers a and b?
G = √(ab), since a, G, b form a G.P. with G/a = b/G.
If a, b, c are in A.P., what relation holds among them?
2b = a + c (the middle term is the arithmetic mean of the other two).
If a, b, c are in G.P., what relation holds among them?
b² = ac (the middle term is the geometric mean of the other two).
If a, b, c are in H.P., what relation holds among them?
b = 2ac/(a + c), i.e. 1/a, 1/b, 1/c are in A.P. so 2/b = 1/a + 1/c.
What is the cofactor of an element aᵢⱼ in a determinant?
Cᵢⱼ = (−1)^(i+j) · Mᵢⱼ, where Mᵢⱼ is the minor of aᵢⱼ (the determinant left after deleting row i and column j).
NED Admission Test Mathematics FAQ
What is in the NED Admission Test Mathematics syllabus?
NED Admission Test 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, Trigonometry, Functions and Limits, Differentiation, Integration, Analytic Geometry, Vectors and Complex Numbers. Together they contain 49 topics.
How many chapters are in NED Admission Test Mathematics?
12 chapters, containing 49 topics. The largest chapter is Sequences and Series, with 5 topics.
Are there flashcards for NED Admission Test Mathematics?
Yes — a 69-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.