Mathematics Paper 1 (English)

November 2011 — Grade 12 / Matric — Mathematics

Past Paper 2011 Grade 12 English Mathematics Hub →

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🎯 150 marks ❓ 12 questions ⏱️ 3h 📄 8 pages 📝 65 items found ∑ 3 math symbols 📚 6 topics 🔑 1 key info

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12.2is attached at the end of this question paper. Write your centre number and examination number on this sheet in the spaces provided and insert the page inside the back c over of your ANSWER An information sheet, with formulae, is in

Q1— Section header —

1.1.2(4)4

1.1.3(4)4

1.2xy

1.2.1(3) and

Q2— Section header —

2.213

Q3— Section header —

3.251 52 [9] Mathematics/P1 3 DBE/November 20119

1.1Solve for

1.1.1(3\ Consider the equation: 0 Calculate the values of the ratio yx. (3\ 1.2.2 Hence, calculate the values of if = 8. (5\

Q2— Section header —

2.1.1Arithmetic (2\

2.1.2Geometric (3\ Determine the value of P if

2.3Prove that for any arithmetic sequence of which the first term is and the constant difference is , the sum to terms can be expressed as

Q3— Section header —

3.1Write down the next TWO terms. (2\ Calculate (5\

3.3Prove that ALL the terms of this infinite sequence will be divisible by 3. (2\

Q4— Section header —

Q5— Section header —

5.1Consider the function:

5.2bx ax < 0,

4.1Calculate the second difference of this quadratic pattern. (5\

4.2Hence, or otherwise, calculate th e first term of the pattern. (2\

Q5— Section header —

5.1.2Calculate the coordinates of the . (3\

5.1.3Sketch the graph of in your ANSWER BOOK, showing clearly the asymptotes and the intercepts with the axes.

5.1.4is 0 (2\

5.1.5Calculate the average gradient of between = 0. (4\ Draw a sketch graph of , where < 0, < 0 and

Q6— Section header —

6.4= ... (2)2

6.5, if about the (1)1

6.6Calculate

6.1Determine the coordinates of A and B. (4\

6.2Write down an equation of th . (1\ Determine an equation of if 8 Determine an equation of in the form Write down an equation of is the reflection of -axis.

Q7— Section header —

Q8— Section header —

8.2.1dx dy

7.1How many years will it take for an article to depreciate to half its value according to the reducing-balance method at 7% per annum?

7.2Two friends each receive an amount of R6 000 to invest for a period of 5 years. They Radesh: 8,5% per annum simple interest. At the end of the 5 years, Radesh will receive a bonus of exactly 5% of the principal amount.

7.3Nicky opened a savings account with a single deposit of R1 000 on 1 April 2011. She then makes 18 monthly deposits of R700 at th e end of every month. Her first payment is made on 30 April 2011 and her last payment on 30 September 2012. The account

Q8— Section header —

8.2Evaluate: dxdy if if

Q9— Section header —

Q10— Section header —

10.1For which values of is the graph of decreasing?

9.1Show that = 43. (7\

9.2Determine an equation of the tangent to the graph of = 1. (5\

9.3Determine the has a point of inflection. (2\

Q10— Section header —

10.2At which value of does the graph of have a local minimum? Give reasons for

Q11— Section header —

Q12— Section header —

11.1What is the initial volume of the water in the tank? (1\

11.2Write down TWO different expressions for th e rate of change of the volume of water

11.3Determine the value of (that is, the rate at which water flows out of the tank\ (2\

Q12— Section header —

12.1Write down ALL the constraints, in terms of and , to represent the above information.

12.2Represent the constraints graphicall y on the attached DIAGRAM SHEET. Clearly indicate the feasible region.

12.3The cost of hiring a red bus is R600 for the day and the cost of hiring a blue bus is R300 for the day. Write down

12.412.4.1 Determine ALL possible values of and so that the cost will be a minimum.

12.4.2Calculate the minimum co st of hiring the buses. (2\

12.5If exactly 12 bus drivers are to be us ed, determine the number of each type of bus which the school will now need to still ensure minimum cost. TOTAL: 150 EXAMINATION NUMBER:

Q12— Section header —

Mathematical Content

f(x)limtrig

Topics Identified

AlgebraGeometryTrigonometryAnalytical GeometryFinancial MathsSequences

Mark Allocation

Total150 marks

Sections19 + 13 + 9 + 7 + 19 + 14 + 16 + 12 + 14 + 4 + 6 + 17 = 150 marks

Per-question sum85 marks

Key Information

Contact Number0111213141 · 0212223242

Paper information

SubjectMathematics

Year2011

SessionNovember

TypePast Paper

PaperPaper 1

LanguageEnglish

Pages10

Downloads5

Examination context

Decade2010s

Years ago15y

SeasonSpring (SH)

Start daySaturday

Exam periodNovember 2011

Days since exam5,467

About 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.

Mathematics Memo 1 (English) →

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Pages10

Archived on8 September 2026

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