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NTS NAT-IGS Mathematics Syllabus
The Mathematics syllabus for NTS NAT-IGS in full: 6 chapters and 22 topics, every one listed below, plus 50 Mathematics flashcards with answers.
Mathematics syllabus: all 6 chapters
Expand any chapter to see its topics and sub-topics.
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Sets, Functions and Groups
3 topics- Sets and Set Operations
- Relations and Functions
- Types of Functions
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Algebra and Matrices
6 topics- Matrices and Determinants
- Quadratic Equations and Roots
- Partial Fractions
- Sequences and Series
- Permutations and Combinations
- Binomial Theorem
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Trigonometry
4 topics- Trigonometric Ratios and Identities
- Angles and Their Measurement
- Trigonometric Functions and Graphs
- Solution of Triangles
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Analytic Geometry
3 topics- Straight Lines
- Circle and Conic Sections
- Distance and Section Formula
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Calculus
4 topics- Limits and Continuity
- Differentiation
- Applications of Derivatives
- Integration
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Vectors
2 topics- Vector Algebra
- Dot and Cross Product
NTS NAT-IGS Mathematics flashcards — 50 questions with answers
What is a set?
A well-defined collection of distinct objects, called its elements or members.
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}.
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}.
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}.
State De Morgan's laws for sets.
(A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.
If a set has n elements, how many subsets does it have?
2^n subsets (including the empty set and the set itself).
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.
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).
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.
Define a reflexive relation.
A relation R on set A is reflexive if (a, a) ∈ R for every a ∈ A.
Define a symmetric relation.
A relation R is symmetric if whenever (a, b) ∈ R, then (b, a) ∈ R.
Define a transitive relation.
A relation R is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.
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.
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.
What is a bijective function?
A function that is both one-to-one (injective) and onto (surjective); it has an inverse.
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.
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.
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.
What is an identity matrix?
A square matrix with 1's on the main diagonal and 0's elsewhere; it satisfies AI = IA = A.
What is the transpose of a matrix?
The matrix obtained by interchanging its rows and columns, denoted A^T.
Show the other 30 Mathematics flashcards
How is the determinant of a 2×2 matrix [[a, b], [c, d]] calculated?
det = ad − bc.
When is a square matrix singular?
When its determinant equals zero; a singular matrix has no inverse.
State the formula for 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 condition must two matrices satisfy to be multiplied (AB)?
The number of columns of A must equal the number of rows of B.
What is the standard (general) form of a quadratic equation?
ax² + bx + c = 0, where a ≠ 0.
State the quadratic formula for ax² + bx + c = 0.
x = (−b ± √(b² − 4ac)) / (2a).
What is the discriminant and what does it determine?
D = b² − 4ac; it determines the nature of the roots: D > 0 two distinct real roots, D = 0 one repeated real root, D < 0 complex roots.
For ax² + bx + c = 0, what is the sum and product of the roots?
Sum of roots = −b/a; product of roots = c/a.
What is partial fraction decomposition used for?
To express a proper rational function as a sum of simpler fractions with linear or quadratic denominators.
For a repeated linear factor (x − a)² in the denominator, what partial fraction form is used?
A/(x − a) + B/(x − a)².
For an irreducible quadratic factor (ax² + bx + c) in the denominator, what numerator form is used?
A linear numerator: (Ax + B)/(ax² + bx + c).
What is an arithmetic sequence (A.P.)?
A sequence in which each term differs from the previous by a constant common difference d.
State the nth term formula of an arithmetic progression.
a_n = a + (n − 1)d, where a is the first term and d the common difference.
State the formula for the sum of the first n terms of an A.P.
S_n = (n/2)[2a + (n − 1)d] or S_n = (n/2)(a + l), where l is the last term.
What is a geometric sequence (G.P.)?
A sequence in which each term is obtained by multiplying the previous term by a constant common ratio r.
State the nth term formula of a geometric progression.
a_n = a·r^(n−1), where a is the first term and r the common ratio.
State the formula for the sum to infinity of a geometric series.
S∞ = a/(1 − r), valid when |r| < 1.
State the formula for n factorial (n!).
n! = n × (n − 1) × (n − 2) × ... × 2 × 1, with 0! = 1.
What is the formula for permutations nPr?
nPr = n! / (n − r)!
What is the formula for combinations nCr?
nCr = n! / [r!(n − r)!]
What is the key difference between permutations and combinations?
Permutations count arrangements where order matters; combinations count selections where order does not matter.
State the general (binomial) theorem for (a + b)^n.
(a + b)^n = Σ from r=0 to n of nCr · a^(n−r) · b^r.
What is the general term in the expansion of (a + b)^n?
T_(r+1) = nCr · a^(n−r) · b^r.
How many terms are there in the expansion of (a + b)^n?
n + 1 terms.
Define the six trigonometric ratios in a right triangle.
sin = opp/hyp, cos = adj/hyp, tan = opp/adj, csc = hyp/opp, sec = hyp/adj, cot = adj/opp.
State the fundamental Pythagorean trigonometric identity.
sin²θ + cos²θ = 1.
State the other two Pythagorean identities.
1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ.
State the relationship between radians and degrees.
π radians = 180 degrees, so 1 radian = 180/π ≈ 57.296°.
State the formula relating arc length, radius, and central angle in radians.
s = rθ, where s is arc length, r the radius, and θ the angle in radians.
What are the period and range of the sine and cosine functions?
Both have period 2π and range [−1, 1].
NTS NAT-IGS Mathematics FAQ
What is in the NTS NAT-IGS Mathematics syllabus?
NTS NAT-IGS Mathematics is split into 6 chapters: Sets, Functions and Groups, Algebra and Matrices, Trigonometry, Analytic Geometry, Calculus and Vectors. Together they contain 22 topics.
How many chapters are in NTS NAT-IGS Mathematics?
6 chapters, containing 22 topics. The largest chapter is Algebra and Matrices, with 6 topics.
Are there flashcards for NTS NAT-IGS Mathematics?
Yes — a 50-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.