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Sample Rwanda Advanced Level National Examination Practice Questions

Try these sample questions to review concepts for the Rwanda Advanced Level National Examination exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Differentiate the function f(x) = (3x² - 5)⁴ with respect to x using the chain rule.
A.f'(x) = 4(3x² - 5)³
B.f'(x) = 12x(3x² - 5)³
C.f'(x) = 6x(3x² - 5)⁴
D.f'(x) = 24x(3x² - 5)³
Explanation: Let u = 3x² - 5, so f(u) = u⁴. By the chain rule, df/dx = (df/du) × (du/dx) = 4u³ × (6x) = 24x(3x² - 5)³.
2Find the derivative with respect to x of the function g(x) = (2x + 1) / (x² + 3) using the quotient rule.
A.g'(x) = (-2x² - 2x + 6) / (x² + 3)²
B.g'(x) = (6x² + 2x + 6) / (x² + 3)²
C.g'(x) = (-2x² - 2x + 6) / (x² + 3)
D.g'(x) = (2x² - 2x - 6) / (x² + 3)²
Explanation: By the quotient rule, d/dx[u/v] = (u'v - uv') / v². Here u = 2x + 1 → u' = 2, and v = x² + 3 → v' = 2x. Thus g'(x) = [2(x² + 3) - (2x + 1)(2x)] / (x² + 3)² = [2x² + 6 - (4x² + 2x)] / (x² + 3)² = (-2x² - 2x + 6) / (x² + 3)².
3Find the gradient of the tangent to the curve x² + 2xy + y³ = 9 at the point (2, 1) using implicit differentiation.
A.-2/3
B.6/7
C.-6/7
D.-4/5
Explanation: Differentiating implicitly with respect to x: 2x + 2(y + x dy/dx) + 3y² dy/dx = 0 → 2x + 2y + (2x + 3y²) dy/dx = 0 → dy/dx = -(2x + 2y) / (2x + 3y²). At (2, 1): dy/dx = -[2(2) + 2(1)] / [2(2) + 3(1²)] = -(4 + 2) / (4 + 3) = -6/7.
4A manufacturer wants to design an open-topped rectangular water reservoir with a square base of side x meters and height h meters. If the total volume is fixed at 32 m³, what value of x minimizes the total surface area of the tank?
A.2 meters
B.4 meters
C.8 meters
D.16 meters
Explanation: Volume V = x²h = 32 → h = 32 / x². Surface area of open tank A = x² + 4xh = x² + 4x(32 / x²) = x² + 128/x. Differentiating: dA/dx = 2x - 128/x² = 0 → 2x³ = 128 → x³ = 64 → x = 4 meters. The second derivative d²A/dx² = 2 + 256/x³ > 0, confirming a local minimum.
5Evaluate the indefinite integral: ∫ (2x) / (x² + 5) dx.
A.ln(x² + 5) + C
B.1 / (x² + 5)² + C
C.2 ln(x² + 5) + C
D.(x² + 5)² + C
Explanation: Let u = x² + 5, then du = 2x dx. The integral transforms to ∫ (1/u) du = ln|u| + C = ln(x² + 5) + C (since x² + 5 > 0 for all real x).
6Evaluate the indefinite integral ∫ x e^(2x) dx using integration by parts.
A.(1/2)x e^(2x) - (1/2)e^(2x) + C
B.x e^(2x) - e^(2x) + C
C.(1/4)x² e^(2x) + C
D.(1/2)x e^(2x) - (1/4)e^(2x) + C
Explanation: Integration by parts formula: ∫ u dv = uv - ∫ v du. Let u = x → du = dx, and dv = e^(2x) dx → v = (1/2)e^(2x). Then ∫ x e^(2x) dx = (1/2)x e^(2x) - ∫ (1/2)e^(2x) dx = (1/2)x e^(2x) - (1/4)e^(2x) + C.
7What is the area of the finite region bounded by the parabola y = x² and the line y = 4?
A.16/3
B.32/3
C.16
D.8
Explanation: The intersection points are found by setting x² = 4 → x = -2 and x = 2. Area = ∫_{-2}^{2} (4 - x²) dx = [4x - x³/3]_{-2}^{2} = (8 - 8/3) - (-8 - (-8)/3) = (16/3) - (-16/3) = 32/3.
8The region bounded by the curve y = √x, the x-axis, and the vertical lines x = 0 and x = 4 is rotated through 360° about the x-axis. What is the volume of the solid of revolution formed?
A.16π
B.4π
C.8π
D.16π/3
Explanation: Volume of revolution V = π ∫_{a}^{b} y² dx = π ∫_{0}^{4} (√x)² dx = π ∫_{0}^{4} x dx = π [x²/2]_{0}^{4} = π (16/2 - 0) = 8π.
9Given the 2×2 matrix A = [[3, 5], [1, 2]], what is the inverse matrix A⁻¹?
A.[[2, -5], [-1, 3]]
B.[[-2, 5], [1, -3]]
C.[[3, -5], [-1, 2]]
D.[[1/3, 1/5], [1, 1/2]]
Explanation: For A = [[a, b], [c, d]], det(A) = ad - bc = (3)(2) - (5)(1) = 6 - 5 = 1. The inverse A⁻¹ = (1/det(A)) [[d, -b], [-c, a]] = 1 · [[2, -5], [-1, 3]] = [[2, -5], [-1, 3]].
10Using Cramer's rule, solve for x in the system of linear equations: 2x + 3y = 8 and 5x - y = 3.
A.x = 2
B.x = 3
C.x = -1
D.x = 1
Explanation: Determinant of coefficients D = |[2, 3], [5, -1]| = (2)(-1) - (3)(5) = -2 - 15 = -17. Determinant for x: D_x = |[8, 3], [3, -1]| = (8)(-1) - (3)(3) = -8 - 9 = -17. Therefore x = D_x / D = -17 / -17 = 1.

About the Rwanda Advanced Level National Examination Exam

The Advanced Level (General Education) National Examination is Rwanda's examination at the end of Senior 6, set and administered by NESA. Each candidate sits the written papers of one subject combination, such as Physics-Chemistry-Mathematics (PCM) or History-Geography-Literature in English (HGL), together with Entrepreneurship II, General Studies and Communication Skills, and English II. Science combinations also sit practical examinations. The Rwanda Advanced Certificate of Education is awarded for a weighted average of at least 50%. This page offers independent practice by OpenExamPrep: English-language multiple-choice questions with explanations drawn from mathematics, sciences, economics and entrepreneurship, history and geography, general studies and English. The questions are a study adaptation, not an official translation or a simulation of the written or practical papers, and they do not cover every combination subject (for example Computer Science, Psychology, Literature, Français or Kiswahili).

Exam sponsor: National Examination and School Inspection Authority (NESA), Ministry of Education (MINEDUC). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

For 2025-2026, National Science Practical Examinations (PBA) ran from 1 May to 19 June 2026 for all S6 candidates in science combinations, and the written papers ran from 15 to 21 July 2026 in 3-hour morning and afternoon sessions. Candidates sit the papers of their combination (PCM, PCB, MCB, MPG, MPC, MCE, MEG, LFK, HLP or HGL) plus Entrepreneurship II, General Studies and Communication Skills, and English II; PCB candidates also sit Subsidiary Mathematics. Papers are set in English except the language papers (Ikinyarwanda, Français and Kiswahili).

Time Limit

3 hours per written paper; science practicals are scheduled separately

Passing Score

The 2024 amendment to the Ministerial Instructions awards the Rwanda Advanced Certificate of Education for a weighted average of at least 50%, with each subject weighted by its weekly teaching hours. Core-subject bands are A 80–100%, B 75–79%, C 70–74%, D 65–69%, E 60–64%, S 50–59% (minimum pass) and F 0–49%; subsidiary subjects are graded S (50–100%) or F (0–49%).

Exam / Certification Fees

No candidate fee is published for school-based candidates, who are registered by their school in SDMS. Private candidates (for example earlier A-Level sitters or people who completed O-Level in 2020/2021 or earlier) register in SDMS and pay a non-refundable 15,000 RWF through Irembo; for 2026 registration ran from 25 February to 27 March 2026.

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.

~19% of this bank

Advanced Mathematics

Differentiation and integration, optimization, matrices and Cramer's rule, vectors, complex numbers, progressions, binomial expansion, circles and probability.

~15% of this bank

Physics

Moment of inertia, angular momentum, SHM, orbits, thermodynamics, Coulomb's law, capacitors, magnetic force, Faraday's law, AC, interference, gratings, photoelectricity and half-life.

~14% of this bank

Chemistry

Hess's law, ΔG, Kp and Kc, Le Chatelier, weak acids and buffers, Ksp, rate equations, Arrhenius, cell potentials, Nernst, SN2, Markovnikov and benzene.

~14% of this bank

Biology and Health Sciences

DNA replication, translation, the lac operon, RuBisCO and C4 plants, action potentials and synapses, insulin and ADH, cytotoxic T cells, Mendelian and population genetics, electrophoresis.

~12% of this bank

Economics and Entrepreneurship

Elasticity and revenue, marginal utility and cost, efficiency, GDP, automatic stabilizers, BNR policy rate, comparative advantage, balance of payments, NPV, quick ratio and the Business Model Canvas.

~12% of this bank

History and Geography

Population density, demographic transition, the Kigali Master Plan, FONERWA, the Abiru, Belgian colonial policy, the Genocide Convention, power sharing, Pan-Africanism, AfCFTA, IHL and the Peace of Westphalia.

~11% of this bank

General Studies and Communication Skills

Deduction and induction, fallacies, falsifiability, sampling, informed consent, lateral reading, communication noise, SDG 4, ethics, the UDHR and public audit.

~3% of this bank

English II

Formal subjunctive after 'recommend that', effect versus affect, and concessive connectors.

Preparing for the Rwanda Advanced Level National Examination Exam

What You Need to Know

  • Passing score: The 2024 amendment to the Ministerial Instructions awards the Rwanda Advanced Certificate of Education for a weighted average of at least 50%, with each subject weighted by its weekly teaching hours. Core-subject bands are A 80–100%, B 75–79%, C 70–74%, D 65–69%, E 60–64%, S 50–59% (minimum pass) and F 0–49%; subsidiary subjects are graded S (50–100%) or F (0–49%).
  • Assessment: For 2025-2026, National Science Practical Examinations (PBA) ran from 1 May to 19 June 2026 for all S6 candidates in science combinations, and the written papers ran from 15 to 21 July 2026 in 3-hour morning and afternoon sessions. Candidates sit the papers of their combination (PCM, PCB, MCB, MPG, MPC, MCE, MEG, LFK, HLP or HGL) plus Entrepreneurship II, General Studies and Communication Skills, and English II; PCB candidates also sit Subsidiary Mathematics. Papers are set in English except the language papers (Ikinyarwanda, Français and Kiswahili).
  • Time limit: 3 hours per written paper; science practicals are scheduled separately
  • Exam / certification fees: No candidate fee is published for school-based candidates, who are registered by their school in SDMS. Private candidates (for example earlier A-Level sitters or people who completed O-Level in 2020/2021 or earlier) register in SDMS and pay a non-refundable 15,000 RWF through Irembo; for 2026 registration ran from 25 February to 27 March 2026. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
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Rwanda Advanced Level National Examination: Suggested Study Strategy

1Focus first on the papers of your own combination, then on the papers every candidate sits: Entrepreneurship II, General Studies and Communication Skills, and English II.
2Write out full calculus, physics and chemistry solutions with units, because the official papers are marked on written working.
3If you are in a science combination, prepare for the practical examinations, which take place weeks before the written papers.

Frequently Asked Questions

What papers do Rwanda A-Level candidates sit?

Each candidate sits the papers of one combination, such as PCM, PCB, MCB, MPG, MPC, MCE, MEG, LFK, HLP or HGL in 2025-2026, plus Entrepreneurship II, General Studies and Communication Skills, and English II. Candidates in science combinations also take National Science Practical Examinations (PBA).

How are A-Level results graded?

Under the 2024 Ministerial Instructions, core subjects are graded from A (80–100%) to S (50–59%, minimum pass) and F (0–49%), and subsidiary subjects are graded S (50–100%) or F. The Rwanda Advanced Certificate of Education is awarded for a weighted average of at least 50%, with subjects weighted by weekly teaching hours.

When do the A-Level national examinations take place?

For 2025-2026, science practical examinations ran from 1 May to 19 June 2026 and the written papers ran from 15 to 21 July 2026, in 3-hour sessions from 8:30 to 11:30 and from 2:00 to 5:00.

Can I sit the A-Level national examination as a private candidate?

Yes, if you meet NESA's private-candidate criteria, for example having sat A-Level before or having completed O-Level in 2020/2021 or earlier. Private candidates register in SDMS, pay a non-refundable 15,000 RWF through Irembo and must retake all subjects of their combination; earlier A-Level grades cannot be carried forward.

Are these practice questions the same format as the real A-Level papers?

No. This is independent practice by OpenExamPrep: English-language multiple-choice questions with explanations drawn from several combinations. The official papers are written and practical examinations, so also practise full written answers, calculations and practical skills for your own combination.