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Free Practice Questions for Grade 7 Mathematics

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Key Facts: Grade 7 Mathematics Exam

3012

Grade 7 Mathematics code on the ECoL 2025 final timetable

1h30

Written end-of-level duration on the 2025 final timetable

4 levels

Achievement reporting: Advanced, Proficient, Basic, Below Basic

5 subjects

Mathematics is one of five subjects averaged for ECoL Top Ten ranking

ECoL Grade 7 Mathematics (timetable code 3012) is a written 1h30 end-of-level paper reported on four achievement levels. These 100 MCQs are a study adaptation with real calculations, not an official paper simulation.

Sample Grade 7 Mathematics Practice Questions

Try these sample questions to review concepts for the Grade 7 Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set. Set A = {2, 4, 6, 8} and set B = {3, 6, 9}. Which elements are in A ∩ B?
A.{6}
B.{2, 4, 6, 8, 3, 9}
C.{2, 3, 4, 6, 8, 9}
D.{1, 5, 7, 10}
Explanation: A ∩ B is the intersection: elements in both A and B. Only 6 is in both, so A ∩ B = {6}.
2Universal set U = {a, b, c, d, e, f}. Set P = {a, c, e} and set Q = {b, c, d}. How many elements are in P ∪ Q?
A.3
B.4
C.5
D.6
Explanation: P ∪ Q = {a, b, c, d, e}: five distinct elements. Element f is in U but not in P ∪ Q.
3In a class of 40 learners, 25 study Sesotho (set S), 22 study English (set E), and 12 study both. How many study only Sesotho?
A.12
B.13
C.22
D.25
Explanation: Only Sesotho = |S| − |S ∩ E| = 25 − 12 = 13.
4Universal set U has 50 elements. Set A has 28 elements, set B has 20 elements, and |A ∩ B| = 8. How many elements of U are in neither A nor B?
A.6
B.10
C.18
D.40
Explanation: |A ∪ B| = 28 + 20 − 8 = 40. Neither = 50 − 40 = 10.
5In the number 3 852 761 409, what is the place value of the digit 5?
A.5 million
B.50 million
C.500 million
D.5 billion
Explanation: The places are: 3 billions, 8 hundred millions, 5 ten millions, … Place value of 5 = 5 × 10 000 000 = 50 million.
6What is 2 040 000 700 written in expanded form?
A.2×1 000 000 000 + 4×10 000 000 + 7×100
B.2×1 000 000 000 + 4×1 000 000 + 7×100
C.2×100 000 000 + 4×10 000 000 + 7×100
D.2×1 000 000 000 + 4×10 000 000 + 7×10
Explanation: 2 040 000 700 = 2 billion + 40 million + 700 = 2×1 000 000 000 + 4×10 000 000 + 7×100.
7Which statement is true about 1 099 999 999 and 1 100 000 000 − 1?
A.1 099 999 999 is greater
B.They are equal
C.1 100 000 000 − 1 is greater
D.They cannot be compared
Explanation: 1 100 000 000 − 1 = 1 099 999 999, so the two expressions are equal.
8Share M 360 in the ratio 2 : 3 between Thabo and Lineo. How much does Lineo receive?
A.M 120
B.M 144
C.M 216
D.M 240
Explanation: Parts = 2 + 3 = 5. One part = 360 ÷ 5 = M 72. Lineo (3 parts) = 3 × 72 = M 216.
9M 480 is shared between Palesa and Kabelo in the ratio 5 : 7. How much more does Kabelo get than Palesa?
A.M 40
B.M 80
C.M 200
D.M 280
Explanation: Parts = 12. One part = 480 ÷ 12 = M 40. Difference = 2 parts = M 80 (Kabelo 280 − Palesa 200).
10Neo and Mpho share money in the ratio 4 : 5. If Neo receives M 320, what is the total amount shared?
A.M 400
B.M 640
C.M 720
D.M 1 600
Explanation: Neo’s 4 parts = M 320, so 1 part = 80. Total 9 parts = 9 × 80 = M 720.

About the Grade 7 Mathematics Exam

Mathematics is a compulsory Grade 7 End-of-Level subject. Scope follows NCDC Grade 7 Numerical and Mathematical outcomes: sets, place value, ratio and rate, financial mathematics, shape constructions, polygon angles, nets, surface area and volume, transformations, simple equations, linear graphs, mean/median and probability—with emphasis on application.

Exam sponsor: Examinations Council of Lesotho (ECoL); curriculum scope from NCDC Integrated Primary Curriculum Grade 7 (Numerical and Mathematical learning area). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written end-of-level paper; 2025 final timetable code 3012, 1 hour 30 minutes. Per the 2024 Grade 7 Achievement Report, Top Ten is ranked on the average percentage mark of five subjects — Sesotho, English, Mathematics, Science & Technology and Social Science.

Time Limit

1 hour 30 minutes (2025 final timetable: 09:00–10:30 on 28 October 2025). Confirm current year.

Passing Score

Achievement levels Advanced, Proficient, Basic, Below Basic (Index 1–4). No single percentage pass mark.

Exam / Certification Fees

School candidates: confirm the live 2026 Grade 7 Examinations Fees table at examscouncil.org.ls (deadline 30 May 2026).

Exam sponsor website

Reported exam pass rate: Not published as a single pass %.. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

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.

No official % weights published — distribute by LO coverage

Number, sets, ratio and rate

Universal set with two sets; place value to billions; ratio sharing; rate; dividing fractions and decimals; rounding to thousandths.

No official % weights published

Financial mathematics

Percentage profit and loss, commission, discount and mini buying/selling project calculations.

No official % weights published

Shape, space and measurement

Constructions (parallelogram, rhombus, kite, trapezium); interior/exterior polygon angles; nets; surface area and volume of prisms and cylinders; volume–capacity links; angle properties; translations, reflections, 90°/180° rotations.

No official % weights published

Algebra, graphs, data and probability

Letter unknowns in one- and two-digit equations; Cartesian linear graphs; median and mean; simple probability experiments.

Preparing for the Grade 7 Mathematics Exam

What You Need to Know

  • Passing score: Achievement levels Advanced, Proficient, Basic, Below Basic (Index 1–4). No single percentage pass mark.
  • Assessment: Written end-of-level paper; 2025 final timetable code 3012, 1 hour 30 minutes. Per the 2024 Grade 7 Achievement Report, Top Ten is ranked on the average percentage mark of five subjects — Sesotho, English, Mathematics, Science & Technology and Social Science.
  • Time limit: 1 hour 30 minutes (2025 final timetable: 09:00–10:30 on 28 October 2025). Confirm current year.
  • Exam / certification fees: School candidates: confirm the live 2026 Grade 7 Examinations Fees table at examscouncil.org.ls (deadline 30 May 2026). Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Grade 7 Mathematics: Suggested Study Strategy

1Show full working for multi-step profit/loss, surface area and volume items—method marks matter on written papers.
2Practise nets of cubes, cuboids, triangular prisms and pyramids until you can match net to solid quickly.
3Drill fraction and decimal division without a calculator where the official paper expects mental/written methods.
4Use Lesotho maloti (M) consistently in financial problems and check percentage formulas (profit ÷ cost × 100).
5For probability, list sample spaces carefully before calculating fractions.

Frequently Asked Questions

What is Grade 7 Mathematics in Lesotho?

It is the compulsory ECoL Grade 7 End-of-Level Mathematics assessment for primary leavers. Scope comes from the NCDC Integrated Primary Curriculum Grade 7 Numerical and Mathematical learning area. It is not LGCSE Mathematics 0178.

How long is the official paper?

The 2025 final timetable lists Mathematics code 3012 for 1 hour 30 minutes (09:00–10:30 on 28 October 2025). Always confirm the live timetable for the sitting year.

Is there a percentage pass mark?

No. ECoL reports Advanced, Proficient, Basic and Below Basic achievement levels. Top Ten ranking uses average percentage of five subjects including Mathematics, but that is a ranking rule, not a pass mark.

Are these official exam questions?

No. Official assessment is a written paper, not multiple-choice. These MCQs are study adaptations with genuine calculation items covering topics from NCDC Grade 7 outcomes.