Mathematics N5 — Document

April 2018 — N5 — Mathematics

N5 2018 Nated Engineering

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📋 Document Analysis

🎯 100 marks ⏱️ 3h 📄 6 pages 📝 43 items found ∑ 2 math symbols 📚 6 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 the following limit: (3\

1.2Given: , calculate the numerical value of: HINT:

1.2.1(3\

1.2.2(1\

1.3Determine the value(s\f for which is discontinuous if (3\ [10]10

Q2— Section header —

2.1Determine the derivative of from first principles. (5\

2.2Make a neat sketch of the graph for the range (2\

2.3Calculate of the following, by making use of the derivatives of and , as well as the rules of differentiation: HINT: (4\

2.4Determine in each of the following cases: (Simplification NOT required\

2.4.1(2\

2.4.2(4\

2.5Calculate with the aid of logarithmic differentiation if (4\

2.6Determine of the implicit function (4\ [25] (16030175\25

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 is ranging from to (2\

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 this value and one approximation of Taylor' s/ Newton' s method to determine a better ap

3.2A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0 at what rate is the radius decreasing when the area of the sheet is 12

3.3cylindrical can with bottom but no top with a volume of 30 must be constructed. Determine the dimensi ons of the can that will minimis e the amount of material

Q4— Section header —

4.1Determine in each of the following cases

4.1.1(3\

4.1.2(3\

4.1.3(2\

4.1.4(4\

4.1.5(3\

4.2Determine by resolving the integral into partial fractions: (5\ [20]20

Q5— Section header —

5.1Evaluate the definite integral (4\

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 second moment of area of a rectangular lamina with sides and about a side (4\ [19] (16030175\19

Q6— Section header —

6.1Determine the particular solution of , given when (4\

6.2Determine the general olution of (2\ [6] TOTAL 100 (16030175\6

Mathematical Content

f(x)trig

Topics Identified

AlgebraCalculusGeometryTrigonometryAnalytical GeometryFunctions

Mark Allocation

Total100 marks

Sections10 + 25 + 20 + 20 + 19 + 6 = 100 marks

Paper information

TitleDocument

SubjectMathematics

LevelN5

Document typeQuestion paper

Year2018

MonthApril

Pages11

Downloads3

Examination context

Decade2010s

Years ago8y

SeasonAutumn (SH)

Start daySunday

Exam periodApril 2018

Days since exam3,114

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 size366.8 KB

Pages11

Archived on8 September 2026

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