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Key Facts: Exame Nacional de Matemática (12.ª Classe) Exam

57

English-language MCQ study adaptations in this bank

OpenExamPrep reviewed bank

15 top-level items

Top-level structure of the published 2026 official paper

INADE published paper

120 + 30

Official minutes plus tolerance

Decreto Executivo 81/26

0–200 → 0–20

Official scoring conversion

Decreto Executivo 81/26

Official paper: 15 top-level items, 120 minutes plus 30 minutes tolerance, scored 0–200 and converted to 0–20. Practice bank: 57 English-language MCQ study adaptations covering topics from the published scope, not an official format simulation.

Sample Exame Nacional de Matemática (12.ª Classe) Practice Questions

Try these sample questions to review concepts for the Exame Nacional de Matemática (12.ª Classe) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 57+ question experience with AI tutoring.

1What is the domain of the real function f(x) = sqrt((3x - 6)/(x + 1))?
A.(-inf, -1) U [2, +inf)
B.(-1, 2]
C.[-1, 2]
D.(-inf, -1] U [2, +inf)
Explanation: For the square root to be defined in R, the radicand must be non-negative: (3x - 6)/(x + 1) >= 0. The zeros of the numerator and denominator are x = 2 and x = -1, respectively. Testing intervals shows that the quotient is positive on (-inf, -1) and [2, +inf). The point x = -1 must be strictly excluded because division by zero is undefined.
2Given the bijective function f(x) = (2x + 5)/(x - 3) for x != 3, what is its inverse function f^(-1)(x)?
A.f^(-1)(x) = (x - 3)/(2x + 5)
B.f^(-1)(x) = (3x + 5)/(x - 2)
C.f^(-1)(x) = (3x - 5)/(x + 2)
D.f^(-1)(x) = (2x - 5)/(x + 3)
Explanation: Set y = (2x + 5)/(x - 3). Multiply both sides by (x - 3) to get y(x - 3) = 2x + 5 => yx - 3y = 2x + 5. Rearrange terms containing x: yx - 2x = 3y + 5 => x(y - 2) = 3y + 5. Solve for x: x = (3y + 5)/(y - 2). Replacing y with x gives f^(-1)(x) = (3x + 5)/(x - 2).
3Given the functions f(x) = sqrt(x - 4) and g(x) = x^2 - 5, what is the composite function (f o g)(x) and its natural domain in R?
A.(f o g)(x) = sqrt(x^2 - 9) with domain (-inf, -3] U [3, +inf)
B.(f o g)(x) = x - 3 with domain [3, +inf)
C.(f o g)(x) = sqrt(x^2 - 9) with domain [-3, 3]
D.(f o g)(x) = x^2 - 9 with domain R
Explanation: The composite function is (f o g)(x) = f(g(x)) = sqrt((x^2 - 5) - 4) = sqrt(x^2 - 9). The domain requires the radicand to be non-negative: x^2 - 9 >= 0 => (x - 3)(x + 3) >= 0, which yields x in (-inf, -3] U [3, +inf).
4Which of the following real functions is an odd function (função ímpar)?
A.f(x) = x^2 + cos(x)
B.f(x) = x^3 / (x^2 + 1)
C.f(x) = |x| - 3x^2
D.f(x) = e^x - e^(-x) + 2
Explanation: A function is odd if f(-x) = -f(x) for all x in its domain. Evaluating f(-x) = (-x)^3 / ((-x)^2 + 1) = -x^3 / (x^2 + 1) = -f(x). Thus, f(x) = x^3 / (x^2 + 1) is odd.
5Solve the logarithmic equation ln(x + 2) + ln(x - 1) = ln(10) in the set of real numbers.
A.x = -4 and x = 3
B.x = 3
C.x = 4
D.x = ln(10)
Explanation: The existence domain requires x + 2 > 0 and x - 1 > 0, which means x > 1. Using logarithm properties: ln((x + 2)(x - 1)) = ln(10) => (x + 2)(x - 1) = 10 => x^2 + x - 2 = 10 => x^2 + x - 12 = 0. Factoring gives (x + 4)(x - 3) = 0, so x = -4 or x = 3. Since x > 1, only x = 3 is a valid solution.
6What is the range (contradomínio / conjunto de chegada) of the real function f(x) = 4 - 3e^(-2x)?
A.(-inf, 4)
B.(4, +inf)
C.[1, 4]
D.(-inf, +inf)
Explanation: For any real x, the exponential e^(-2x) is strictly positive, so 3e^(-2x) in (0, +inf). Multiplying by -1 gives -3e^(-2x) in (-inf, 0). Adding 4 shifts the interval to (-inf, 4). Therefore, the range is D'_f = (-inf, 4).
7Determine the value of the constant k such that the piecewise function f(x) is continuous at x = 1, where f(x) = 2x + k for x <= 1 and f(x) = x^2 - 3x + 6 for x > 1.
A.k = 1
B.k = 2
C.k = 4
D.k = -2
Explanation: For f(x) to be continuous at x = 1, we must have lim_{x -> 1^-} f(x) = lim_{x -> 1^+} f(x) = f(1). Left limit and value: f(1) = 2(1) + k = 2 + k. Right limit: lim_{x -> 1^+} (x^2 - 3x + 6) = 1^2 - 3(1) + 6 = 4. Equating both sides gives 2 + k = 4 => k = 2.
8The graph of y = f(x) has a local maximum at the point P(-2, 5). What are the coordinates of the corresponding local maximum on the graph of g(x) = 3f(x - 4) + 2?
A.(2, 17)
B.(-6, 17)
C.(2, 15)
D.(-6, 7)
Explanation: The transformation f(x - 4) shifts the graph horizontally to the right by 4 units: x = -2 + 4 = 2. The vertical scaling by 3 and shift by +2 transforms the y-coordinate: y = 3(5) + 2 = 17. Thus, the new maximum is at (2, 17).
9Solve the inequality log_2(x^2 - 3x) <= 2 in the set of real numbers.
A.[-1, 4]
B.[-1, 0) U (3, 4]
C.(0, 3)
D.(-inf, -1] U [4, +inf)
Explanation: First, the domain requires x^2 - 3x > 0 => x(x - 3) > 0 => x in (-inf, 0) U (3, +inf). Next, applying the base-2 exponential (since 2 > 1, the inequality direction is preserved): x^2 - 3x <= 2^2 = 4 => x^2 - 3x - 4 <= 0 => (x - 4)(x + 1) <= 0 => x in [-1, 4]. Intersecting with the domain yields [-1, 0) U (3, 4].
10The polynomial P(x) = x^3 - 4x^2 + ax + b leaves a remainder of 2 when divided by (x - 1) and a remainder of -12 when divided by (x + 1). Find the values of a and b.
A.a = 6 and b = -1
B.a = 5 and b = 0
C.a = -6 and b = 1
D.a = 4 and b = -2
Explanation: By the Remainder Theorem, P(1) = 2 and P(-1) = -12. From P(1) = 1^3 - 4(1^2) + a(1) + b = 2 => -3 + a + b = 2 => a + b = 5. From P(-1) = (-1)^3 - 4((-1)^2) + a(-1) + b = -12 => -5 - a + b = -12 => -a + b = -7. Adding the two linear equations: 2b = -2 => b = -1. Substituting b into a + b = 5 yields a = 6.

About the Exame Nacional de Matemática (12.ª Classe) Exam

This is the INADE 12th-grade national examination in Mathematics (Matemática), code 122, for eligible students following the Angolan curriculum. The official assessment is an in-person written paper centered on constructed mathematical reasoning and calculations, with some shorter selection or completion tasks and uses Portuguese. This page provides an English-language MCQ study adaptation only; official names and target-language material integral to language skills are preserved.

Exam sponsor: Instituto Nacional de Avaliação e de Desenvolvimento da Educação (INADE), Ministério da Educação (MED), Angola. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

INADE administers the 12th-grade Mathematics (Matemática) paper (code 122) under the 2025/2026 national-exam regulation. The official Information-Prova and published paper define the scope reflected below. The assessment is an in-person written paper centered on constructed mathematical reasoning and calculations, with some shorter selection or completion tasks; its official language setting is Portuguese.

Time Limit

120 minutes (+30 minutes tolerance)

Passing Score

The paper is scored from 0 to 200 points and converted to the 0–20 scale. Decreto Executivo 81/26 assigns weighting and progression rules to separate learning-assessment regulations and does not publish a standalone 10/20 pass mark for this paper.

Exam / Certification Fees

No separate candidate exam fee is published in the official 2025/2026 INADE national-exam materials.

Exam sponsor website

Reported exam pass rate: No current subject-specific national pass rate was found in the official INADE materials reviewed.. 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.

Published scope

Plane analytic geometry

Point sets, distance, lines, circles, ellipses, and geometric conditions in the plane.

Published scope

Trigonometry

Angles, identities, functions, equations, and applications.

Published scope

Sequences

Arithmetic and geometric sequences, terms, sums, monotonicity, and limits.

Published scope

Real functions

Polynomial, rational, exponential, logarithmic, and trigonometric functions and their representations.

Published scope

Limits, continuity, and derivatives

Limits, continuity, differentiation, tangents, monotonicity, extrema, and applications.

Preparing for the Exame Nacional de Matemática (12.ª Classe) Exam

What You Need to Know

  • Passing score: The paper is scored from 0 to 200 points and converted to the 0–20 scale. Decreto Executivo 81/26 assigns weighting and progression rules to separate learning-assessment regulations and does not publish a standalone 10/20 pass mark for this paper.
  • Assessment: INADE administers the 12th-grade Mathematics (Matemática) paper (code 122) under the 2025/2026 national-exam regulation. The official Information-Prova and published paper define the scope reflected below. The assessment is an in-person written paper centered on constructed mathematical reasoning and calculations, with some shorter selection or completion tasks; its official language setting is Portuguese.
  • Time limit: 120 minutes (+30 minutes tolerance)
  • Exam / certification fees: No separate candidate exam fee is published in the official 2025/2026 INADE national-exam materials. Official sources

Using Our Practice Resources

  • Work through all 57 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Exame Nacional de Matemática (12.ª Classe): Suggested Study Strategy

1Use the official Information-Prova to organize review around: Plane analytic geometry; Trigonometry; Sequences; Real functions; Limits, continuity, and derivatives.
2Work through the published official paper and its classification criteria to practise the real response types and required working.
3Use this MCQ bank for concept checks, then practise explanations, calculations, source analysis, or extended writing in the official assessment language.

Frequently Asked Questions

What is the official format?

INADE publishes 15 top-level items for the 2026 paper. It is an in-person written paper centered on constructed mathematical reasoning and calculations, with some shorter selection or completion tasks, not a 100-question MCQ test.

How long is the official paper?

The regulation sets 120 minutes plus 30 minutes tolerance for 12th-grade national papers.

How is it scored?

The official paper totals 200 raw points, converted to the 0–20 scale. The current exam regulation refers weighting and progression to separate learning-assessment rules.

Who is eligible?

Eligible 12th-grade students following the Angolan curriculum must be registered in PGDEN and meet the admission conditions in Decreto Executivo 81/26, including the attendance and discipline requirements.

Does this bank reproduce the official exam?

No. These 57 questions are English-language MCQ study adaptations. They are not an official translation, do not reproduce the official item mix, and do not substitute for written-response practice.