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Key Facts: SEE Optional Mathematics Nepal Exam

75

Theory Marks

25

Internal Assessment Marks

3 hours

Theory Paper Duration

35%

Minimum Theory Score

NEB

Conducting Board

The SEE Class 10 Optional Mathematics examination is conducted by the National Examinations Board (NEB) of Nepal through its Office of the Controller of Examinations (Class 10). It consists of a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment, and students need at least 35% in theory to avoid a Non-Graded (NG) result. OpenExamPrep offers free independent practice questions on algebra and functions, coordinate geometry, trigonometry, vectors, and transformations. OpenExamPrep's questions are an independent English-language multiple-choice study adaptation of the curriculum topics. They are not an official translation of the board paper or a simulation of its written format.

Sample SEE Optional Mathematics Nepal Practice Questions

Try these sample questions to review concepts for the SEE Optional Mathematics Nepal exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If f(x) = 2x + 3 and g(x) = x² - 1 are two real-valued functions, what is the value of the composite function (f ∘ g)(3)?
A.19
B.17
C.80
D.72
Explanation: To evaluate the composite function (f ∘ g)(3) = f(g(3)), first evaluate g(3): g(3) = 3² - 1 = 9 - 1 = 8. Then evaluate f at this output: f(8) = 2(8) + 3 = 16 + 3 = 19.
2If f: R → R is defined by f(x) = (3x + 4) / 5, what is the inverse function f⁻¹(x)?
A.(5x + 4) / 3
B.(3x - 5) / 4
C.(4x - 5) / 3
D.(5x - 4) / 3
Explanation: To find the inverse function f⁻¹(x), set y = f(x): y = (3x + 4) / 5. Multiply both sides by 5: 5y = 3x + 4. Solve for x: 3x = 5y - 4, so x = (5y - 4) / 3. Interchanging variables yields f⁻¹(x) = (5x - 4) / 3.
3Given the linear function f(x) = 2x + a. If (f ∘ f)(2) = 23, what is the value of the constant a?
A.3
B.7.5
C.5
D.15
Explanation: First, evaluate the inner function: f(2) = 2(2) + a = 4 + a. Next, evaluate f(f(2)) = f(4 + a) = 2(4 + a) + a = 8 + 2a + a = 8 + 3a. We are given (f ∘ f)(2) = 23, so 8 + 3a = 23. Subtracting 8 from both sides yields 3a = 15, which gives a = 5.
4If f(x) = 2x - 3 and g(x) = 3x + 1, find the value of (f ∘ g)⁻¹(17).
A.3
B.10
C.101
D.25/6
Explanation: Find the composite function (f ∘ g)(x) = f(g(x)) = f(3x + 1) = 2(3x + 1) - 3 = 6x + 2 - 3 = 6x - 1. If (f ∘ g)⁻¹(17) = x, then by definition (f ∘ g)(x) = 17. Setting 6x - 1 = 17 gives 6x = 18, so x = 3.
5A rational function is given by f(x) = (ax + 3) / (2x - 5) for x ≠ 5/2. If the function is its own inverse (f = f⁻¹), what is the value of the constant a?
A.-5
B.3
C.2
D.5
Explanation: Let y = (ax + 3) / (2x - 5). To find f⁻¹(x), interchange x and y: x = (ay + 3) / (2y - 5). Clearing fractions gives x(2y - 5) = ay + 3, so 2xy - 5x = ay + 3. Rearranging terms in y gives 2xy - ay = 5x + 3, or y(2x - a) = 5x + 3, so f⁻¹(x) = (5x + 3) / (2x - a). For f(x) = f⁻¹(x), we equate coefficients of the two rational expressions: (ax + 3)/(2x - 5) = (5x + 3)/(2x - a). Comparing corresponding coefficients directly gives a = 5.
6What is the remainder when the polynomial P(x) = 2x³ - 5x² + 4x - 7 is divided by (x - 2)?
A.11
B.-3
C.-7
D.-6
Explanation: According to the Remainder Theorem, when a polynomial P(x) is divided by (x - a), the remainder is equal to P(a). Here, a = 2. Evaluating P(2): P(2) = 2(2)³ - 5(2)² + 4(2) - 7 = 2(8) - 5(4) + 8 - 7 = 16 - 20 + 8 - 7 = -3.
7If (x - 3) is a factor of the polynomial P(x) = x³ - kx² + 2x - 6, what is the value of k?
A.3
B.-3
C.9
D.1
Explanation: By the Factor Theorem, (x - 3) is a factor of P(x) if and only if P(3) = 0. Substituting x = 3 into P(x): P(3) = (3)³ - k(3)² + 2(3) - 6 = 27 - 9k + 6 - 6 = 27 - 9k. Setting 27 - 9k = 0 gives 9k = 27, which yields k = 3.
8The polynomials P(x) = 2x³ + ax² + 3x - 5 and Q(x) = x³ + 2x² - 4x + a leave the same remainder when divided by (x - 2). What is the value of a?
A.3
B.-2
C.4
D.-3
Explanation: By the Remainder Theorem, the remainders are P(2) and Q(2). Calculate P(2): P(2) = 2(2)³ + a(2)² + 3(2) - 5 = 2(8) + 4a + 6 - 5 = 16 + 4a + 1 = 4a + 17. Calculate Q(2): Q(2) = (2)³ + 2(2)² - 4(2) + a = 8 + 2(4) - 8 + a = 8 + 8 - 8 + a = a + 8. Since P(2) = Q(2): 4a + 17 = a + 8, which simplifies to 3a = 8 - 17 = -9, giving a = -3.
9One of the roots of the cubic equation x³ - 6x² + 11x - 6 = 0 is x = 1. What are the other two roots?
A.-2 and -3
B.1 and 6
C.2 and 3
D.-1 and 6
Explanation: Since x = 1 is a root, (x - 1) is a factor of x³ - 6x² + 11x - 6. Dividing x³ - 6x² + 11x - 6 by (x - 1): x³ - 6x² + 11x - 6 = (x - 1)(x² - 5x + 6). Factoring the quadratic quotient: x² - 5x + 6 = (x - 2)(x - 3). Therefore, the other two roots are x = 2 and x = 3.
10When the polynomial 3x³ - 4x² + 2x - 5 is divided by (x - 1) using synthetic division, what is the quotient polynomial?
A.3x² - x + 1
B.3x² + x - 1
C.3x² - 7x + 9
D.3x² - 4x + 2
Explanation: List the coefficients of 3x³ - 4x² + 2x - 5: [3, -4, 2, -5] with root divisor 1. Bring down the leading coefficient 3. Multiply 3 by 1 = 3; add to -4: -4 + 3 = -1. Multiply -1 by 1 = -1; add to 2: 2 + (-1) = 1. Multiply 1 by 1 = 1; add to -5: -5 + 1 = -4 (remainder). The quotient coefficients are [3, -1, 1], representing the quadratic polynomial 3x² - x + 1.

About the SEE Optional Mathematics Nepal Exam

The SEE Class 10 Optional Mathematics examination is the board examination for Grade 10 students in Nepal who take Optional Mathematics. Based on the Curriculum Development Centre (CDC) curriculum, it covers algebra and functions, coordinate geometry, trigonometry, vectors, and transformations. OpenExamPrep's questions are an independent English-language multiple-choice study adaptation of the curriculum topics. They are not an official translation of the board paper or a simulation of its written format.

Exam sponsor: National Examinations Board (NEB) / Office of the Controller of Examinations (Class 10), Sanothimi, Bhaktapur. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written board examination: a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment.

Time Limit

3 hours (theory paper)

Passing Score

At least 35% in the theory paper (below that: Non-Graded, NG)

Exam / Certification Fees

Set annually by NEB; paid through the school

Exam sponsor website

Reported exam pass rate: Not published by subject. Under NEB's letter-grading rules, a theory score below 35% is recorded as Non-Graded (NG) for that subject. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

20% of practice bank

Algebra and Functions

Functions, polynomials, and matrices and determinants.

25% of practice bank

Coordinate Geometry

Angle between lines, pair of straight lines, and circles.

25% of practice bank

Trigonometry

Multiple and sub-multiple angles, conditional identities, equations, and heights and distances.

15% of practice bank

Vectors

Scalar product and vector geometry.

15% of practice bank

Transformations

Reflections, rotations, enlargements, combined transformations and transformation matrices.

Preparing for the SEE Optional Mathematics Nepal Exam

What You Need to Know

  • Passing score: At least 35% in the theory paper (below that: Non-Graded, NG)
  • Assessment: Written board examination: a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment.
  • Time limit: 3 hours (theory paper)
  • Exam / certification fees: Set annually by NEB; paid through the school Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

SEE Optional Mathematics Nepal: Suggested Study Strategy

1Master step-by-step algebraic derivations for composite and inverse functions, and practice solving systems using both Cramer's rule and matrix inversion.
2Memorize and verify all conditional trigonometric identities in triangles (A + B + C = 180°), as these frequently appear as 4-mark and 5-mark long answer questions.
3Understand the geometric vector proofs (such as angle in a semicircle and rhombus diagonals), ensuring every step states vector dot product properties explicitly.
4Practice sketch diagrams for heights and distances and pair of straight lines problems to avoid sign errors in trigonometric and coordinate geometry calculations.

Frequently Asked Questions

What is the format of the SEE Class 10 Optional Mathematics examination?

The official assessment is a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment. It is a written board examination, not a multiple-choice test.

What score is needed to pass SEE Class 10 Optional Mathematics?

Under NEB's letter-grading rules, students need at least 35% of the theory marks. A lower theory score is recorded as Non-Graded (NG) for the subject.

What happens if a student is Non-Graded (NG) in Optional Mathematics?

Students who are NG in up to two subjects can sit the grade-increment (supplementary) examination announced by NEB after the results; others take the subject again in a later regular examination.

Are these practice questions official NEB papers?

No. OpenExamPrep's questions are an independent English-language multiple-choice study adaptation of the curriculum topics. They are not an official translation of the board paper or a simulation of its written format. OpenExamPrep is independent and is not affiliated with or endorsed by NEB or the Curriculum Development Centre (CDC).