Free Practice Questions for LGCSE Mathematics (0178)

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Key Facts: LGCSE Mathematics (0178) Exam

0178

Official LGCSE Mathematics syllabus code

ECoL / NCDC Mathematics syllabus

Core 1 & 3 / Extended 2 & 4

Paper routes

LGCSE Mathematics 0178 assessment criteria

35% + 65%

Short-answer paper + structured paper weighting

LGCSE Mathematics 0178 syllabus

A*–G / C–G

Extended / Core available grades (U ungraded)

ECoL grading

M910

2026 private fee for one LGCSE subject entry

ECoL examinations fees 2026

Oct/Nov

Main examination series

LGCSE Mathematics syllabus availability

100

Free practice MCQs on this page

OpenExamPrep study adaptation

LGCSE Mathematics 0178 is assessed in the October/November series through two written papers per tier: Core (Papers 1 & 3; grades C–G) or Extended (Papers 2 & 4; grades A*–G). Papers 1 and 2 ban calculators; Papers 3 and 4 require a non-programmable scientific calculator. The 100 questions on this page are an English-language MCQ study adaptation, not an official ECoL paper simulation.

Sample LGCSE Mathematics (0178) Practice Questions

Try these sample questions to review concepts for the LGCSE Mathematics (0178) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which of the following is a prime number?

A.51

B.57

C.59

D.63

Explanation: A prime number has exactly two distinct positive factors: 1 and itself. 59 is only divisible by 1 and 59. 51 = 3×17, 57 = 3×19, and 63 = 7×9, so all three are composite.

2Find the highest common factor (HCF) of 36 and 54.

A.6

B.9

C.18

D.12

Explanation: 36 = 2² × 3² and 54 = 2 × 3³. The HCF uses the lowest powers of common primes: 2¹ × 3² = 18.

3Find the lowest common multiple (LCM) of 12 and 18.

A.36

B.6

C.72

D.54

Explanation: 12 = 2² × 3 and 18 = 2 × 3². The LCM takes the highest powers: 2² × 3² = 36.

4Calculate 3/4 + 2/5.

A.5/9

B.23/20

C.6/20

D.1

Explanation: Common denominator 20: 3/4 = 15/20 and 2/5 = 8/20. Sum = 23/20.

5Convert 0.375 to a fraction in lowest terms.

A.3/8

B.375/1000

C.3/5

D.37/100

Explanation: 0.375 = 375/1000. Divide numerator and denominator by 125: 3/8.

6Write 0.00056 in standard form.

A.5.6 × 10^-4

B.5.6 × 10^-3

C.56 × 10^-5

D.5.6 × 10^4

Explanation: Standard form is A × 10^n with 1 ≤ A < 10. Moving the decimal four places right gives 5.6, so 5.6 × 10^-4.

7Calculate 2^3 × 2^4.

A.2^7

B.2^12

C.4^7

D.2^1

Explanation: When multiplying powers with the same base, add the indices: 2^(3+4) = 2^7.

8Evaluate 5^-2.

A.1/25

B.-25

C.-1/25

D.25

Explanation: A negative index means reciprocal: 5^-2 = 1/5^2 = 1/25.

9A jacket costs M400. In a sale it is reduced by 15%. What is the sale price?

A.M340

B.M360

C.M385

D.M60

Explanation: 15% of 400 = 0.15 × 400 = 60. Sale price = 400 − 60 = M340. Equivalently, 85% of 400 = 0.85 × 400 = 340.

10Express 3:12 in its simplest form.

A.1:4

B.3:4

C.1:3

D.4:1

Explanation: Divide both parts by their HCF 3: 3÷3 : 12÷3 = 1:4.

About the LGCSE Mathematics (0178) Exam

LGCSE Mathematics (0178) is Lesotho’s senior secondary mathematics qualification, developed by the National Curriculum Development Centre (NCDC) in collaboration with ECoL and adopted from IGCSE Mathematics (0580). It offers Core and Extended routes covering number, algebra, space and shape, and statistics and probability.

Exam sponsor: Examinations Council of Lesotho (ECoL). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Core: Paper 1 (short answer, 1 hour, 60 marks, 35%) + Paper 3 (structured, 2 hours, 100 marks, 65%). Extended: Paper 2 (short answer, 1½ hours, 70 marks, 35%) + Paper 4 (structured, 2½ hours, 130 marks, 65%).

Time Limit

Core: 1 hour + 2 hours. Extended: 1½ hours + 2½ hours

Passing Score

Letter grades A*–G (U = ungraded). Core available grades C–G; Extended A*–G. Grade C or better is commonly treated as credit-level.

Exam / Certification Fees

Private candidates: M910 for one LGCSE subject on the 2026 ECoL fee table (scale rises to M2730 for 8 subjects). School candidates register through centres. Confirm current fees at examscouncil.org.ls.

Exam sponsor website

Reported exam pass rate: Not published by ECoL. 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.

Core 30–35%; Extended 15–20%

Number

Directed numbers in practical contexts; natural numbers, integers, primes, composites, HCF and LCM; rational and irrational numbers; number sequences and simple nth terms; squares, square roots, cubes and cube roots; fractions, decimals and percentages; ordering with inequality symbols; BODMAS with directed numbers; estimation, significant figures, decimal places, and upper/lower bounds; positive, negative, zero and fractional indices; standard form A × 10^n.

Core 20–25%; Extended 35–40%

Algebra and Graphs

Letters for generalised numbers; substitution into formulae; expanding brackets; factorising (common factors, difference of two squares, perfect squares, quadratics); algebraic fractions; linear equations and inequalities; simultaneous linear equations; quadratic equations; changing the subject; sequences including quadratic and higher Extended forms; coordinate geometry of straight lines; graphs of linear and quadratic relationships and interpretation of travel graphs.

Core and Extended 30–35%

Space and Shape

Measuring and constructing lines and angles; angle bisectors and perpendicular bisectors; scale drawings; loci; three-figure bearings and multi-stage journeys; geometrical terms, polygons, similarity and congruence; Pythagoras; right-angled trigonometry and Extended non-right-angled methods; perimeter, area, surface area and volume (including circles, sectors, prisms, cylinders, pyramids, cones and spheres); geometric transformations; column vectors and vector geometry.

Core and Extended 10–15%

Statistics and Probability

Collecting and organising data; mean, median, mode and range; frequency tables and grouped data estimates; pie charts, bar charts and related diagrams; cumulative frequency ideas; simple probability; combined events; tree diagrams and complementary events.

Preparing for the LGCSE Mathematics (0178) Exam

What You Need to Know

Passing score: Letter grades A*–G (U = ungraded). Core available grades C–G; Extended A*–G. Grade C or better is commonly treated as credit-level.
Assessment: Core: Paper 1 (short answer, 1 hour, 60 marks, 35%) + Paper 3 (structured, 2 hours, 100 marks, 65%). Extended: Paper 2 (short answer, 1½ hours, 70 marks, 35%) + Paper 4 (structured, 2½ hours, 130 marks, 65%).
Time limit: Core: 1 hour + 2 hours. Extended: 1½ hours + 2½ hours
Exam / certification fees: Private candidates: M910 for one LGCSE subject on the 2026 ECoL fee table (scale rises to M2730 for 8 subjects). School candidates register through centres. Confirm current fees at examscouncil.org.ls. Official sources

Using Our Practice Resources

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LGCSE Mathematics (0178): Suggested Study Strategy

1Drill non-calculator arithmetic and algebraic manipulation for Papers 1 and 2 — sign errors and order-of-operations mistakes cost easy marks.

2Memorise key formulae (area, volume, Pythagoras, SOHCAHTOA, sector and arc formulae) and practise showing four-figure working before three-figure final answers on calculator papers.

3Balance Core topics (strong number and space weightings) with Extended algebra emphasis if you aim for A*–B grades.

4Practise bearings, scale drawings, loci language, and multi-step mensuration with units consistent throughout.

5For statistics, always state whether you mean estimated mean from midpoints of groups, and check probability answers lie between 0 and 1.

Frequently Asked Questions

What is LGCSE Mathematics 0178?

Syllabus 0178 is the Examinations Council of Lesotho (ECoL) Mathematics syllabus for the Lesotho General Certificate of Secondary Education. It is a senior secondary qualification developed with the National Curriculum Development Centre (NCDC) and adopted from IGCSE Mathematics (0580), offered at Core and Extended levels.

What is the paper structure for LGCSE Mathematics?

Core candidates sit Paper 1 (short answer, 1 hour, 60 marks, 35%) and Paper 3 (structured, 2 hours, 100 marks, 65%). Extended candidates sit Paper 2 (short answer, 1½ hours, 70 marks, 35%) and Paper 4 (structured, 2½ hours, 130 marks, 65%). Papers 1 and 2 prohibit calculators; Papers 3 and 4 allow a silent non-programmable scientific calculator with trigonometric functions.

What grades are available for Core and Extended?

Core is graded C, D, E, F and G. Extended is graded A*, A, B, C, D, E, F and G. U means ungraded. Grade C or better is commonly treated as credit-level for further study; there is no single published numeric percentage pass mark.

When is LGCSE Mathematics examined?

The main examination series is October/November. Availability is open to school and private candidates. Check the current ECoL timetable and registration deadlines on examscouncil.org.ls (for example, 2026 financial registration deadlines are published on the examinations-fees page).

How much does private-candidate entry cost?

On the 2026 ECoL fee table, private LGCSE candidates pay from M910 for one subject up to M2730 for eight subjects. School candidates are registered through their centres. Always confirm the live fee schedule on examscouncil.org.ls before registering.

Are these official ECoL examination questions?

No. Official LGCSE Mathematics uses written short-answer and structured papers, not multiple-choice. This bank is an original English-language MCQ study adaptation covering topics from syllabus 0178 content for practice of number, algebra, geometry, mensuration, trigonometry, statistics and probability.