# Mathematics Grade 11 P2 Eastern Cape November 2017 QP (Eng)

> Grade 11 Mathematics Paper 2 question paper from the Eastern Cape November Exam 2017 (English), 16 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/nsc-gr11-mathematics-p2-nov2017-finals-english/7691746d-833e-42dc-9469-94179effa146
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Language: English
- Document type: Question paper
- Year: 2017
- Exam period: Eastern Cape November Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 16

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## About this document

Mathematics · Grade 11 · Eastern Cape November Exam · 2017 · English. 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.

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          *Imat2*

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Mathematics/P2 2 DBE/November 2017

CAPS — Grade 11

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

_

3.

This question paper consists of 12 questions.
Answer ALL the questions in the 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.
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.

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EASTERN C4&PE

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Mathematics/P2 3 DBE/November 2017

CAPS — Grade 11

QUESTION 1

1.1

Mr Brown conducted a survey on the amount of airtime (in rands) EACH student had
on his or her cellphone. He summarised the data in the box and whisker diagram
below.

10 12 14

16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66

Tid Write down the five-number summary of the data. (2)
1.1.2 Determine the interquartile range. (1)
oe Comment on the skewness of the data. (1)
1.2 A group of 13 students indicated how long it took (in hours) before their cellphone
batteries required recharging. The information is given in the table below.
if
5 8 10 _ 20 ay 48 50 50 63 y | 107

1.2.1 Calculate the value of y if the mean for this data set is 41. (2)
1.2.2 If y=94, calculate the standard deviation of the data. (1)
1.2.3 The mean time before another group of 6 students needed to recharge the

batteries of their cellphones was 18 hours. Combine these groups and

calculate the overall mean time needed for these two groups to recharge

the batteries of their cellphones. (3)
[10]

comment 2
EASTERN CAPE

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Mathematics/P2

QUESTION 2

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4

CAPS ~ Grade 11

DBE/November 2017

A student conducted a survey among his friends and relatives to determine the relationship
between the age of a person and the number of marketing phone calls he or she received within
one month. The information is given in the table below.

AGE OF PERSON FREQUENCY CUMULATIVE
IN SURVEY FREQUENCY
20 <x <30 7 7
30<x<40 27
40 <x <50 25
Ll 64
60<x<70 72
7 -D 4
Cl 80
2.1 Complete the frequency and cumulative frequency columns in the table given in the
ANSWER BOOK.
2.2 How many people participated in this survey?
23 Write down the modal class.
2.4 Draw an ogive (cumulative frequency graph) to represent the data on the grid given in
the ANSWER BOOK.
2.5 Determine the percentage of marketing calls received by people older than 54 years.

Copyright reserved

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(4)
(1)
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(3)

(3)
[12]

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Mathematics/P2 5) DBE/November 2017
CAPS ~ Grade 11

QUESTION 3

A(-2 ; -5), B, C and Dare the vertices of quadrilateral ABCD such that diagonal
AC is perpendicular to diagonal BD at T.
The equation of BTD is givenby 2y+x=18 and AB= 15 units.

a
Cc
B
it
15
fe) x
A(-2:-5) D
3.1 Determine the gradient of line AC. (2)
32 Determine the equation of AC in the form y=mx+c. (2)
3.3 If the equation of AC is y=2x—1, calculate the coordinates of T. (3)
3.4 If ABCD isa kite with AB = BC:
3.4.1 Determine the coordinates of C (2)
3.4.2 Calculate the length of BT (4)
3.4.3 Write down the length of the radius of the circle passing through
points B, C and T (2)

{15]

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EASTERN CAPE

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Mathematics/P2 6 DBE/November 2017
CAPS - Grade 11

QUESTION 4

C, a point on the x-axis, A(-5 ; -3) and B(4; 12) are the vertices of a triangle.
AB intersects the x-axis at E.
ABC=0 and BEC=a.

4,
B(4: 12)
6
LZ — .
ACS ;-3)
4.1 Calculate the gradient of AB.
4.2 Determine the coordinates of point E.
43 Determine the size of a. Round off to the nearest whole number.
4.4 If 0=76°, determine the equation of the line through A parallel to BC.

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EASTERN CAPE

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Mathematics/P2 7U DBE/November 2017
CAPS - Grade 11

QUESTION 5

5.1 Simplify fully: sin(90°— x). cos(180° + x)+tan x. cos x. sin (x-180°) (6)

5.2 Prove, WITHOUT using a calculator, that

5.3

5.4

sin 315°.tan210°.sin 190° —V2

cos 100°.sin 120° 3 (6)

In the diagram below, R is a point in the first quadrant such that TOR =a@ .
RO is extended to P such that OP=2RO and TOP=f.
It is given that sina = 2 :

fy

R
(6 De
fe) T ox
ly

WITHOUT using a calculator, determine:
5.3.1 The value of tana (3)
5.3.2 The value of sin (3)
539 The coordinates of P (4)

yee in@—tan@. cos’
Prove the identity: ee = tan@ (4)
cos@—1+sin’ 6

[26]

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EASTERN CAPE

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Mathematics/P2 8 DBE/November 2017
CAPS ~ Grade 11
QUESTION 6
6.1 Determine the general solution for sin(x—30°)= cos2x (5)
6.2 Consider the functions f(x)=sin(x-30°) and g(x)=cos2x
6.2.1 Write down the period of g. (1)
6.2.2 State the range of /f. (2)
6.2.3 On the grid provided in the ANSWER BOOK, draw the graphs of
—|—h—™mr™éi<“—SO—CS—C—sSsSr—s—s
Clearly show ALL intercepts with the axes, turning points and end points. (5)
6.2.4 Write down the x-coordinates of the points of intersection of f and g in
the interval x €[-90°;180°]. (3)
[16]
QUESTION 7

In APQR, QR=3 units,PR = x units, PQ = 2x unitsand POR Oo

Q
2%
3
P
_
R
x +3
TA Show that cos 6 = re (3)
7.2 If x=2,4 units:
ve | Calculate 0 (3)
7.2.2 Calculate the area of APQR (2)
Ts) Calculate the values of x for which the triangle exists. (4)
[12]

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EASTERN CAPE

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Mathematics/P2 9 DBE/November 2017
CAPS ~ Grade 11

QUESTION 8

A pyramid with a square base with a side length of 16 cm is sketched below. P lies on the
square base directly below A.
The volume of the pyramid is 640 cm’.

Volume of pyramid = yan

16 cm
8.1 Show that the perpendicular height of the pyramid, AP, is 7,5 cm. (2)
8.2 Hence, determine the total surface area of the pyramid. (4)

[6]

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EASTERN CAPE

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Mathematics/P2 10 DBE/November 2017
CAPS — Grade 11

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

9.1 In the diagram below, O is the centre of the circle and point T lies on chord RS.
Prove the theorem which states that if OT | RTS then RT= TS.

(5)
9.2 In the diagram, O is the centre of circle ABD. F is a point on chord AB such that
DOF 1 AB. AB=FD=8cm and OF = xcm.
D
Determine the length of the radius of the circle. (5)

[10]

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Mathematics/P2

QUESTION 10

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10
CAPS ~ Grade 11

M is the centre of the circle SVQR having equal chords SV and QR.
RP and QP are tangents to the circle at R and Q respectively such that RPQ = 70°.

DBE/November 2017

10.1 Calculate the size of R,.

10.2 Calculate the size of Q,.

10.3 Determine the size of M, :

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(2)

(3)
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Mathematics/P2 12 DBE/November 2017
CAPS - Grade 11
QUESTION 11

In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D.
DB bisects ABC. Let B, =%

11.1 Prove that BC|| OD (4)

11.2 Showthat C =90° (3)
[7]

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EASTERN CAPE

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Mathematics/P2 13 DBE/November 2017

CAPS — Grade 11

QUESTION 12

In the diagram below, two circles touch each other externally at point P.
QPR is acommon tangent to both circles at P. EDRC isa tangent to circle PBFC at C.

RCA=y and DAC=x. AD||BC.

E
12.1 Name, with reasons, FOUR other angles equal to x. (7)
12.2 Show that EPA=x+y (4)
12.3 Determine the numerical value of x+y, if it is given that DCTP is a cyclic
quadrilateral. (4)
{15}

TOTAL: 150

coer MALE

A

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