Mathematics NCV Level 4 — Exam Paper

November 2020 — NCV Level 4 — Mathematics

NCV Level 4 2020 NCV Fundamentals

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🎯 1 marks ⏱️ 3h 📄 15 pages 📝 38 items found ∑ 3 math symbols 📚 4 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 —

1.1Various options are given as possible answers to the following questions. Choose the correct answer and write only the letter (A D\ next to the question number (1.1.1

1.1.5\ in the ANSWER BOOK.

1.1.1If where and are real numbers and , then the product will always be

1.1.2Given . Then

1.1.4The complex number in polar form is

1.1.5Solve for and if

1.2The Argand diagram represents two complex numbers in the form Use the information on the diagram below to answer questions

1.2.1to 1.2.3 Various options are given as possible an swers . Choose the correct answer and write only the letter (A D\next to the question number (1.2.1

1.2\in the ANSWER BOOK. GRAPH

1.2.1The product of in polar form, with positive rgument and 1262412

1.2Apply De Moivre's heorem and simplify to polar form with positive rgument where

1.2simplified and in polar form with positive rgument where

1.3Simplify he following complex expression and write the answer in the form (3\

1.4Solve for and in the following identity an d express any non real solutions in the form (5\

Q2— Section header —

2.1Given When is divided by the remainder is Determine the value of k by applying the remainder theorem. (2\

2.2Given:

2.2.1Use the factor theorem to show that is a factor of (1\

2.2.2Hence, factorise completely. (4\ 2. and are third

2.4Given where and Use ADDENDUM A and draw a neat graph of on the same system of axes, learly showing the line about which reflects

Q3— Section header —

3.1Given the function , determine the derivative of by applying first principles. (3\

3.2Use differentiation rules to determine the derivatives of each of the following, leaving your answer with positive exponents and in surd form where applicable:

3.2.1(2\

3.2.2(4\

3.2.3(3\

3.2.4(2\

3.3Given 3. .1 Determine the y intercept of

Q4— Section header —

4.1Determine the following integrals and simplify the answers. Leave the answer with positive exponents and in surd form where applicable.

4.1.1(3\

4.1.2(5\

4.2The velocity equation of an object is given as metres per second, where is time in seconds. Determine the distance travelled between and . Apply integration to solve the problem. Hint:

4.3A skateboard ramp has to be built using the function for the design.

4.3.1Determine the area of the bricked section enclosed by the curve of the lines and the

4.3.2Use calculus methods to d etermine the maximum gradient of the ramp (2\ [16]16

Q2— Section header —

Mathematical Content

f(x)limtrig

Topics Identified

AlgebraCalculusTrigonometryAnalytical Geometry

Mark Allocation

Total100 marks

Sections19 + 25 + 16 + 15 = 75 marks

Paper information

TitleExam Paper

SubjectMathematics

LevelNCV Level 4

Document typeQuestion paper

Year2020

MonthNovember

Pages15

Downloads3

Examination context

Decade2020s

Years ago6y

SeasonSpring (SH)

Start daySunday

Exam periodNovember 2020

Days since exam2,168

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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