Mathematics NCV Level 4 — Exam Paper
November 2019 — NCV Level 4 — Mathematics
NCV Level 4
2019
NCV Fundamentals
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1.1.1Various options are given as possible answers to the following questions. Choose the answer and write only one of the letters (A D\ next to the question number (1.1.1
1.1.5\ in the ANSWER BOOK.
1.1.1simplif
1.1.4If is plotted on a complex plane, then it will be in the First Second Third
1.1.5
1.2Solve fo in the equation and express any non real sol tions in the
1.3Simplify and leave the answer in rectangular form, with a rational denominator: (3\
1.4Apply De Moivre's theorem t o calculate the following, leaving your answer in polar form, with a positive argument: (5\
1.5Solve for and in the following equation and express any non real solutions in the form (6\ [21]21
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2.1If is divided by , it leaves a remainder of Determine the value of (2\
2.2The expression has the remainder of when it is divided by If it is also given that is a factor of apply the
2.3The figure below represents the graphs of the following functions: and for GRAPH
2.3.1Does exist at (1\
2.3.2Write down the domain of (1\
2.3.3Write down the range of (1\
2.3.4Determine the equation of (1\
2.3.5Determine the equation of (2\
2.3.6Determine the range (3\
2.3.7Sketch on ADDENDUM A and show all intercepts with axes. Also draw the line about which and is symmetric. Clearly show the nature of the start and end points of (3\
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3.1Given the function . Determine the derivative of making use of first principles. (3\
3.2Use differentiation rules to determine the derivatives of the following, leaving your answer with POSITIVE EXPONENTS and in SURD form wh ere applicable:
3.2.1(5\
3.2.2(3\
3.2.3(3\
3.2.4(3\ [17]17
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4.1Determine the following integral s and simplify the answers. Leave the answer with positive exponent and in surd form where applicable:
4.1.1(3\
4.1.2(4\
4.2Evaluate the definite integral (2\ (\52 fxx (\ fx
4.3A game reserve has an irregular shape and a river flow through it. The owner needs to determine the approximate area of the game reserve. The level 4 students used several points to determine the following sample regression e
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5.1A skateboarder practices on a ramp shown below. Her equation of motion is given by where is the height in metres and is the time in seconds. GRAPH
5.1.1Determine t he equation that will describe her velocity in terms of (1\
5.1.2Calculate her maximum velocity. (3\
5.1.3Determine the height at the time when she is at maximum velocity. (1\
5.1.4Determine her acceleratio n at seconds. (2\
5.2The third degree polynomial is given.
5.2.1Apply the factor theorem or any other method to factorise completely. (4\ 42 stt
5.2Refering to QUESION 5.2.1 above choose the correct graph which represents the above third degree polynomial Choose the answer and write only one of the letters (A D\ next to the question number (5.2.2\ in the ANSWER BOOK.
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6.1An entrepreneur sells fresh juice mix in cups. The mixture consists of oranges and pears. Let the quantity of oranges be and the quantity of pears be . The shaded area in the diagram repr
6.1.1Referring to the feasible region in graph 4, what is the minimum quantity of pears that could be used in the mi xture? (1\
6.1.2Will a mixture of 60 pears and 20 oranges meet the requirements of the feasible region Explain your answer. (2\ 10501064
6.1.3The constraints that describe the feasible region on graph 4 above are: Apply this knowledge and write down the constraints that will describe the new fe asible region in Graph 5 below. GRAPH
6.2A group of civil engineering students intends to do paving using two different colours of bricks, grey bricks batches\and red bricks batches\They must use at most 300 batches of grey bricks and at least 150 batc
6.2.1Two of the constraints are and . Model the other constraints in respect of the above information in terms of and (2\ 40
6.2.2Use the attached ADDENDUM B and complete the following questions. a\ Using a scale of 1 unit is 50 bricks, represent graphically the
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Mathematical Content
3
f(x)limtrig
Topics Identified
4
AlgebraCalculusTrigonometryStatistics
Mark Allocation
Total100 marks
Sections21 + 19 + 17 + 14 + 13 + 16 = 100 marks
Paper information
TitleExam Paper
SubjectMathematics
LevelNCV Level 4
Document typeQuestion paper
Year2019
MonthNovember
Pages16
Downloads5
Examination context
Decade2010s
Years ago7y
SeasonSpring (SH)
Start dayFriday
Exam periodNovember 2019
Days since exam2,535
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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