100+ Free MATSEC IM Pure Mathematics Practice Questions

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

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2026 Statistics

Key Facts: MATSEC IM Pure Mathematics Exam

IM 27

Official MATSEC Intermediate subject code

MATSEC 2026 syllabi catalogue

A–E / F

Subject grade scale (A highest pass; F fail)

Matriculation Examination Regulations 2025

10 / 8 / 6 / 4 / 2

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

Matriculation Examination Regulations 2025

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

Matriculation Examination Regulations 2025

EUR 40

Revision of Paper fee at IM 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

100

Free practice MCQs on this page (study adaptation)

OpenExamPrep

MATSEC Intermediate Matriculation Pure Mathematics (IM 27) is a University of Malta MATSEC subject assessed under the 2026 syllabus (one written paper: 3 hours). Results use grades A–E (pass) or F; IM grade points contribute to the Matriculation Certificate (minimum 44 points). The 100 questions on this page are an English-language MCQ study adaptation, not an official MATSEC format simulation.

Sample MATSEC IM Pure Mathematics Practice Questions

Try these sample questions to test your MATSEC IM Pure Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Simplify √48 − √12.

A.2√3

B.4√3

C.√36

D.6√2

Explanation: √48 = √(16×3) = 4√3 and √12 = √(4×3) = 2√3, so √48 − √12 = 4√3 − 2√3 = 2√3.

2Rationalise the denominator of 3/(√5 − √2).

A.√5 + √2

B.√5 − √2

C.3(√5 + √2)

D.(√5 + √2)/3

Explanation: Multiply numerator and denominator by √5 + √2: 3(√5 + √2)/((√5)² − (√2)²) = 3(√5 + √2)/(5 − 2) = 3(√5 + √2)/3 = √5 + √2.

3Simplify (8x⁶y⁻³)/(2x²y).

A.4x⁴/y⁴

B.4x⁴y⁴

C.6x⁴/y²

D.4x⁸/y²

Explanation: 8/2 = 4, x⁶/x² = x⁴, and y⁻³/y = y⁻⁴, so the expression is 4x⁴y⁻⁴ = 4x⁴/y⁴.

4Evaluate 27^(2/3).

A.9

B.18

C.3

D.81

Explanation: 27^(2/3) = (27^(1/3))² = 3² = 9, or equivalently (27²)^(1/3) = 729^(1/3) = 9.

5Solve 2^(x+1) = 32 for x.

A.4

B.5

C.3

D.16

Explanation: 32 = 2⁵, so 2^(x+1) = 2⁵ gives x + 1 = 5, hence x = 4.

6If log₁₀ x = 3, what is the value of x?

A.1000

B.30

C.100

D.3

Explanation: By definition, log₁₀ x = 3 means 10³ = x, so x = 1000.

7Solve log₂(x − 1) = 3 for x.

A.9

B.7

C.8

D.4

Explanation: log₂(x − 1) = 3 means x − 1 = 2³ = 8, so x = 9. Check: log₂ 8 = 3 and domain x − 1 > 0 is satisfied.

8Simplify log₃ 81 − log₃ 9.

A.2

B.4

C.1

D.3

Explanation: Using the quotient law: log₃ 81 − log₃ 9 = log₃(81/9) = log₃ 9 = 2. Alternatively log₃ 81 = 4 and log₃ 9 = 2, so 4 − 2 = 2.

9If f(x) = 2x − 5, find f(4).

A.3

B.−3

C.13

D.8

Explanation: To evaluate a function at a value, substitute that value for x throughout the rule. Here f(4) = 2(4) − 5 = 8 − 5 = 3. Follow the order of operations: multiply before subtracting.

10Which statement about f(x) = x² is true?

A.It is many-one

B.It is one-one on ℝ

C.Its range is ℝ

D.Its domain is only non-negative reals

Explanation: On the usual domain ℝ, f(x) = x² takes the same value for x and −x (e.g. f(2) = f(−2) = 4), so it is many-one. The range is [0, ∞), not all reals.

About the MATSEC IM Pure Mathematics Exam

Malta Intermediate Matriculation (IM) Pure Mathematics — IM 27 (2026) is administered by the MATSEC Examinations Board (University of Malta). Intermediate 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). Assessment for IM 27 follows the official 2026 syllabus scheme: One written paper of 3 hours under IM 27 2026 Pure Mathematics covering pure topics at Intermediate level. Available in September session. 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 or project work.

Assessment

One written paper of 3 hours under IM 27 2026 Pure Mathematics covering pure topics at Intermediate level. Available in September session.

Time Limit

One written paper: 3 hours

Passing Score

Subject results are graded A, B, C, D, E (pass, A highest) or F (fail). For the Matriculation Certificate, Intermediate Level grade points are: A=10, B=8, C=6, D=4, E=2. 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 Intermediate Matriculation (IM) level EUR 40, and change in school EUR 35. Examination fees are not refundable. (MATSEC Examinations Board, University of Malta)

MATSEC IM Pure Mathematics Exam Content Outline

Core

Algebra and functions

Core

Coordinate geometry

Core

Trigonometry

Core

Differentiation

Core

Integration

Core

Sequences and series

Core

Vectors

Core

Probability and statistics basics where included

Core

Equations and inequalities

Core

Proof and mathematical reasoning

How to Pass the MATSEC IM 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, Intermediate Level grade points are: A=10, B=8, C=6, D=4, E=2. 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: One written paper of 3 hours under IM 27 2026 Pure Mathematics covering pure topics at Intermediate level. Available in September session.
Time limit: One written paper: 3 hours
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 Intermediate Matriculation (IM) level EUR 40, and change in school EUR 35. Examination fees are not refundable.

Keys to Passing

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MATSEC IM Pure Mathematics Study Tips from Top Performers

1Work from the official IM 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, 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.

Frequently Asked Questions

What is MATSEC Intermediate Matriculation Pure Mathematics?

Malta Intermediate Matriculation (IM) Pure Mathematics — IM 27 (2026) is an Intermediate Matriculation subject administered by the MATSEC Examinations Board at the University of Malta under the official 2026 syllabus (IM 27). Intermediate subjects contribute grade points toward the Matriculation Certificate.

How is MATSEC IM Pure Mathematics assessed?

One written paper of 3 hours under IM 27 2026 Pure Mathematics covering pure topics at Intermediate level. Available in September session. Official papers are not fixed multiple-choice totals.

How much does MATSEC IM registration cost?

What grades and points apply at Intermediate Level?

Are these official MATSEC examination questions?

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

100+ Free MATSEC IM Pure Mathematics Practice Questions

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Key Facts: MATSEC IM Pure Mathematics Exam

Sample MATSEC IM Pure Mathematics Practice Questions

About the MATSEC IM Pure Mathematics Exam

MATSEC IM Pure Mathematics Exam Content Outline

How to Pass the MATSEC IM Pure Mathematics Exam

What You Need to Know

Keys to Passing

MATSEC IM Pure Mathematics Study Tips from Top Performers

Frequently Asked Questions