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Key Facts: Matemática A (Prova 635) Exam

635

National exam code for Matemática A

EduQA Informação-Prova 2026

150 minutes

Duration: 150 minutes (+ 30 minutes tolerance)

EduQA Informação-Prova 2026

0–200

Scoring scale; admission minimums are set by institutions (never below 95)

JNE/DGES Guia Geral de Exames 2026

€0 / €3

Free for on-time students in compulsory education; €3 per exam in other cases

JNE/DGES Guia Geral de Exames 2026

EduQA

Exam papers prepared by EduQA, I. P. (successor to IAVE)

Decreto-Lei n.º 105/2025

Portugal's Exame Nacional de Matemática A (635) is a 12th-grade national exam prepared by EduQA (formerly IAVE): 150 minutes (+ 30 minutes tolerance), scored 0–200. This free bank offers 100 English-language multiple-choice questions on functions and calculus, exponentials and logarithms, trigonometry and analytic geometry, sequences, combinatorics and probability, statistics and complex numbers.

Sample Matemática A (Prova 635) Practice Questions

Try these sample questions to review concepts for the Matemática A (Prova 635) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In a 3D Cartesian frame Oxyz, consider the points A(1, -2, 3) and B(4, 2, -1). What are the coordinates of the vector AB?

A.(5, 0, 2)

B.(-3, -4, 4)

C.(3, 0, -4)

D.(3, 4, -4)

Explanation: The vector AB is determined by subtracting the coordinates of A from B: AB = B - A = (4 - 1, 2 - (-2), -1 - 3) = (3, 4, -4).

2What is the center C and radius r of the sphere defined by the Cartesian equation (x - 2)^2 + (y + 3)^2 + z^2 = 25?

A.C(-2, 3, 0) and r = 5

B.C(2, -3, 0) and r = 25

C.C(2, -3, 0) and r = 5

D.C(2, 3, 0) and r = 5

Explanation: The standard Cartesian equation of a sphere is (x - x0)^2 + (y - y0)^2 + (z - z0)^2 = r^2. Here, x0 = 2, y0 = -3, z0 = 0, and r = sqrt(25) = 5, yielding center C(2, -3, 0) and radius r = 5.

3In the Cartesian plane Oxy, what is the slope (declive) of the straight line defined by the vector equation (x, y) = (1, 2) + k(3, -6), where k in R?

A.-1/2

B.2

C.3

D.-2

Explanation: A direction vector of the line is v = (vx, vy) = (3, -6). The slope m is given by vy / vx = -6 / 3 = -2.

4Given the vectors u = (2, -1, 3) and v = (4, 5, -1) in R^3, what is the value of their scalar product (produto escalar) u . v?

A.10

B.6

C.0

D.-2

Explanation: The scalar product is computed by summing the products of corresponding coordinates: u . v = (2)(4) + (-1)(5) + (3)(-1) = 8 - 5 - 3 = 0. Therefore, the vectors are perpendicular.

5What is the exact value of cos(7*pi/6)?

A.-1/2

B.sqrt(3)/2

C.1/2

D.-sqrt(3)/2

Explanation: Since 7*pi/6 = pi + pi/6, it lies in the third quadrant where cosine is negative: cos(7*pi/6) = -cos(pi/6) = -sqrt(3)/2.

6In the interval [0, 2*pi], how many distinct solutions does the equation 2*sin(x) + sqrt(3) = 0 have?

A.1

B.2

C.3

D.4

Explanation: Rewriting gives sin(x) = -sqrt(3)/2. In [0, 2*pi], the sine function is negative in the 3rd and 4th quadrants, yielding exactly two solutions: x = 4*pi/3 and x = 5*pi/3.

7Consider the plane alpha defined by 2x - y + 3z - 5 = 0 and the straight line r defined by (x, y, z) = (1, 0, -2) + k(1, a, -1), k in R. For what value of the real parameter a is the line r parallel to the plane alpha?

A.-1

B.1

C.5

D.-5

Explanation: A line is parallel to a plane if and only if its direction vector v = (1, a, -1) is orthogonal to the normal vector of the plane n = (2, -1, 3). Setting v . n = 0 gives (1)(2) + (a)(-1) + (-1)(3) = 0 <=> 2 - a - 3 = 0 <=> -a - 1 = 0 <=> a = -1.

8In the Cartesian space Oxyz, what is the Cartesian equation of the plane passing through point P(1, -1, 2) that is perpendicular to the line passing through A(2, 1, 0) and B(5, -2, 1)?

A.3x - 3y + z + 8 = 0

B.3x + 3y + z - 2 = 0

C.3x - 3y + z - 8 = 0

D.x - y + 2z - 6 = 0

Explanation: The normal vector n to the plane is parallel to AB = B - A = (5 - 2, -2 - 1, 1 - 0) = (3, -3, 1). The equation of the plane is 3(x - 1) - 3(y - (-1)) + 1(z - 2) = 0 <=> 3x - 3 - 3y - 3 + z - 2 = 0 <=> 3x - 3y + z - 8 = 0.

9In R^3, what is the distance from the point P(2, -1, 4) to the plane alpha defined by 2x + 2y - z + 8 = 0?

A.6

B.3

C.2/3

D.2

Explanation: The distance formula from (x0, y0, z0) to ax + by + cz + d = 0 is d = |a*x0 + b*y0 + c*z0 + d| / sqrt(a^2 + b^2 + c^2). Here, numerator is |2(2) + 2(-1) - 1(4) + 8| = |4 - 2 - 4 + 8| = |6| = 6. Denominator is sqrt(2^2 + 2^2 + (-1)^2) = sqrt(4 + 4 + 1) = 3. Thus d = 6 / 3 = 2.

10What is the cosine of the angle theta between the vectors u = (1, 2, 2) and v = (0, 3, 4)?

A.7/15

B.14/15

C.2/3

D.14/25

Explanation: The scalar product is u . v = (1)(0) + (2)(3) + (2)(4) = 0 + 6 + 8 = 14. The norms are ||u|| = sqrt(1^2 + 2^2 + 2^2) = sqrt(9) = 3, and ||v|| = sqrt(0^2 + 3^2 + 4^2) = sqrt(25) = 5. Therefore, cos(theta) = (u . v) / (||u|| * ||v||) = 14 / (3 * 5) = 14/15.

About the Matemática A (Prova 635) Exam

The Exame Final Nacional de Matemática A (prova 635) is a 12th-grade national secondary exam in Portugal. Since the 2025 reorganization of the Ministry of Education (Decreto-Lei n.º 105/2025), exam papers are prepared by EduQA — Instituto de Educação, Qualidade e Avaliação, I. P., which succeeded IAVE, and the exams are organized and graded under the Júri Nacional de Exames. Written exam on Matemática A (10th–12th grades) with a formula sheet. In 2026 statistical inference, primitives/integrals and matrices are not assessed, and some items are offered in two versions for students who followed the 2018 or the 2023 Aprendizagens Essenciais. The paper combines selection items (such as multiple choice) and constructed-response items, scored out of 200 points; answers are written on answer sheets that are later digitized. The exam covers functions and calculus, exponentials and logarithms, trigonometry and analytic geometry, sequences, combinatorics and probability, statistics and complex numbers. It counts towards the subject's final grade and can be used as an admission exam (prova de ingresso) for higher education where a course requires it. This bank is an independent English-language multiple-choice study adaptation with 100 original practice questions. It is not affiliated with EduQA or the JNE and does not reproduce the official paper or its constructed-response tasks.

Exam sponsor: EduQA, I. P. (exam papers; successor to IAVE since 2025) with the Júri Nacional de Exames (JNE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written exam on Matemática A (10th–12th grades) with a formula sheet. In 2026 statistical inference, primitives/integrals and matrices are not assessed, and some items are offered in two versions for students who followed the 2018 or the 2023 Aprendizagens Essenciais. The paper combines selection items (such as multiple choice) and constructed-response items, scored out of 200 points; answers are written on answer sheets that are later digitized.

Time Limit

150 minutes (+ 30 minutes tolerance)

Passing Score

Scored 0–200; counts 25% of the subject grade for internal students; admission-exam minimums are set by institutions (never below 95/200)

Exam / Certification Fees

€0 for on-time students in compulsory education; €3 per exam in other cases; €25 + €3 per exam if registering late

Exam sponsor website

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

Official sources

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.

~23% of this bank

Functions and calculus

Limits, continuity, derivatives and optimization.

~18% of this bank

Combinatorics and probability

Counting, Newton's binomial and probability.

~17% of this bank

Geometry and trigonometry

Analytic geometry and trigonometric functions.

~16% of this bank

Complex numbers

Algebraic and trigonometric forms, operations and the complex plane.

~13% of this bank

Exponentials and logarithms

Exponential and logarithmic functions and models.

~10% of this bank

Sequences

Arithmetic and geometric sequences, limits.

~3% of this bank

Statistics

Univariate statistics and linear transformations of data.

Preparing for the Matemática A (Prova 635) Exam

What You Need to Know

Passing score: Scored 0–200; counts 25% of the subject grade for internal students; admission-exam minimums are set by institutions (never below 95/200)
Assessment: Written exam on Matemática A (10th–12th grades) with a formula sheet. In 2026 statistical inference, primitives/integrals and matrices are not assessed, and some items are offered in two versions for students who followed the 2018 or the 2023 Aprendizagens Essenciais. The paper combines selection items (such as multiple choice) and constructed-response items, scored out of 200 points; answers are written on answer sheets that are later digitized.
Time limit: 150 minutes (+ 30 minutes tolerance)
Exam / certification fees: €0 for on-time students in compulsory education; €3 per exam in other cases; €25 + €3 per exam if registering late Official sources

Using Our Practice Resources

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Matemática A (Prova 635): Suggested Study Strategy

1Practise with the official formula sheet that accompanies the exam, and solve past papers under timed conditions (150 minutes + 30 minutes tolerance).

2Review notable limits for exponential and logarithmic functions (lim (e^x - 1)/x as x -> 0 and lim (ln(x + 1))/x as x -> 0), as they frequently appear in indeterminate form evaluations.

3Practice De Moivre's theorem and geometric loci in the Argand plane (|z - z0| <= r and arg(z - z0) = theta) until complex number operations become second nature.

4Utilize tree diagrams and two-way contingency tables to solve complex conditional probability problems and Bayes' rule calculations methodically.

5Memorize the definitions of horizontal, vertical, and oblique asymptotes (y = mx + b where m = lim f(x)/x and b = lim (f(x) - mx)) to solve rational and composite function problems efficiently.

Frequently Asked Questions

Who prepares and grades the exam?

Since the 2025 reorganization (Decreto-Lei n.º 105/2025), exam papers are prepared by EduQA — Instituto de Educação, Qualidade e Avaliação, I. P., which succeeded IAVE. The exams are run in schools and graded under the Júri Nacional de Exames (JNE).

How is the exam structured?

Is there a pass mark?

No single pass mark: the exam is scored 0–200. For internal students it counts for 25% of the final subject grade (CFD = 0.75 × internal grade + 0.25 × exam); for external candidates the exam grade is the subject grade, so at least 95/200 is needed. When used as an admission exam (prova de ingresso), each higher-education institution sets the minimum, never below 95/200.

How much does it cost?

Free for students in compulsory education who register on time and for internal students in the 1st phase; €3 per exam for 2nd-phase grade improvement, for external candidates (autopropostos) outside compulsory education and for external grade improvement; late registration costs €25 plus €3 per exam (JNE/DGES Guia Geral de Exames 2026).

Which topics are excluded in 2026?

The 2026 Informação-Prova excludes statistical inference, primitives and integrals, and matrices; the exam includes paired items for students who followed the 2018 or the 2023 Aprendizagens Essenciais.

How does this practice bank relate to the official exam?

This bank is an independent English-language multiple-choice study adaptation with 100 original practice questions. It is not affiliated with EduQA or the JNE and does not reproduce the official paper or its constructed-response tasks. Use it to review content and concepts alongside official Informação-Prova documents and past papers.

Free Practice Questions for Matemática A (Prova 635)

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