# Mathematics Grade 11 P2 Gauteng November 2016 Question Paper

> Grade 11 Mathematics Paper 2 question paper from the Gauteng November 2016, 16 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/gr11-math-p2-november-2016-question-paper/297e58c4-3784-404c-820e-c21fca095021
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper
- Year: 2016
- Exam period: Gauteng November
- Paper: 2
- Curriculum: CAPS
- Pages: 16

Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 11](https://www.hlayiso.com/library/grade-11) › [Mathematics](https://www.hlayiso.com/library/grade-11/mathematics) › [Mathematics Grade 11 P2 Gauteng November 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p2-november-2016-question-paper/297e58c4-3784-404c-820e-c21fca095021)

## About this document

Mathematics · Grade 11 · Gauteng November · 2016. Question paper, 16 pages. Read online or download the PDF.

Read it free online on the page above; download the PDF from there.

## Document text

Text extracted from the PDF. Layout, diagrams and tables may not survive extraction.

### Page 1

Downloaded from hlayiso.com

basic education

SE.
y y Department:
4 Ky Basic Education
SSG REPUBLIC OF SOUTH AFRICA
NATIONAL
SENIOR CERTIFICATE
GRADE 11
i MATHEMATICS P2 i:
F NOVEMBER 2016 :

Cee ee ee ee ee

MARKS: 150

TIME: 3 hours

This question paper consists of 13 pages and a 22-page answer book.

ANN

*L6P2*
Copyright reserved FUN ANAC UO A EE A Please turn over

### Page 2

Downloaded from hlayiso.com

Mathematics/P2 2 DBE/November 2016

NSC - Grade 11

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

This question paper consists of 12 questions.
Answer ALL the questions in the SPECIAL ANSWER BOOK provided.

Clearly show ALL calculations, diagrams, graphs et cetera that you used to determine
the answers.

Answers only will NOT necessarily be awarded full marks.
If necessary, round off answers to TWO decimal places, unless stated otherwise.
Diagrams are NOT necessarily drawn to scale.

You may use an approved scientific calculator (non-programmable and
non-graphical), unless stated otherwise.

Write neatly and legibly.

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 3

Downloaded from hlayiso.com

Mathematics/P2 3 DBE/November 2016
NSC - Grade 11

QUESTION 1

The table below shows the number of cans of food collected by 9 classes during a charity
drive.

5 8 15 20 25 27 31 36 75
1.1 Calculate the range of the data. qd)
1.2 Calculate the standard deviation of the data. (2)
1.3 Determine the median of the data. qd)
1.4 Determine the interquartile range of the data. (3)
1.5 Use the number line provided in the ANSWER BOOK to draw a box and whisker
diagram for the data above. @)
1.6 Describe the skewness of the data. qd)
1.7 Identify outliers, if any exist, for the above data. qd)
[12]
QUESTION 2
The table below shows the time (in minutes) that 200 learners spent on their cellphones during
a school day.
TIME SPENT
(IN MINUTES) FREQUENCY
95 <x<105 15
105<x<115 27
115<x<125 43
125<x<135 52
135<x< 145 28
145 <x< 155 21
155 <x< 165 10
165<x<175 4
2.1 Complete the cumulative frequency column in the table provided in the ANSWER
BOOK. (2)
2.2 Draw a cumulative frequency graph (ogive) of the data on the grid provided. (3)
2.3 Use the cumulative frequency graph to determine the value of the lower quartile. (2)
2.4 Determine, from the cumulative frequency graph, the number of learners who used
their cellphones for more than 140 minutes. (2)
[9]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 4

Mathematics/P2 4 DBE/November 2016

Downloaded from hlayiso.com

NSC - Grade 11

QUESTION 3

In the diagram, A(6;— 2), B(2; 15) and C(—4; 3) are the vertices of AABC.
M is the midpoint of AB. N is a point on CA such that MN || BC.

3.1

3.2

3.3

3.4

3.5

Copyrigherssened FUN ANAC UO A EE A Peseta over

~

y
B(2 ; 15)

C4 ; 3)

ve

fe) |
A(6 ; -2)

Determine the coordinates of M, the midpoint of AB.
Determine the gradient of line MN.
Hence, or otherwise, determine the equation of line MN, inthe form y=mx+c.

Calculate, with reasons, the coordinates of point N.

If ABCD (in that order) is a parallelogram, determine the coordinates of point D.

(2)
(3)
(2)
(4)

(4)
[15]

### Page 5

Mathematics/P2 5 DBE/November 2016

Downloaded from hlayiso.com

NSC - Grade 11

QUESTION 4

In the diagram, R and A are the x- and y-intercepts respectively of the straight line AR.

The equation of ARis y= -pxe4. Another straight line cuts the y-axis at P(O0; 2) and

passes through the points M(k;0) and N(3 ; 4).

a and £ are the angles of inclination of the lines MN and AR respectively.

41

4.2

43

44

Copyrigherssened FUN ANAC UO A EE A Peseta over

Le

Ay
4 ) R\

Given that M, P and N are collinear points, calculate the value of k.

Determine the size of 8, the obtuse angle between the two lines.

Calculate the length of MR.

Calculate the area of AMNR.

(3)
(4)
GB)

(3)
[13]

### Page 6

Downloaded from hlayiso.com

Mathematics/P2 6 DBE/November 2016
NSC - Grade 11

QUESTION 5

5.1 In the diagram below, P(-8 ; f) is a point in the Cartesian plane such that

OP = 17 units and reflex XOP=0.

y
(|
oO x
17
P(-8; 1)
$5.11 Calculate the value of ¢. (2)
5.1.2 Determine the value of each of the following WITHOUT using a
calculator:
(a) cos(—0) (2)
(b) 1-sind (2)
5.2 If sinl7°= a, WITHOUT using a calculator, express the following in terms
of a:
5.2.1 tan17° (3)
5.2.2 sin 107° (2)
5.2.3 cos” 253° + sin? 557° (4)
53 Simplify fully, WITHOUT the use of a calculator:
cos(—225°).sin 135° + sin 330° 6)
tan 225°
ae 1 -1
5.4 Prove the identity: =, 5 (4)
(cosx+1)(cosx-1) tan*x.cos*x
5.5 Determine the general solution for 2sin x.cos x =cos x. (6)
[31]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 7

Downloaded from hlayiso.com

Mathematics/P2 7 DBE/November 2016
NSC - Grade 11

QUESTION 6

In the diagram the graphs of f(x)=cosx and g(x)=sin(x+b) are drawn for
the interval —180°< x < 90°.

ty |
30 30 90”
4 1 (st 4

6.1 Write down the value of 5. qd)
6.2 Write down the period of g. qd)
6.3 Write down the value(s) of x in the interval -180°< x <90° for which

S(x)— g(x)=0. (2)
6.4 For which values of x in the interval -180°< x < 90° is sin(90°-x) > g(x)? (3)
6.5 The graph of h is obtained by shifting f 3 units upwards. Determine the range of h. (2)

9]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 8

Downloaded from hlayiso.com

Mathematics/P2 8 DBE/November 2016
NSC - Grade 11
QUESTION 7
7A In the figure below, acute-angled AABC is drawn having C at the origin.
. B
x
| ,
TAA Prove that c? =a? +b? —2abcosC. (6)
b b- 4
71.2 Hence, deduce that 1+cosC= (at b+ lat b—oe) 4)
2ab
72 Quadrilateral ABCD is drawn with BC=235m and AB=90,52m. It is also

given that ADB =31,23°; DAB=1 09,16° and CBD = 48,88°.

A

Determine the length of:

721 BD (3)
7.2.2 cD (3)
[16]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 9

Downloaded from hlayiso.com

Mathematics/P2 9 DBE/November 2016
NSC - Grade 11

QUESTION 8

The diagram below shows a water tank which is made up of a cylinder and cone having equal
radii. The height of the tank is 1,8m and the radius is 0,5 m. The angle between the
perpendicular height, AB, and the slant height, AC, of the conical section is 35,5°.

Volume of cone aperh

Total surface area of cone =r? +21
Volume of cylinder = 1r7h

Total surface area of cylinder = 2777+ 2arh

1,8m

8.1 Calculate the perpendicular height, AB, of the cone. (2)

8.2 When the tank is full, an electric pump switches on and pumps the water from the
tank into an irrigation system at a rate of 0,52 m’/h. The pump automatically

switches off when the tank is 7 full.

Calculate how long, in hours, the pump feeds water into the irrigation system. (4)
[6]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 10

Downloaded from hlayiso.com

Mathematics/P2 10 DBE/November 2016
NSC - Grade 11

Give reasons for your statements and calculations in QUESTIONS 9, 10, 11 and 12.

QUESTION 9
91 Complete the statement so that it is TRUE:

The angle subtended by an arc at the centre of a circle is ... (2)
9.2 O is the centre of circle TNSPR. POS=60° and PS =NT.

T
N
R
1
P s

Calculate the size of:

9.2.1 PRS (2)

9.2.2 NST (2)

[6]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 11

Downloaded from hlayiso.com

Mathematics/P2 11 DBE/November 2016
NSC - Grade 11

QUESTION 10

D, E, F, G and H are points on the circumference of the circle.
G, =x+20° and H=2x+10°. DEI| FG.

10.1 Determine the size of DEG in terms of x. (2)
10.2 Calculate the size of DHG. (4)
[6]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 12

Downloaded from hlayiso.com

Mathematics/P2 12 DBE/November 2016
NSC - Grade 11

QUESTION 11

O is the centre of the circle PTR. N is a point on chord RP such that ON 1 PR.
RS and PS are tangents to the circle at R and P respectively.

RS = 15 units; TS =9 units; RPS = 42,83°.
P
d |

15
R

11.1 Calculate the size of NOR. (5)

11.2 Calculate the length of the radius of the circle. (4)
[9]

Copyrigherssened FUN ANAC UO A EE A Peseta over

### Page 13

Downloaded from hlayiso.com

Mathematics/P2 13 DBE/November 2016
NSC - Grade 11

QUESTION 12

12.1 Use the diagram below to prove the theorem which states that EFG = EDF.

D.

F G (5)

12.2 In the diagram below, BOC is a diameter of the circle. AP is a tangent to the circle
at A and AE=EC.

P

Prove that:

12.2.1 BA||OD (4)
12.2.2 AOCD is a cyclic quadrilateral 6)
12.2.3 DC isa tangent to the circle at C (4)

[18]

TOTAL: 150

Copyrigherssened FUN ANAC UO A EE A
Pa

### Page 14

Downloaded from hlayiso.com

### Page 15

Downloaded from hlayiso.com

### Page 16

Downloaded from hlayiso.com

## Related documents

- [Gr11 Math P2 (Afrikaans) November 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p2-afrikaans-november-2016-question-paper/8c810d47-4010-4894-ae81-1c209d8e67f4) — Mathematics · QP · 2016 · Afr
- [Gr11 Math P1 November 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p1-november-2016-question-paper/159ea3da-41f3-4dcb-82d8-aeb9f1794ecd) — Mathematics · QP · 2016
- [Gr11 Math P1 (Afrikaans) November 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p1-afrikaans-november-2016-question-paper/e18ca4fc-229b-4d0b-8b3f-ec859a499bea) — Mathematics · QP · 2016 · Afr
- [MATHS P2 GR11 QP NOV2016 English](https://www.hlayiso.com/library/maths-p2-gr11-qp-nov2016-english/8e51b3ab-c405-4dab-b3be-458409636e04) — Mathematics · QP · 2016 · Eng
- [Gr11 Math P2 June 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p2-june-2016-question-paper/aa2249f8-80f3-42ba-b4b6-0ebec49b6fc6) — Mathematics · QP · 2016
- [Gr 11 Mathematics P2 (English) November 2022 Question Paper](https://www.hlayiso.com/library/gr-11-mathematics-p2-english-november-2022-question-paper/130a0fe0-0914-40c3-aedd-67a7e297f1cd) — Mathematics · QP · 2022 · Eng

## More from Grade 11 Mathematics

- [Grade 11 Mathematics P1 November 2026 Mock Memo](https://www.hlayiso.com/library/grade-11-mathematics-2026-november-mock-exam-memorandum-paper-1/470265ad-99e7-4e3e-af02-0c28a273b390) — Memo · 2026 · Eng
- [MATHS P1 MEMO GR11 NOV 2025 E+A watermark](https://www.hlayiso.com/library/maths-p1-memo-gr11-nov-2025-e-a-watermark/5af2bd74-cc9d-4651-895a-310a59d8ce25) — Memo · 2025
- [MATHS P2 MEMO GR 11 NOVEMBER 2025 (ENG & AFR) watermark](https://www.hlayiso.com/library/maths-p2-memo-gr-11-november-2025-eng-afr-watermark/6bc83e22-926c-4a81-95ea-4dee0141ce24) — Memo · 2025 · Afr
- [KZN Maths Grade 11 November 2025 P2 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-11-november-2025-p2-and-memo/a2aac931-a969-41c8-bde2-85d23035d042) — QP + Memo · 2025
- [MATHS P2 ANSWER BOOK GR11 2024 ENG AFR D watermark](https://www.hlayiso.com/library/maths-p2-answer-book-gr11-2024-eng-afr-d-watermark/91fd4f6b-a252-4d30-b6b1-f8f546015336) — Addendum · 2024 · Afr
- [MATHS P2 GRADE 11 NOV 2024 ENG AFR MARKING GUIDELINE watermark](https://www.hlayiso.com/library/maths-p2-grade-11-nov-2024-eng-afr-marking-guideline-watermark/0f16be7d-4a28-41e1-9e8d-57c649490c1c) — Memo · 2024 · Eng

## Collection

- [Grade 11 past papers](https://www.hlayiso.com/grade-11/past-papers)

---

Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. When citing, link the page URL above, not a PDF or /api/ URL.