Mathematics NCV Level 4 — Document
November 2024 — NCV Level 4 — Mathematics
NCV Level 4
2024
NCV Fundamentals
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Q1— Section header —
1.1In the figu re below, XYZ is a tangent to the circle at point Y. and Determine the size of the following angles giving reasons:
1.1.4(8\ (105 01064\ Copyright reserved Please turn over
1.2In the figure below, COT is the diameter of the circle centred at O. TG is a tangent to the circle at T and GC cuts the circle at W. M is the midpoint of C W. Prove, giving reasons that OTGM is a cyclic quadrilateral.
1.3In the figure below, the circle with centre passes through the origin and intersects the at and the
1.3.1 Calculate the coordinates of (2\
1.3.2 Calculate the length of the radius of the circle (Leave your answer in surd form\ (3 (105 01064\
1.3.3 Determine the equation of the circle in the form: (2
1.3.4 Determine the equation of the tangent to the circle in the form: (3\
1.3.5 Determine the coordinates of S. (2\ [25
Q2— Section header —
2.1Simplify the following without using a ca lculator:
2.1.1(2\
2.1.2(3\
2.1.3(4\
2.2Calculate the values of given that where (4\
2.3Prove the following trigonometric identities:
2.3.1(3\
2.3.2(3\ (105 01064\ Copyright reserved Please turn over
2.4The figure below is an event centre where the rectangular walls STRQ and STUV are vertical to the horizontal plane RTU. Metallic poles are erected along RQ and UV and extended to points P and W respectively.
2.4.1The length of
2.4.2The length of
2.4.325
Q3— Section header —
3.1Use Addendum A (attached\aw a scatter plot for the above information. (3\
3.2Use the information above to calculate the sample regression equation by the method of least squares. Use Addendum B (attached\ (5\
3.3Draw the regression equa
Q3— Section header —
3.4The biologist reviews similar research and determines that pollutant levels above 16 are likely to result in the death of a chick soon after hatching. Using t he regression
Q3— Section header —
3.5Calculate the standard deviation of the pollutant levels. (3\ [15]15
Q4— Section header —
4.1Def ine the following terminologies as used in probabilities. In each case, write down a formula that matches the definition.
4.1.1Mutually inclusive events
4.1.2
4.2A test was given to 91 students and the t able below shows the grades received by the students. The students received an A, B or a C in the test Total Male (M\ 16
4.2.1Determine the values of X and Y. (2\
4.2.2If a student is selected at random, what is the probability of selecting a student (a\ hat obtained grade A in the test. (1\ (b\
4.2.3correct to 1 decimal place to justify your answer. (3\ [15 (105 01064\
Q5— Section header —
5.1Simple interest and compound interest are two methods of appreciation. Under which method will investments appreciate faster? (1\
5.2A woman invested a certain amount of money into an account that yields a 5,5% simple interest per annum. Given that she had R22 464 at the end of 8 years, calculate how much she initially invested into the account.
5.3Salome opened a tax free investment account with Standard Bank and deposited R17 500 into the account. She i hen her son will be going to university. Given that the account earns interest at 7,5% per annum
5.3.1The amount of her investment after 12 years. (2\
5.3.2 The interest her investment would earn after 12 years. (1\
5.4Musi bought a car for R350 000. The value of the car depreciates at 20% p.a. on the same model and t ype. However, the value of the new car appreciates at 5% p.a. simple in for the new car? (5\
5.5Define the following terminology as used in taxation:
5.5.1Tax able income
5.5.2
5.6Mary, a 70 year old netball coach with no dependents has the following financial details: Gross monthly salary R150 000 13 th cheque
5.6.1Calculate the amount of tax that Mary must pay or receive after a SARS assessment. (5\
5.6.2Mary seems to be paying too much tax to SARS. Advise her on how to legally reduce the amount o f tax paid to SARS. (1\ [20] TOTAL: 100 (10501064\ Copyright reserved20
3.3(10501064\ Copyright reserved ADDENDUM B EXAMINATION NUMBER: CENTR NUMBER:
3.2NOTE Choose between OPTION 1 and OPTION 2 OPTION 1 Pollutant
Mathematical Content
2
f(x)trig
Topics Identified
7
AlgebraGeometryTrigonometryAnalytical GeometryStatisticsProbabilityFinancial Maths
Mark Allocation
Total100 marks
Sections25 + 15 + 20 = 60 marks
Paper information
TitleDocument
SubjectMathematics
LevelNCV Level 4
Document typeQuestion paper
Year2024
MonthNovember
Pages13
Downloads4
Examination context
Decade2020s
Years ago2y
SeasonSpring (SH)
Start dayFriday
Exam periodNovember 2024
Days since exam707
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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