100+ Free MCA Second Engineer Mathematics Practice Questions

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MCA Management Level (III/2) Naval Architecture (040-34) — Second/Chief Engineer

Practice Questions100 questions

2026 Statistics

Key Facts: MCA Second Engineer Mathematics Exam

≥50%

Official Academic Pass Mark

MSN 1857 / MSN 1857 Amendment 1

040-35

Current Subject Code (Management Engineer Maths)

Qualifications Scotland/MCA examination timetable

Written paper

Official Assessment Format

GOV.UK Second Engineer Mathematics syllabus / SQA-MCA written exams

~£140

Recent Academic Sitting Fee (confirm)

Approved-centre Qualifications Scotland entry schedules

8 topics

Official Syllabus Sections

GOV.UK Mathematics Written Examination Syllabus

Free 2026

This Practice Bank

OpenExamPrep English MCQ study adaptation

Free 100-question English MCQ study bank for MCA Second Engineer / management Mathematics (MSN 1857 ≥50% pass). Official exam: Qualifications Scotland/MCA written calculation paper (040-35), not MCQ. Fee: confirm centre schedule (recent academic sittings often listed near £140). Syllabus: arithmetic, algebra, logs, graphs, trigonometry, mensuration, differentiation and integration. Not an official paper simulation.

Sample MCA Second Engineer Mathematics Practice Questions

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

1A pump discharges 480 m3 of bilge water in 4 hours. A second pump of equal capacity is started after 1 hour so both finish the remaining work. How long after the second pump starts is the discharge complete?

A.1.5 hours

B.1.75 hours

C.2 hours

D.2.5 hours

Explanation: One pump rate = 480/4 = 120 m3/h. After 1 hour, 120 m3 is discharged and 360 m3 remains. With both pumps: 240 m3/h, so remaining time = 360/240 = 1.5 hours after the second pump starts.

2Express the ratio 2.4 : 3.6 in simplest whole-number form.

A.2 : 3

B.3 : 4

C.4 : 6

D.24 : 36

Explanation: Divide both terms by 1.2: 2.4/1.2 = 2 and 3.6/1.2 = 3, so 2 : 3. Equivalently, multiply by 5 to get 12 : 18 then divide by 6.

3A steel shaft diameter is measured as 50.00 mm. The true diameter is 49.75 mm. What is the percentage error based on the true value, rounded to three decimal places?

A.0.500%

B.0.503%

C.0.250%

D.0.502%

Explanation: Error = 50.00 - 49.75 = 0.25 mm. Percentage error = (0.25/49.75)*100 = 0.502512...%. Rounded to three decimal places: 0.503%.

4A casting cools and contracts by 1.5% of its hot length. If the hot length is 2.400 m, what is the cold length?

A.2.364 m

B.2.376 m

C.2.388 m

D.2.412 m

Explanation: Contraction = 1.5% of 2.400 m = 0.015 * 2.400 = 0.036 m. Cold length = 2.400 - 0.036 = 2.364 m.

5An electric motor consumes 24 kWh in 8 hours at constant load. What is the average power?

A.2 kW

B.3 kW

C.4 kW

D.192 kW

Explanation: Average power (kW) = energy (kWh) / time (h) = 24/8 = 3 kW.

6Two similar solid castings are geometrically similar. The larger has linear scale 1.5 times the smaller. If the smaller mass is 80 kg and density is the same, what is the larger mass?

A.120 kg

B.180 kg

C.270 kg

D.360 kg

Explanation: Mass scales with volume, and volume scales as the cube of linear dimensions. Scale factor k = 1.5, so mass ratio = 1.5^3 = 3.375. Larger mass = 80 * 3.375 = 270 kg.

7Express 7/8 as a percentage.

A.75%

B.87.5%

C.88%

D.112.5%

Explanation: 7/8 = 0.875. As a percentage: 0.875 * 100% = 87.5%.

8A store issues 360 kg of packing compound over 9 days at a steady rate. At the same rate, how many days will 200 kg last?

A.4 days

B.5 days

C.5.5 days

D.6 days

Explanation: Daily rate = 360/9 = 40 kg/day. Days for 200 kg = 200/40 = 5 days.

9A workshop job is quoted as 48 man-hours. If 6 fitters work at equal efficiency, how many hours will the job take (assuming continuous parallel work)?

A.6 hours

B.8 hours

C.12 hours

D.48 hours

Explanation: Man-hours = number of workers * hours. Hours = 48/6 = 8 hours.

10A quantity increases from 250 to 300. What is the percentage gain based on the original value?

A.16.7%

B.20%

C.25%

D.50%

Explanation: Increase = 50. Percentage gain = (50/250)*100% = 20%.

About the MCA Second Engineer Mathematics Exam

MCA Second Engineer Mathematics is the written academic module that underpins calculation competence for Second Engineer unlimited (STCW III/2) and the combined management-level academic suite. The official GOV.UK syllabus covers arithmetic (ratios, percentages, scale, rates), algebra (indices, factorisation, linear/simultaneous/quadratic equations, variation), logarithms as supporting knowledge, graphs (including linearisation and pV^n log plots), trigonometry, mensuration of plane figures and solids, differentiation (including rates and max/min), and integration (including areas and polytropic work integrals). MSN 1857 requires a pass mark of at least 50% in each Second Engineer academic examination at this level, including Mathematics. The live paper is a worked written examination administered by Qualifications Scotland for the MCA (040-35 on current management engineer timetables). This free bank is an English-language multiple-choice study adaptation of that syllabus — not an official paper simulation.

Assessment

IDENTITY NOTE (verified 2026-08-08): there is no longer a separate Second Engineer and Chief Engineer academic examination. From 1 January 2017 the two were combined into a single Management Level (STCW III/2) paper per subject (MSN 1857 (M+F)), and Qualifications Scotland — which replaced the SQA on 1 February 2026 — timetables only the 040 Management Engineer series for 2025/26 and 2026/27. This page covers Management Level paper 040-35 Mathematics, which is sat once and counts towards both the Second Engineer and the Chief Engineer Certificate of Competency. Official: written examination covering arithmetic, algebra, logarithms (assumed knowledge), graphs, trigonometry, mensuration, differentiation and integration as set out in the GOV.UK Second Engineer Mathematics syllabus. Management engineer diets list the paper as 040-35 Mathematics. This practice set converts that assessable calculation knowledge into four-option MCQs with worked numeric answers.

Time Limit

As stated on the current Qualifications Scotland/MCA paper for the diet (includes 15 minutes reading time under published examination conduct regulations); confirm the front-cover allowance when booking

Passing Score

At least 50% in the Mathematics academic examination (MSN 1857 / MSN 1857 Amendment 1: pass mark of at least 50% in all SQA/MCA Second Engineer academic examinations at this level, including Mathematics)

Exam Fee

Approximately £140 per academic subject sitting for 040-35 Mathematics on recent approved-centre entry schedules — confirm the current Qualifications Scotland/MCA fee with your examination centre (fees are revised periodically) (Maritime and Coastguard Agency (MCA) / Qualifications Scotland (written examinations administered for and on behalf of the MCA))

MCA Second Engineer Mathematics Exam Content Outline

12%

Arithmetic

Ratios, proportions, percentages, percentage error and change, similarity/scale (length, area, volume, mass), rates, averages, man-hours and kWh

20%

Algebra

Indices, brackets, expansion, factorisation, algebraic fractions, linear and simultaneous equations, quadratics, transposition, direct and inverse variation

Logarithms

Definition and laws of logarithms, common logs, natural logs and base e (supporting calculation skill per syllabus)

10%

Graphs

Abscissa/ordinate, dependent variables, straight-line law, linearisation, simultaneous and quadratic roots, log plots for engineering laws

15%

Trigonometry

Degrees and radians, trig ratios and reciprocals, Pythagoras, sine rule, cosine rule, allied angles, triangle solution and area

15%

Mensuration

Areas of rectangles, triangles, trapeziums, circles, annuli, ellipses, sectors; volumes and surface areas of prisms, cylinders, cones, spheres; mass from density

13%

Calculus — Differentiation

Power rule, constants, sin/cos/ln derivatives, rates of change, velocity and acceleration, turning points, max/min problems

10%

Calculus — Integration

Indefinite integrals and +C, definite integrals, sin/cos integrals, area under a curve, polytropic ∫ p dV forms

How to Pass the MCA Second Engineer Mathematics Exam

What You Need to Know

Passing score: At least 50% in the Mathematics academic examination (MSN 1857 / MSN 1857 Amendment 1: pass mark of at least 50% in all SQA/MCA Second Engineer academic examinations at this level, including Mathematics)
Assessment: IDENTITY NOTE (verified 2026-08-08): there is no longer a separate Second Engineer and Chief Engineer academic examination. From 1 January 2017 the two were combined into a single Management Level (STCW III/2) paper per subject (MSN 1857 (M+F)), and Qualifications Scotland — which replaced the SQA on 1 February 2026 — timetables only the 040 Management Engineer series for 2025/26 and 2026/27. This page covers Management Level paper 040-35 Mathematics, which is sat once and counts towards both the Second Engineer and the Chief Engineer Certificate of Competency. Official: written examination covering arithmetic, algebra, logarithms (assumed knowledge), graphs, trigonometry, mensuration, differentiation and integration as set out in the GOV.UK Second Engineer Mathematics syllabus. Management engineer diets list the paper as 040-35 Mathematics. This practice set converts that assessable calculation knowledge into four-option MCQs with worked numeric answers.
Time limit: As stated on the current Qualifications Scotland/MCA paper for the diet (includes 15 minutes reading time under published examination conduct regulations); confirm the front-cover allowance when booking
Exam fee: Approximately £140 per academic subject sitting for 040-35 Mathematics on recent approved-centre entry schedules — confirm the current Qualifications Scotland/MCA fee with your examination centre (fees are revised periodically)

Keys to Passing

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

MCA Second Engineer Mathematics Study Tips from Top Performers

1Drill factorisation and the quadratic formula until both are automatic — many later mechanics and heat calculations start from rearranged algebra

2Practise percentage error with the true value in the denominator, and always state whether a change is gain or contraction

3For similar solids, scale mass and volume with the cube of the linear factor; areas scale with the square

4Memorise sin/cos/tan of 0°, 30°, 45°, 60°, 90° and convert fluently between degrees and radians (π rad = 180°)

5Use sine rule for ASA/AAS-type data and cosine rule when you have two sides and the included angle or three sides

6On graphs, rewrite laws such as y = a x^2 + b as y = aX + b with X = x^2; for pV^n = C use log p against log V so slope = −n

7Differentiate first for max/min: set dy/dx = 0, then use the sign of d²y/dx² (or first-derivative sign chart) to classify

8For polytropic work, remember n ≠ 1 → (p1V1 − p2V2)/(n − 1) and n = 1 → pV ln(V2/V1); the live paper is calculation-heavy, not multiple choice

Frequently Asked Questions

What is the MCA Second Engineer Mathematics exam?

It is the Qualifications Scotland/MCA written academic examination in mathematics for Second Engineer unlimited (STCW III/2) and the management engineer academic suite. The official GOV.UK syllabus covers arithmetic through basic calculus as used in marine engineering calculations.

What is the official pass mark?

MSN 1857 (and Amendment 1) requires a pass mark of at least 50% in each SQA/MCA Second Engineer academic examination at this level. Mathematics is listed among those academic subjects.

Is the real exam multiple choice?

No. The official assessment is a worked written calculation paper. These free practice items are an English-language multiple-choice study adaptation of the same syllabus topics — not an official Qualifications Scotland/MCA paper simulation.

What topics does the syllabus cover?

Arithmetic; algebra; logarithms (supporting knowledge); graphs; trigonometry; mensuration; differentiation; and integration, as published in the GOV.UK Second Engineer Mathematics Written Examination Syllabus.

How much does the exam cost?

Academic subject fees are set through Qualifications Scotland/MCA and charged via approved centres. Recent centre schedules have listed 040-35 Mathematics near £140 per sitting; always confirm the current fee before booking.

Who administers the exam?

Written papers are administered by Qualifications Scotland for and on behalf of the Maritime and Coastguard Agency (MCA) at MCA-approved examination centres.

What is subject code 040-35?

On current management engineer (REG III/2 unlimited) timetables, Mathematics is listed as examination 040-35. Diets are published by Qualifications Scotland/MCA (typically multiple sittings per year).

Does a Mathematics pass expire after three years?

Engineering Knowledge written passes are subject to a three-year validity window for CoC issue. Management-level academic subjects including Mathematics are treated under the separate academic-pass rules in the Qualifications Scotland/MCA regulations (not the same 3-year EK rule). Confirm CoC assembly timing against the current MSN 1857 Amendment 1.