Mathematics N5 — Document

April 2021 — N5 — Mathematics

N5 2021 Nated Engineering

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🎯 100 marks ⏱️ 3h 📄 5 pages 📝 47 items found ∑ 1 math symbols 📚 5 topics

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Questions — A Preview of What to Expect in the Document

This section provides a quick preview of questions from the document. It may not display every question or the complete wording of each one. For the full content, including diagrams, tables and other information, view the original PDF above.

Q1— Section header —

1.1Determine each of the following limits:

1.1.1(4\

1.1.2(2\

1.2Given: alculate the numerical value of each of the following:

1.2.1(2\

1.2.2(1\

1.3Determine the value(s\ of for which is discontinuous if (2\ [11]11

Q2— Section header —

2.1Given Determine the simplest form of each of the following:

2.1.1(2\

2.1.2(1\

2.1.3(1\

2.1.4(1\

2.2Calculate of the following by us ing the derivatives of and , as well as the rules of differentiation: HINT

2.3Determine in each of the following cases implification not required\

2.3.2

2.4Calculate with the aid of logarithmic differentiation if (4\

2.5Determine of the implicit function (4\ [22]22

Q3— Section header —

3.1Given:

3.1.1Determine the coordinates of the turning points of (2\

3.1.2Draw up a table of and , where from to (3\

3.1.3Draw a neat graph of between the values

Q3— Section header —

3.1.4One root of the equation is close to Use Taylor's/Newton' s method once to determine a better approximation of this root ( oot correct to THREE

3.2Find the TWO positive numbers whose product is 750, and for which the sum of ONE number and TEN times the other number is a minimum. (5\ [15]15

Q4— Section header —

4.1Determine in each of the following cases:

4.1.1(3\

4.1.2(3\

4.1.3(4\ (16030175\ Copyright reserved

4.1.4(4\

4.1.5(4\

4.2Determine by resolving the integral in partial fractions: (5\ [23]23

Q5— Section header —

5.1Evaluate the definite integral (3\

5.2Given and

5.2.1Calculate the coordinates of the points of intersection. (2\

5.2.2Make a neat sketch to show the enclosed area, the representative strip and the point of intersection. (2\

Q5— Section header —

5.2.4Calculate the volume of the solid of revolution formed when the area in

Q5— Section header —

5.3Calculate the moment of inertia of a circular lamina of radius and mass about an axis through its centre and perpendicular to the plane of the lamina. (5\ [20]20

Q6— Section header —

6.1De termine the general solution of: (3\

6.2Determ ine the particular solution of the following: (6\ [9] TOTAL 100 (16030175\9

Mathematical Content

f(x)

Topics Identified

AlgebraCalculusGeometryAnalytical GeometryFunctions

Mark Allocation

Total100 marks

Sections11 + 22 + 15 + 23 + 20 + 9 = 100 marks

Paper information

TitleDocument

SubjectMathematics

LevelN5

Document typeQuestion paper

Year2021

MonthApril

Pages10

Downloads3

Examination context

Decade2020s

Years ago5y

SeasonAutumn (SH)

Start dayThursday

Exam periodApril 2021

Days since exam2,018

About Mathematics examination preparation

TVET Mathematics at N-level combines algebra, trigonometry, geometry, and calculus. The examination tests both computational accuracy and the ability to apply mathematical methods to engineering and technical contexts.

How to use this resource for revision

A TVET past examination paper is most useful when it is treated as an active revision exercise. Try the questions yourself before checking the corresponding memorandum. Where you make an error, identify the reason — was it a knowledge gap, a calculation mistake, an interpretation issue, or an examination technique problem?

For stronger examination practice, complete the paper without unnecessary interruptions and keep track of the questions that take the most time. Afterwards, review the memorandum and separate knowledge gaps from mistakes caused by interpretation, calculation, structure, or examination technique.

algebraic manipulation

trigonometric problem solving

calculus techniques

geometric reasoning

applying maths to engineering contexts

A practical revision approach

Practice showing full working on every question — the marking memorandum allocates substantial method marks. For N4–N6 levels, focus on calculus and geometry as these carry the heaviest mark weightings.

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File size293.6 KB

Pages10

Archived on8 September 2026

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