Technical Mathematics P1 (English)

Exemplars 2018 — Grade 12 / Matric — Technical Mathematics

Past Paper 2018 Grade 12 English Mathematics Hub →

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🎯 150 marks ❓ 9 questions ⏱️ 3h 📄 8 pages 📝 54 items found ∑ 3 math symbols 📚 6 topics

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4.2.4and QUESTION

7.4on the ANSWER SHEET provided Number the answers correctly according to the numbering system used in this question paper. Clearly show ALL calculations, diagrams, graphs et

Q1— Section header —

1.1Given Solve for if:

1.1.1(2\

1.1.2and then represent the solution on a number line. (4\

1.2Solve for if (rounded off to TWO decimal places\ (4\

1.3Solve algebraically for and simultaneously if: and (6\

1.4The two diagrams below represent a metal rod with an initial length which is then stretched (elongated\ to a length The strain measure is defined as the ratio of elongation with respect to the original

1.4.1Express as the subject of the formula. (3\

1.4.2Hence, or otherwise, calculate the value of if and (2\

Q1— Section header —

1.5Write the simplified value of in scientific notation without any rounding. (2\ [25]25

Q2— Section header —

2.1Given: Determine the value(s\f for which will be:

2.1.3Undefined Non real Rational (give only ONE integer\ (1\ (2\

2.2Determine the value of for which the equation will have equal roots. (4\ [8]8

Q3— Section header —

3.1Simplify the following without the use of a calculator (show ALL steps\

3.1.1(3\

3.1.2(4\

3.1.3(4\

3.2Solve for (4\

3.3Express the complex number in trigonometric (polar\orm. (5\

3.4Solve for and if (5\ 24]

Q4— Section header —

4.1The graphs of the functions defined by and are shown in the figure below. is a point of intersection of and Point and

4.1.5The coordinates of The coordinates of turning point The numerical value of The equation of the asymptote of The values of for which (2\ (3\

4.2Given and

4.2.5Write down the equations of the asymptotes of Determine the intercept of

Q5— Section header —

5.1The nominal interest rat e charged on an investment is 7, 2 % compounded half yearly. Calculate the annual effective interest rate for the investment. (3\

5.2The air pressure of a punctured tyre deflated from 220 kPa to 70 kPa at a decreasing rate of 8% per minute. Determine (to the nearest minute\ how long it took the tyre to deflate from 220 kPa to 70 kPa.

5.3Mrs Rethabile invested an amount of R150 000 to buy a drilling machine for her engineering company. Interest, compounded quarterly, is calculated at a rate of 10 5% p.a. for 5 years. At the end of the third year, Mrs Rethabile withdrew an

Q6— Section header —

6.1Determine the average gradient of between the points where and (4\

6.2Determine from FIRST PRINCIPLES if (5\

6.3Determine if (4\

6.4Determine the equation of the tangent to the curve defined by at the point where (5\ [18]18

Q7— Section header —

7.1Show that is a factor of (2\

7.2Hence, or otherwise, find the intercepts of (3\

7.3Determine the coordinates of the turning points of (5\

7.4Sketch the graph of on the ANSWER SHEET provided Cl early show ALL

Q8— Section header —

8.1An industrial open water tank as shown in the picture below has an inlet pipe and an outlet pipe. The depth of the water in the tank changes continually.

8.1.2The depth of the water in the tank at 11:00 The rate of change of the depth of the water in the tank at 12:00 (2\ (3\

8.2The profit (in R1000s\yielded by a company using a machine that produces bottle caps is dependent on the average speed at which the machine runs

8.2.3Calculate the average speed at which neither a profit nor a loss is yielded. Determine at what average speed the machine should run so that the maximum profit is obtained. Hence, or otherwise, calculate the resulting maximum profit.

Q9— Section header —

9.1Determine the following integral: (4\

9.2The sketch below represents the graph of the function defined by Determine the shaded area bounded by a curve defined by and the axis. (5\

4.2.4QUESTION

7.4-8 -6 -4 -2 -6

Multiple Choice Options

A)..

Mathematical Content

f(x)limtrig

Topics Identified

AlgebraCalculusGeometryTrigonometryAnalytical GeometryFinancial Maths

Mark Allocation

Total150 marks

Sections25 + 8 + 25 + 14 + 18 + 14 + 13 + 9 = 126 marks

Paper information

SubjectTechnical Mathematics

Year2018

SessionExemplars

TypePast Paper

PaperPaper 1

LanguageEnglish

Pages11

Downloads6

Examination context

Decade2010s

Years ago8y

Season—

Start day—

Exam period—

Days since exam—

About Technical Mathematics examination preparation

Grade 12 Mathematics combines algebra, calculus, geometry, and trigonometry. Paper 1 focuses on algebra and calculus, while Paper 2 tests geometry, trigonometry, and analytical geometry.

Every available Grade 12 Mathematics past paper and memorandum is collected in the Mathematics hub at mathematics.freemode.co.za — browse all years, sessions and languages in one place.

How to use this resource for revision

A 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.

interpreting mathematical problems

selecting appropriate methods

showing sufficient working

checking calculations and answers

working accurately under time constraints

A practical revision approach

Allocate roughly 1.5 minutes per mark. Show full working — the memorandum allocates substantial method marks, meaning partial solutions can still earn 60%+ when the working is logically structured.

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Corresponding marking memorandum

Marking memorandum available

Use the corresponding memorandum after completing the paper to review your answers and identify areas that require further revision. The memorandum shows the marking approach used by DBE examiners, including method-mark allocations.

Technical Mathematics P1 Memo (English) →

File details

File size542.4 KB

Pages11

Archived on7 September 2026

File age46d

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