100+ Free Assam HSLC Class 10 Elective Advanced Mathematics Practice Questions

Prepare for the Assam State School Education Board (ASSEB/SEBA) High School Leaving Certificate (HSLC) Elective Advanced Mathematics Examination exam with instant access — no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately

100+ Questions

100% Free

Loading practice questions...

Same family resources

Explore More Assam ASSEB HSLC Elective Subjects

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

2026 Statistics

Key Facts: Assam HSLC Class 10 Elective Advanced Mathematics Exam

8 Core Topics

Prescribed syllabus units for ASSEB Class 10 Elective Advanced Mathematics

ASSEB Advanced Mathematics Curriculum

3 Hours

Total duration of the final HSLC board examination paper

Assam State Board Regulations

100 Marks

Total marks for the written Advanced Mathematics paper

ASSEB Board Examination Scheme

30%

Minimum passing percentage requirement

ASSEB Evaluation Criteria

100 MCQs

Number of practice questions in this OpenExamPrep question bank with step-by-step worked solutions

OpenExamPrep

Assam HSLC Elective Advanced Mathematics evaluates Class 10 students across Sets, Complex Numbers, Inequalities, Sequences and Series, Quadratic Equations, Trigonometry, Coordinate Geometry, and Permutations & Combinations with comprehensive step-by-step problem-solving focus.

Sample Assam HSLC Class 10 Elective Advanced Mathematics Practice Questions

Try these sample questions to test your Assam HSLC Class 10 Elective Advanced Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In a survey of a Class 10 section, 35 students like Mathematics, 28 like Advanced Mathematics, and 50 like at least one of the two subjects. How many students like both Mathematics and Advanced Mathematics?

A.13

B.15

C.18

D.22

Explanation: By the cardinal formula for the union of two sets, n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Here, n(M) = 35, n(AM) = 28, and n(M ∪ AM) = 50. Substituting these values into the formula gives 50 = 35 + 28 - n(M ∩ AM) => 50 = 63 - n(M ∩ AM) => n(M ∩ AM) = 63 - 50 = 13. Therefore, 13 students like both subjects.

2If a finite set S contains 5 distinct elements, what is the total number of elements in its power set P(S)?

A.10

B.25

C.32

D.64

Explanation: The power set P(S) of a set S is the set of all subsets of S. If a set S has n elements, the total number of subsets (elements in the power set) is given by 2^n. For n = 5, n(P(S)) = 2^5 = 32.

3Let set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}. Find the symmetric difference A Δ B.

A.{3, 4}

B.{1, 2, 5, 6}

C.{1, 2, 3, 4, 5, 6}

D.{1, 2}

Explanation: The symmetric difference of two sets A and B, denoted by A Δ B, is defined as A Δ B = (A \ B) ∪ (B \ A) or (A ∪ B) \ (A ∩ B). Here, A \ B = {1, 2} and B \ A = {5, 6}. Thus, A Δ B = {1, 2} ∪ {5, 6} = {1, 2, 5, 6}.

4In a class of 100 students, 60 study Mathematics, 45 study Physics, and 35 study Chemistry. 20 study Math and Physics, 15 study Physics and Chemistry, 15 study Math and Chemistry, and 10 study all three subjects. How many students study none of these three subjects?

A.0

B.5

C.10

D.15

Explanation: Using the three-set principle of inclusion-exclusion: n(M ∪ P ∪ C) = n(M) + n(P) + n(C) - n(M ∩ P) - n(P ∩ C) - n(M ∩ C) + n(M ∩ P ∩ C). Substituting the given values: n(M ∪ P ∪ C) = 60 + 45 + 35 - 20 - 15 - 15 + 10 = 140 - 50 + 10 = 100. Since total students = 100 and n(M ∪ P ∪ C) = 100, the number of students studying none is 100 - 100 = 0.

5If n(A) = 4 and n(A × B) = 24, find the number of elements in set B.

A.4

B.6

C.8

D.20

Explanation: The number of elements in the Cartesian product of two sets A and B is given by n(A × B) = n(A) × n(B). Given n(A) = 4 and n(A × B) = 24: 24 = 4 × n(B) => n(B) = 24 / 4 = 6.

6How many proper subsets does a set containing 6 elements have?

A.64

B.63

C.36

D.32

Explanation: The total number of subsets of a set with n elements is 2^n. A proper subset is any subset except the set itself. Therefore, the number of proper subsets is 2^n - 1. For n = 6: 2^6 - 1 = 64 - 1 = 63.

7Let Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set A = {2, 4, 6, 8}, and set B = {6, 7, 8, 9}. Find the complement of (A ∪ B), i.e., (A ∪ B)'.

A.{1, 3, 5, 10}

B.{6, 8}

C.{1, 2, 3, 4, 5}

D.{7, 9}

Explanation: First, find the union A ∪ B by combining all elements of A and B: A ∪ B = {2, 4, 6, 7, 8, 9}. The complement (A ∪ B)' consists of all elements in U that are NOT in A ∪ B. Comparing with U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}: (A ∪ B)' = {1, 3, 5, 10}.

8If A and B are disjoint sets with n(A) = 15 and n(B) = 22, what is n(A ∪ B)?

A.7

B.15

C.37

D.330

Explanation: Two sets A and B are disjoint if they have no common elements, meaning A ∩ B = ∅, so n(A ∩ B) = 0. Using the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B): n(A ∪ B) = 15 + 22 - 0 = 37.

9Given A = {x ∈ N | x is a multiple of 3, x ≤ 15} and B = {x ∈ N | x is an even number, x ≤ 15}. Find set difference A \ B.

A.{3, 9, 15}

B.{6, 12}

C.{2, 4, 8, 10, 14}

D.{3, 6, 9, 12, 15}

Explanation: First list elements of set A: A = {3, 6, 9, 12, 15}. List elements of set B: B = {2, 4, 6, 8, 10, 12, 14}. The set difference A \ B consists of elements in A that are NOT in B. Removing the even numbers (6, 12) from A yields A \ B = {3, 9, 15}.

10Let relation R on natural numbers N be defined by R = {(x, y) ∈ N × N | 2x + y = 10}. What is the domain of R?

A.{1, 2, 3, 4}

B.{2, 4, 6, 8}

C.{1, 2, 3, 4, 5}

D.{8, 6, 4, 2}

Explanation: Since x, y ∈ N (natural numbers, positive integers): 2x + y = 10 => y = 10 - 2x. For y to be a positive integer (y ≥ 1), 10 - 2x ≥ 1 => 2x ≤ 9 => x ≤ 4.5. Thus x can take natural values 1, 2, 3, 4. The corresponding y values are: x=1 -> y=8; x=2 -> y=6; x=3 -> y=4; x=4 -> y=2. The domain (set of x values) is {1, 2, 3, 4}.

About the Assam HSLC Class 10 Elective Advanced Mathematics Exam

The ASSEB HSLC Class 10 Elective Advanced Mathematics curriculum equips high school students in Assam with advanced mathematical concepts beyond general mathematics, covering rigorous set theory, complex number algebra, quadratic equations, sequence & series (AP, GP, HP), inequalities, plane trigonometry, coordinate geometry, and permutations & combinations.

Assessment

The ASSEB HSLC Class 10 Elective Advanced Mathematics examination is a 3-hour written paper worth 100 marks, containing multiple-choice questions, short answer problems, and detailed multi-step numerical and analytical problems.

Time Limit

3 hours

Passing Score

30% aggregate

Exam Fee

Standard ASSEB board examination fee (Assam State School Education Board (ASSEB))

Assam HSLC Class 10 Elective Advanced Mathematics Exam Content Outline

13%

Sets

Set operations, Venn diagrams, power sets, Cartesian products, equivalence relations, symmetric difference, and cardinal properties of sets.

13%

Complex Numbers

Algebra of complex numbers, imaginary unit i powers, modulus and argument, conjugate properties, polar form, and square roots of complex numbers.

12%

Inequalities

Linear and quadratic inequalities, absolute value inequalities, triangle inequality, interval notation, and graphical solutions on number line.

14%

Sequences and Series

Arithmetic Progression (AP), Geometric Progression (GP), Harmonic Progression (HP), sum to n terms, infinite geometric series, arithmetic and geometric means.

13%

Quadratic Equations

Discriminant analysis, nature of roots, sum and product of roots, formation of quadratic equations, symmetric functions of roots, and maximum/minimum values of quadratic expressions.

13%

Trigonometry

Trigonometric ratios of compound angles, double and triple angles, transformation formulas (sum to product / product to sum), general solutions of trigonometric equations, and properties of triangles.

12%

Coordinate Geometry

Distance and section formulas, area of triangle, locus of moving point, straight line equations (slope-intercept, intercept, normal forms), angle between lines, perpendicular distance, and standard circle equations.

10%

Permutations and Combinations

Fundamental principles of counting, factorial notation, nPr permutations, nCr combinations, circular arrangements, restricted permutations, and practical problem solving.

How to Pass the Assam HSLC Class 10 Elective Advanced Mathematics Exam

What You Need to Know

Passing score: 30% aggregate
Assessment: The ASSEB HSLC Class 10 Elective Advanced Mathematics examination is a 3-hour written paper worth 100 marks, containing multiple-choice questions, short answer problems, and detailed multi-step numerical and analytical problems.
Time limit: 3 hours
Exam fee: Standard ASSEB board examination fee

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

Assam HSLC Class 10 Elective Advanced Mathematics Study Tips from Top Performers

1Master fundamental set cardinal identity formulas: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) and n(A ∪ B ∪ C) to quickly solve multi-set word problems.

2Practice expressing complex numbers in polar form z = r(cos θ + i sin θ) and computing modulus r = sqrt(a^2 + b^2) and principal argument θ.

3Memorize compound angle trigonometric formulas: sin(A ± B), cos(A ± B), tan(A ± B), double angle formulas (sin 2A, cos 2A, tan 2A), and product-to-sum transformations.

4For quadratic equations, memorize relations between roots α and β: α + β = -b/a, αβ = c/a, and symmetric expressions like α^2 + β^2 = (α+β)^2 - 2αβ.

5Use section formula and slope concepts (m = (y2 - y1)/(x2 - x1)) to solve locus and straight-line equations efficiently.

Frequently Asked Questions

What topics are included in the Assam HSLC Elective Advanced Mathematics syllabus?

The syllabus comprises 8 core domains: Sets (operations, Venn diagrams, cardinal formulas), Complex Numbers (algebra, modulus-argument, square roots), Inequalities (linear, quadratic, absolute value), Sequences and Series (AP, GP, HP, infinite series), Quadratic Equations (roots, discriminant, symmetric functions), Trigonometry (compound angles, transformation formulas, equations), Coordinate Geometry (lines, locus, distance formulas, circles), and Permutations & Combinations.

What is the passing mark for the ASSEB HSLC Advanced Mathematics exam?

Students must achieve a minimum of 30% marks (30 out of 100) to pass the subject examination.

Are step-by-step calculations required in ASSEB Class 10 Advanced Mathematics?

Yes, while multiple-choice questions test direct results, understanding the complete step-by-step mathematical derivation is essential for scoring full marks in board descriptive sections.

How are Harmonic Progressions (HP) related to Arithmetic Progressions (AP)?

A sequence of non-zero numbers is in Harmonic Progression (HP) if the reciprocals of its terms form an Arithmetic Progression (AP).

What is the formula for the distance of a point (x1, y1) from a straight line Ax + By + C = 0?

The perpendicular distance d is given by d = |A(x1) + B(y1) + C| / sqrt(A^2 + B^2).

What is De Moivre's formula concept used in complex numbers at Class 10 elective level?

For polar form z = r(cos θ + i sin θ), raising z to integer power n yields z^n = r^n (cos nθ + i sin nθ), which simplifies powers and roots of complex numbers.

100+ Free Assam HSLC Class 10 Elective Advanced Mathematics Practice Questions

Explore More Assam ASSEB HSLC Elective Subjects

Assam ASSEB HSLC Arabic — Elective

Assam ASSEB HSLC Artificial Intelligence and Robotics — Elective

Assam ASSEB HSLC Assamese — Elective

Assam ASSEB HSLC Commerce — Elective

Assam ASSEB HSLC Computer Science — Elective

Assam ASSEB HSLC Dance — Elective