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103+ Free MATSEC AM Pure Mathematics Practice Questions

Prepare for the Malta Advanced Matriculation (AM) Pure Mathematics — AM 27 (2026) exam with instant access — no signup required.

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2026 Statistics

Key Facts: MATSEC AM Pure Mathematics Exam

AM 27

Official MATSEC Advanced subject code

MATSEC 2026 syllabi catalogue

A–E / F

Subject grade scale (A highest pass; F fail)

Matriculation Examination Regulations 2025

30 / 24 / 18 / 12 / 6

AM grade points for grades A / B / C / D / E

Matriculation Examination Regulations 2025

44

Minimum total grade points for Matriculation Certificate (with required subject mix)

Matriculation Examination Regulations 2025

EUR 45

Revision of Paper fee at AM level (from 2026 sessions fee schedule)

MATSEC Examination Fees document

EUR 35

Late registration fee per subject (from 2026 sessions fee schedule)

MATSEC Examination Fees document

103

Free practice MCQs on this page (study adaptation)

OpenExamPrep

MATSEC Advanced Matriculation Pure Mathematics (AM 27) is a University of Malta MATSEC subject assessed under the 2026 syllabus (Two written papers: 3 hours each). Results use grades A–E (pass) or F; AM grade points contribute to the Matriculation Certificate (minimum 44 points). The 103 questions on this page are an English-language MCQ study adaptation, not an official MATSEC format simulation.

Sample MATSEC AM Pure Mathematics Practice Questions

Try these sample questions to test your MATSEC AM Pure Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 103+ question experience with AI tutoring.

1Simplify √12 − 4√27.
A.−10√3
B.−10√27
C.2√3
D.−14√3
Explanation: Write each surd in terms of √3: √12 = 2√3 and √27 = 3√3, so 4√27 = 12√3. Combining like surds gives 2√3 − 12√3 = −10√3. Always reduce every surd to its simplest form before adding or subtracting.
2Rationalise and simplify 3/(2 + √5).
A.3√5 − 6
B.6 − 3√5
C.3(2 + √5)
D.3(2 − √5)
Explanation: Multiply numerator and denominator by the conjugate 2 − √5. The denominator becomes 4 − 5 = −1, so the expression is 3(2 − √5)/(−1) = 3(√5 − 2) = 3√5 − 6. Note that √5 ≈ 2.236, so the answer is positive, as it must be.
3Evaluate 8^(2/3) × 4^(−1/2).
A.2
B.4
C.1
D.1/2
Explanation: Write each base as a power of 2: 8^(2/3) = (2³)^(2/3) = 2² = 4, and 4^(−1/2) = 1/√4 = 1/2. The product is 4 × 1/2 = 2. Fractional indices combine a root (the denominator) with a power (the numerator).
4If log₂x + log₂(x − 2) = 3, the value of x is
A.4
B.2
C.8
D.6
Explanation: Use the addition law: log₂[x(x − 2)] = 3, so x(x − 2) = 2³ = 8, giving x² − 2x − 8 = 0 and (x − 4)(x + 2) = 0. The domain requires x > 2, so x = −2 is rejected and x = 4 is the only solution.
5Using the change of base formula, log₉27 equals
A.3/2
B.2/3
C.3
D.1/2
Explanation: Change to a common base: log₉27 = ln27/ln9 = (3ln3)/(2ln3) = 3/2. Equivalently, 9^(3/2) = 27, which confirms the index directly.
6Express (2x + 1)/[(x − 1)(x + 1)] in partial fractions.
A.(3/2)/(x − 1) + (1/2)/(x + 1)
B.(1/2)/(x − 1) + (3/2)/(x + 1)
C.2/(x − 1) + 1/(x + 1)
D.3/(x − 1) − 1/(x + 1)
Explanation: Write the numerator identity A(x + 1) + B(x − 1) = 2x + 1. Substituting x = 1 gives 2A = 3, so A = 3/2; substituting x = −1 gives −2B = −1, so B = 1/2. Hence the decomposition is (3/2)/(x − 1) + (1/2)/(x + 1).
7When f(x) = x³ − 2x² + x − 5 is divided by x − 2, the remainder is
A.−3
B.3
C.−5
D.1
Explanation: By the remainder theorem the remainder on division by x − 2 is f(2) = 8 − 8 + 2 − 5 = −3. No long division is needed; only the value of the polynomial at the root of the divisor matters.
8The quadratic x² − 5x + 6 = 0 has roots α and β. The value of α³ + β³ is
A.35
B.125
C.65
D.19
Explanation: From the coefficients, α + β = 5 and αβ = 6. Then α² + β² = (α + β)² − 2αβ = 25 − 12 = 13, and α³ + β³ = (α + β)(α² − αβ + β²) = 5(13 − 6) = 35. (Checking directly with roots 2 and 3 gives 8 + 27 = 35.)
9The nature of the roots of 2x² − 4x + 5 = 0 is
A.complex conjugate (non-real)
B.real and equal
C.real and distinct
D.rational and distinct
Explanation: The discriminant is Δ = b² − 4ac = 16 − 40 = −24. A negative discriminant means the roots are non-real, and because the coefficients are real they occur as a conjugate pair.
10Solve x² − 5x + 6 > 0. The solution set is
A.x < 2 or x > 3
B.2 < x < 3
C.x ≤ 2 or x ≥ 3
D.x > 2
Explanation: Factorise to (x − 2)(x − 3) > 0. The parabola opens upwards with roots at 2 and 3, so it is positive outside the roots: x < 2 or x > 3.

About the MATSEC AM Pure Mathematics Exam

Malta Advanced Matriculation (AM) Pure Mathematics — AM 27 (2026) is administered by the MATSEC Examinations Board (University of Malta). Advanced Matriculation subjects form part of the Matriculation Certificate pathway (two Advanced Level subjects, three Intermediate Level subjects and Systems of Knowledge, with group restrictions and a minimum of 44 grade points; AM grade points A=30, B=24, C=18, D=12, E=6). Assessment for AM 27 follows the official 2026 syllabus scheme: Paper I 3 hours: 10 questions (possibly varying difficulty), answer all; 100 marks. Paper II 3 hours: 10 questions, attempt 7; 15 marks each. Knowledge of Paper 1 topics assumed and may be tested in Paper 2. Scientific calculators allowed (no graphical calculators); formula booklet provided. Available in September. This practice bank is an English-language MCQ study adaptation of syllabus knowledge and judgment, not an official paper simulation or substitute for required oral, practical, performance, coursework or project work.

Assessment

Paper I 3 hours: 10 questions (possibly varying difficulty), answer all; 100 marks. Paper II 3 hours: 10 questions, attempt 7; 15 marks each. Knowledge of Paper 1 topics assumed and may be tested in Paper 2. Scientific calculators allowed (no graphical calculators); formula booklet provided. Available in September.

Time Limit

Two written papers: 3 hours each

Passing Score

Subject results are graded A, B, C, D, E (pass, A highest) or F (fail). For the Matriculation Certificate, Advanced Level grade points are: A=30, B=24, C=18, D=12, E=6. The Certificate requires among other criteria a minimum total of 44 grade points from the required subject combination within five years (Matriculation Examination Regulations 2025).

Exam Fee

The MATSEC Examination Fees schedule applicable from the 2026 sessions publishes no base registration fee per subject; only additional charges are listed — late registration EUR 35 per subject, very late registration EUR 70 per subject, Revision of Paper at Advanced Matriculation (AM) level EUR 45, and change in school EUR 35. Examination fees are not refundable. (MATSEC Examinations Board, University of Malta)

MATSEC AM Pure Mathematics Exam Content Outline

Paper 1

Surds, indices, logarithms, partial fractions and quadratics

Surds, rational indices, laws of logarithms, partial fractions, remainder and factor theorem, roots of quadratics and inequalities

Paper 1

Sequences, series and the binomial expansion

Arithmetic and geometric series, sigma notation, sum to infinity and the binomial expansion for rational indices

Paper 1

Enumeration and probability

Counting principles, permutations and combinations, and probability from equally likely outcomes

Paper 1

Graphic techniques, coordinate geometry and functions

Curve sketching and transformations, straight line, loci, circle, functions, inverses, composites, modulus, rational, exponential and logarithmic functions

Paper 1

Trigonometry

Six trigonometric functions, arc length and sector area, identities, general solutions, the R-method and small-angle approximations

Paper 1

Complex numbers, differentiation and integration

Argand diagram, polar form, differentiation rules and applications, integration by substitution, parts and partial fractions, and first-order separable differential equations

Paper 1

Vectors and matrices

Vectors in two and three dimensions, scalar product, lines in space, matrix algebra, 2 x 2 inverses and linear transformations in the plane

Paper 2

Summation of series, Maclaurin's series and mathematical induction

Method of differences, standard results, Maclaurin expansions and proof by induction

Paper 2

Further complex numbers and further vectors

De Moivre's theorem, nth roots, exponential form, loci, vector product, planes, and the triple scalar product

Paper 2

Further curve sketching, further integration and polar coordinates

Asymptotes and rational curves, volumes and arc length of revolution, inverse trigonometric integrals, reduction formulae and polar areas

Paper 2

Further matrices, further differential equations and numerical methods

3 x 3 inverses and systems of equations, integrating factor and second-order linear equations, Newton-Raphson, trapezium and Simpson's rules, and further probability

How to Pass the MATSEC AM Pure Mathematics Exam

What You Need to Know

  • Passing score: Subject results are graded A, B, C, D, E (pass, A highest) or F (fail). For the Matriculation Certificate, Advanced Level grade points are: A=30, B=24, C=18, D=12, E=6. The Certificate requires among other criteria a minimum total of 44 grade points from the required subject combination within five years (Matriculation Examination Regulations 2025).
  • Assessment: Paper I 3 hours: 10 questions (possibly varying difficulty), answer all; 100 marks. Paper II 3 hours: 10 questions, attempt 7; 15 marks each. Knowledge of Paper 1 topics assumed and may be tested in Paper 2. Scientific calculators allowed (no graphical calculators); formula booklet provided. Available in September.
  • Time limit: Two written papers: 3 hours each
  • Exam fee: The MATSEC Examination Fees schedule applicable from the 2026 sessions publishes no base registration fee per subject; only additional charges are listed — late registration EUR 35 per subject, very late registration EUR 70 per subject, Revision of Paper at Advanced Matriculation (AM) level EUR 45, and change in school EUR 35. Examination fees are not refundable.

Keys to Passing

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

MATSEC AM Pure Mathematics Study Tips from Top Performers

1Work from the official AM 27 2026 syllabus learning outcomes and scheme of assessment on um.edu.mt/matsec — examiners mark to those criteria.
2Practise timed written-paper style answers and any required oral, practical, performance or project work; MCQs alone cannot replace those components.
3Note Matriculation Certificate combination rules (groups, prohibited pairings such as Computing with Information Technology, Systems of Knowledge, 44-point minimum) in the Matriculation Examination Regulations 2025.
4Use MATSEC past papers and marking schemes for personal study only; commercial reproduction requires MATSEC permission.
5Register within published First Session and September Second Session windows; late and very late fees apply per the 2026 fee schedule. Revision of Paper at AM level is EUR 45.

Frequently Asked Questions

What is MATSEC Advanced Matriculation Pure Mathematics?

Malta Advanced Matriculation (AM) Pure Mathematics — AM 27 (2026) is an Advanced Matriculation subject administered by the MATSEC Examinations Board at the University of Malta under the official 2026 syllabus (AM 27). Advanced subjects contribute grade points toward the Matriculation Certificate (A=30, B=24, C=18, D=12, E=6).

How is MATSEC AM Pure Mathematics assessed?

Paper I 3 hours: 10 questions (possibly varying difficulty), answer all; 100 marks. Paper II 3 hours: 10 questions, attempt 7; 15 marks each. Knowledge of Paper 1 topics assumed and may be tested in Paper 2. Scientific calculators allowed (no graphical calculators); formula booklet provided. Available in September. Official papers are not fixed multiple-choice totals.

How much does MATSEC AM registration cost?

The MATSEC Examination Fees schedule applicable from the 2026 sessions publishes no base registration fee per subject; only additional charges are listed — late registration EUR 35 per subject, very late registration EUR 70 per subject, Revision of Paper at Advanced Matriculation (AM) level EUR 45, and change in school EUR 35. Examination fees are not refundable.

What grades and points apply at Advanced Level?

Subject results are graded A, B, C, D, E (pass, A highest) or F (fail). For the Matriculation Certificate, Advanced Level grade points are: A=30, B=24, C=18, D=12, E=6. The Certificate requires among other criteria a minimum total of 44 grade points from the required subject combination within five years (Matriculation Examination Regulations 2025).

Are these official MATSEC examination questions?

No. Official MATSEC AM Pure Mathematics uses the written/oral/practical/coursework components set in the AM 27 syllabus—not a fixed multiple-choice paper. This bank is an original English-language MCQ study adaptation for syllabus knowledge practice only.