Mathematics N5 — Document

August 2021 — N5 — Mathematics

N5 2021 Nated Engineering

↓ Download PDF 📄 299.8 KB

Preparing document

📋 Document Analysis

🎯 100 marks ⏱️ 3h 📄 5 pages 📝 46 items found ∑ 1 math symbols 📚 6 topics

See full analysis

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 the following limits:

1.1.1(3\

1.1.2(2\

1.2Given: , calculate the numerical value of:

1.2.1(2\

1.2.2(1\

1.3Determine the value(s\f for which is discontinuous if (2\ [10]10

Q2— Section header —

2.1Given: Determine the simplest form of:

2.1.1(2\

2.1.2(1\

2.1.3(1\

2.1.4(1\

2.2Determine in each of the following cases: (Simplification not required

2.2.2

2.3Calculate if with the aid of logarithmic differentiation (4\

2.4Determine of implicit function (5\ [22]22

Q3— Section header —

3.1Given:

3.1.1Determine the coordinate of the point of inflection of (2\

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

3.1.3Draw a neat graph of between these values and show the turning points on it. (2\

3.1.4One root of the equation is close to Use Taylor's/Newton's method twice to determine a better approximation of this root ( oot correct to THREE decimals\ (4\

3.2We want to build a rectangular box with a base length 6 times the base width, and the box will enclose 20 m . The cost of the material of the sides is R3/m and the cost of the top and bottom is R15/m

Q4— Section header —

4.1Determine in each of the following cases.

4.1.1(4\

4.1.2(4\

4.1.3(5\

4.1.4(2\

4.1.5(4\ (16030175\ Copyright reserved

4.2Determine by resolving the integral into partial fractions: (5\ [24]24

Q5— Section header —

5.1Evaluate the definite integral: (5\

5.2Given : and axis

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\

5.2.3Calculate the magnitude of the area in

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 flywheel of radius 30 cm and thickness of 3 cm about an axis through its centre and perpendicular to the flywheel. The mass of the flywheel is 15 kg. (4\ [20]20

Q6— Section header —

6.1Determine the particular solution of (4\

6.2Determine the general solution of (3\ [7] TOTAL 100 (16030175\7

Mathematical Content

f(x)

Topics Identified

AlgebraCalculusGeometryTrigonometryAnalytical GeometryFunctions

Mark Allocation

Total100 marks

Sections10 + 22 + 17 + 24 + 20 + 7 = 100 marks

Paper information

TitleDocument

SubjectMathematics

LevelN5

Document typeQuestion paper

Year2021

MonthAugust

Pages9

Downloads3

Examination context

Decade2020s

Years ago5y

SeasonWinter (SH)

Start daySunday

Exam periodAugust 2021

Days since exam1,897

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.

File details

File size299.8 KB

Pages9

Archived on8 September 2026

File age46d

ContributorFreeMode

FingerprintD4911AA48914

Questions and learner discussion

No questions or discussions have been posted yet.