Mathematics NCV Level 4 — Exam Paper P2

February 2018 — NCV Level 4 — Mathematics

NCV Level 4 2018 NCV Fundamentals

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🎯 150 marks ⏱️ 3h 📄 2 pages 📝 69 items found 📚 3 topics 🔑 1 key info

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1.1The parents of the children pay a monthly fee, and they also get donations f rom other local businesses. They employ a student to supervise and help the children. Themba and Ayola drew up a budget for September 2017 and kept

1.1.1Calculate the variance for the tota l income (the value of A\. (2\

1.1.2Is there a surplus or a deficit at the end of September (1\

1.1.3Give TWO reasons why there is a v ariance on the surplus/deficit (2\

1.1.4They had expected to enrol 14 children in September, but they actually had 17 enrolments. (a\ Calc ulate how much each parent contributes. (2\

1.1.5Complete the table on ADDENDUM A (attached\ by d raw up a budget for October 2017 ak the following into

1.1.6What TWO things should the brothers consider doing in order o increase the p rofits of their business?

1.2Themba and Ayola decide to get a new computer and printer combo. They have 2 options they can either buy the computer and printer or hire them. OPTION 1: hey can buy the combo

1.2.1The table below shows how the total cost to hire will increase over a period of time (given in months

1.2.2Use ADDENDUM B to draw TWO graphs on the same set of axes. The first graph must show the cost of buying the computer and printer (OPTION1\. Th e second graph must show the cost of hiring the computer and printer (OPTION 2\

1.2.3Which will be the cheaper option if the computer and printer will be used for ONE year?

1.2.4

1.3Themba is 32 years old and has a full time job in the banking industry. He earns a monthly taxable income of R45 000 and pays R10 905 PAYE (Pay as You Earn\ every month. The table below

1.3.1rove that his monthly PAYE amount (R10 905\is correct. Show all calculations. (9\

1.3.2fter a salary increase Themba's annual taxable income is R577 800. What effect will this hav e on his monthly tax deduction? Explain your

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2.1.1Copy and complete the table below show ing the costs using the TWO differ ent options.

2.1.2Write down the general formula for calculating the cost of being a non member by using the following format: (2\

2.1.3Write down the general formula for calculating the cost of being a member by using the following format: (2\

2.1.4After how many hours spent online does it become cheaper to be a member? (2\

2.1.5Use the

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2.2Some of the children are working on a project in their community and need to spend time at the learning centre. The table below shows how long the project will take depending on how many children work on it.

2.2.1Calculate the values of and (2\

2.2.2What type of relationship is represented in the table above Give a reason for your answer. (3\

2.2.3Which is the dependent variable? Give a reason for your answer. (2\

2.2.4If only ONE child worked on the project, how long w ould it take him/her to complete the project (2\

2.2.5Draw a graph (on ADDENDUM C\that represents the information in the table. Label the axes and give the graph a suitable heading. Hand in the ADDENDUM with your

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3.1Refer to the map below to answer the questions. [Source: www.googlem aps.com

3.1.1Themba lives o n 1 st Avenue and Ayola o n Trematon Rd. Which of these home s would be the best place to build the

3.1.2The distance from Themba s house to Ayola s house is 2,72 km . On the map the distance between the 2 houses is 8,5 cm.

3.1.3Use the sca le from

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3.2Given below is the floorplan for the new earning entre. The plan is no t drawn to

3.2.1Calculate the total area of both the omework oom and the c omputer

3.2.2Calcu late the total cost for tiling and carpeting the new entre, considering the following: The toilet will be tiled at a cost of

3.2.3As an alternate option, Th emba gets a quote to complete the tiling and carpeting at a total cost of R5 000 excludin g VAT.

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3.3The diagram below shows the design of a window of the learning centre. There are 2 rectangular glass panes next to each ot her with thin wooden frames surrounding each pane.

3.3.1Calculate how many metres of wood are needed for the frame. (3\

3.3.2What are the dimensions (length and wid th\ each glass pane? (2\

3.3.3Glass is manufactured in large piece . The length and the width of a glass piece is 10 m by 5 m respectively

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4.1The graph below shows the activities of students on a Saturday afternoon. 4.

1.1Give the mathematical name of the graph shown above. (1

4.1.2How many girls spent their Saturday afternoon playing sport? (2

4.1.3Determine the ratio of boys to girls who formed part of this survey. (2\ 10401034 11 NC

4.1.4What percentage of the students surveyed spend their Saturday afternoon at the mall? (3

4.1.5Determine the modal activity. (2

4.2Study the graph show ing the average marks achieved by the children at the earning entre

4.2.1hat is the general trend of this graph? (2

4.2.2Which TWO months showed the biggest improvement in marks? (2\

4.2.3Based on the trend of the graph, what is l ikely to happen in the next few months? (2\ 10401034 12

4.3A survey was done a mongst the children to determine the modes of transport used to get to school. The results have been summarised below. MODES OF TRANSPORT BICYCLE WALK BUS TAXI

4.3.1What is the sample size for this survey? (1

4.3.2What percentage of boys ride bicycles to school? (3

4.3.3What frac tion of the sample are girls? (2

4.3.4If a boy is chosen at random, what is the probability that he will use a taxi to get to school? Express the an swer as a decimal fraction. (3

4.3.5If a child is chosen at random, what is the probability that it will be a girl who walks to school? (2

4.3.6If a child is selected form those that rode in on a bicycle, what is the probability that it wil l be a girl ? (3\

4.3.7If a child is chosen at random, the probability that they will either ride a bicycle or walk to school is 66,67%. Is the above statement TRUE or FALSE? upport your an swer by showing ALL calculations.

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Topics Identified

TrigonometryAnalytical GeometryProbability

Mark Allocation

Total150 marks

Sections40 + 33 + 42 + 35 = 150 marks

Key Information

Websitewww.sars.gov.za

Paper information

TitleExam Paper

SubjectMathematics

LevelNCV Level 4

Document typeQuestion paper

Year2018

MonthFebruary

Pages15

Downloads5

Examination context

Decade2010s

Years ago8y

SeasonSummer (SH)

Start dayThursday

Exam periodFebruary 2018

Days since exam3,173

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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