Mathematics NCV Level 4 — Document

February 2025 — NCV Level 4 — Mathematics

NCV Level 4 2025 NCV Fundamentals

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🎯 100 marks ⏱️ 3h 📄 9 pages 📝 59 items found ∑ 2 math symbols 📚 7 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.

Q3— Section header —

3.4on ADDENDUM B. Detach the ADDENDA and submit them with the answer booklet. Clearly show all calculations, diagrams, graphs, etc. used to determine the answers. Round off answers to THREE decimal places, unless stated differently.

Q1— Section header —

1.1In the figure below, C is the ce ntre of the larger circle and lies on the The smaller circle with cent e at A (2;3\ intersects the larger circle at B

1.1.1The equation of the smaller circle in the form: (2\

1.1.2The equation of the tangent BC. (2\

1.1.3A student claims that the coordinates of point D is Is claim ru e or alse? S ubstantiate

1.2In the figure below N is a point on the circle with centre at O. PN is a tangent to the circle at N, OP || MN

1.3In the figure below O is the centre of the smaller circle ABCD. DC is produced to meet the larger circle AOCE at point E. The chords AC and EO intersect at point M. Let

1.3.1With reasons, name THREE other angles that are equal to (5\ (10501064\

1.3.2Express in terms of Provide a reason for your answer. (2\

1.3.3Calculate in terms of Provide a reason for your answer. (2\

1.3.4Prove that EA = ED. Provide a reason at each stage of your answer. (4\

1.3.5Is AOCD a cyclic quadrilateral? Substantiate your answer. (3\ [25]25

Q2— Section header —

2.1Simplify (3\

2.2Without using a calculator, d etermine the value of in the following for

2.2.1(3\

2.2.2(3\

2.3Prove the following trigonometric identities

2.3.1(3\

2.3.2(4\

2.4In the figure below, the straight line distance between and B is . DC is a vertical tower high with A, B and C being points on the same horizontal plane.

2.4.1The length of BC (2\

2.4.2The value of correct to 2 d ecimal places. (4\

2.4.3The size of (correct to 2 decimal places is an obtuse angle. (3\ [25]25

Q3— Section header —

3.1Use ADDENDUM A (attached\raw a scatter plot for the above information. (3\

3.2Draw a line of best fit (i.e. eyeball method\ on the scatter plot on ADDENDUM A (attached\ (1\

3.3Name the type of relation between and (1\

3.4Use the information above to calculate the sample regression equation by the method of least squares. Use ADDENDUM B (attached\ (5\

3.5Use the regression equa

Q3— Section header —

3.6Calculate the stand ard deviation for the temperature values. (3\ [15]15

Q4— Section header —

4.1The contingency table below contains a record of the different dog types in a city that visited a veterinary doctor for treatment in a given month. The doctor keeps a record of the dogs colour as well.

4.1.1Calculate the values of S, T, U and V. (2\

4.1.2Calculate the probability that a dog chosen at random is not a hite Mastiff. (2\ (10501064\ Copyright reserved

4.1.3substantiate your answer. (3\

4.1.4Represent all the information from the contingency table above in a Venn (2\

4.2Zungu is planning on spending the evening out with his friends but he is undecided on what to wear. He can choose from the follo wing items he placed on his bed: Two pairs of pants: Blue jeans (J\nd White pant

4.2.1Draw a tree diagram to illustrate all possible outcomes. (4\

4.2.2Calculate the probability that Zungu will wear his hite pant ellow

Q5— Section header —

5.1Do assets lose their value faster under the straight line depreciation method or reducing balance depreciation method? (1\

5.2A man bought a brand new car for R400 000 and decided that he will only use it for 10 years and sell it. For the first 7 years the car depreciated on the reducing balance basis at rate of 8 5% per annum and

5.3A consumer buys a washing machine valued at R15, 000 on higher purchase. The deposit is 20% of the cash price. The balance is repaid over 36 months at a simple interest rate of 18% per annum A mandatory monthly insurance of R 50 must be paid

5.3.1The deposit amount.

5.3.2The outstanding balance after the deposit. (1

5.3.3The monthly instalment

5.4Define the following terminology used in taxation

5.4.1Tax threshold

5.4.2

5.5Al fr ida, a 20 year old woma n with no dependents

3.2Interval in seconds Temperature in (10501064\ Copyright reserved ADDENDUM B EXAMINATION NUMBER: CENTRUM NUMBER: 3.

6.513

4.514 15 15 20 25

6.513

4.514 15 15 20 25

Multiple Choice Options

B)Detach the ADDENDA

D)BC is a tangent to the smaller circle at B.

Mathematical Content

f(x)trig

Topics Identified

AlgebraGeometryTrigonometryAnalytical GeometryStatisticsProbabilityFinancial Maths

Mark Allocation

Total100 marks

Sections25 + 25 + 15 + 15 = 80 marks

Paper information

TitleDocument

SubjectMathematics

LevelNCV Level 4

Document typeQuestion paper

Year2025

MonthFebruary

Pages13

Downloads4

Examination context

Decade2020s

Years ago1y

SeasonSummer (SH)

Start daySaturday

Exam periodFebruary 2025

Days since exam618

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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