# Mathematics Grade 11 Paper 1 KZN November 2016 Paper & Memo

> Grade 11 Mathematics Paper 1 question paper and memo from the KZN November Exam 2016, 22 pages. Read online or get the free PDF download.

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- Updated: 2026-09-28
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper and memo
- Year: 2016
- Exam period: KZN November Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 22

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Mathematics · Grade 11 · KZN November Exam · 2016. Question paper and memorandum, 22 pages. Read online or download the PDF.

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### Page 1

MARKS: 150

f ) TIME: 3 hours

Copyright reserved

basic education

Department:
Basic Education

-. NATIONAL
~ SENIOR CERTIFICATE

GRADE I1

This question paper consists of 9 pages.

NI. 0

REPUBLIC OF SOUTH AFRICA

QAP RRP SSAA RS SRR RRR RRR RRR RY
| u MATHEMATICS P1 t
1 i NOVEMBER 2016 "

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### Page 2

Mathematics/P1 2 DBE/November 2016

CAPS ~ Grade 11

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

Ll:

2.

3.

This question paper consists of 10 questions.
Answer ALL the questions.

Number the answers correctly according to the numbering system used in this
question paper.

Clearly show ALL calculations, diagrams, graphs et cetera that you have used in
determining your answers.

Answers only will not necessarily be awarded full marks.

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

If necessary, round off answers to TWO decimal places, unless stated otherwise.
Diagrams are NOT necessarily drawn to scale.

Write neatly and legibly.

Conyright reserved UNA AA A Please tn over

### Page 3

Mathematics/P 1 3 DBE/November 2016
CAPS ~ Grade 11
QUESTION 1
Ld Solve for x in each of the following:
| inn 3x? —-5x~-1=0 (leave your answer correct toT WO decimal places) (3)
1.1.2 x? -6x+8 =0 @)
1.1.3 4x-2x" <0 (4)
Li4 244 26 = 12 (4)
1.1.5 Vx-1+3=x-4 ©)
() 1.2 Solve for x and y simultaneously:
3x-y+2=0 and y=—-x? +2x+8 (6)
13 Show that the roots of 3x? +(k+2)x=1—k are real and rational for all values of &. (4)
[30]
QUESTION 2
21 Simplify fully, WITHOUT using a calculator:
5-2 . gute
J 5
21.41 10°—-10°".2 ©)
) 27m? —V48m'
a2 Ls (3)
12m®
2.2 WITHOUT using a calculator, show that 28 =-2 (4)
, 1+v2 V8
[12]

Comittee

Please turn over

### Page 4

Mathematics/P1 4 DBE/November 2016

CAPS - Grade 11

QUESTION 3

Consider the quadratic pattern: -9;-65;1;12;%5...

3.1 Determine the value of x. (1)
3,2 Determine a formula for the 2” term of the pattern. (4)
33 A new pattern, P,, is formed by adding 3 to each term in the given quadratic

pattern. Write down the general term of P, inthe form P, = an’ +bn+e. 65)
3.4 Which term of the sequence found in QUESTION 3.3 has.a value of 400? tio)
QUESTION 4 C
41 Given the linear pattern: 18; 14;10;...

41.1 Write down the fourth term. qd)

4.1.2 Determine a formula for the general term of the pattern. (2)

4.13 Which term of the pattern will have a value of — 70? @)

4.14 If this linear pattern forms the first differences of a quadratic pattern,

Qn determine the first difference between Qso9 and Qsio. (2)

42 A quadratic pattern has:a constant second difference of 2 and 7; =T, = 29,

4.2.1 Does this pattern have a minimum or maximum value? Justify the ( \
answer. 3).

4.2.2 Determine an expression for the n term in the form
T, =an’ +bnte, (5)

[5]

Conyright reserved INU AE AL AA Please tm over

### Page 5

7)

Mathematics/P1 5

DBE/November 2016
CAPS ~ Grade 11

QUESTION 5

Given: f(x) = 2x +x4+6

5.1
5.2
5.3
5.4
5.5

5.6

Calculate the coordinates of the turning point of f,

Determine the y-intercept of f

Determine the x-intercepts of f.

Sketch the graph of f showing clearly all intercepts with the axes and turning point.
Determine the values of k such that fx) =k has equal roots.

If the graph of f is shifted two units to the right and one unit upwards to form h,
determine the equation A inthe form y= a(x+ p)’ +q.

Conyright reserved NOTA E A Please tam over

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(1)
(4)
(3)
(2)

G3)
[17]

### Page 6

Mathematies/P 1 6 DBE/November 2016
CAPS ~ Grade tl
QUESTION 6
The diagram below shows the graph of f(x) = 5 ~ 1 and g(x) oye
x:
The graph of f intersects the x-axis at A and the y-axis at B.
The graph of f and g intersect at points C and D.
P
A fe) x
Cc
B f
an (
Dd
&

6.1 Write down the equations of the asymptotes of /- (2)
6.2 Determine the domain of f (2) ( ,
6.3 Calculate the length of:

6.3.1 OB 2)

6.3.2 OA (3)
6.4 Determine the coordinates of C and D. (6)

____ 6.5 Use the graphs to obtain the solution to: 5 > a (4)
x3 , ee as
[19]

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### Page 7

Mathematics/P1 7 DBE/November 2016
CAPS ~ Grade 11

QUESTION 7

The sketch below is the graph of f(x) =2.b°"' + q.
The graph of f passes through the points A(1 ;20) and B (-1;y).
The line y=2 is an asymptote of f-

y
ACL; 20)
B(-1;y)
asin nce 2
x
4
a >
7A Show that the equation of f is f(x)=2(@)"" +2
7.2 Calculate the y-coordinate of the point B.
73 Determine the average gradient of the curve between the points A and B.
74 A new function / is obtained when / is reflected about its asymptote.
Determine the equation of A,
75 Write down the range of ,

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### Page 8

Mathematics/P! 8 DBE/November 2016
CAPS ~ Grade 11
QUESTION 8
8.1 A machine costs R25 000 in 2016. Calculate the book value of the machine after
4 years if it depreciates at 9% p.a, according to the reducing balance method. 3)
8.2 The nominal interest rate of an investment is 12,35% p.a., compounded monthly.
Calculate the effective interest rate. (4)
8.3 ‘The value of a property increased from R145 000 to R221 292,32 over 6 years.
Calculate the average annual rate of increase of the property over 6 years. 4)

8.4 Tebogo made an initial deposit of R15 000 into an account that paid interest at 9,6%
p.a., compounded quarterly. Six months later she withdrew R5 000 from the account.
Two yeats after the initial deposit she deposited another R3 500 into this account.
How much does she have in the account 3 years after her initial deposit? (5)

QUESTION 9
91 Given:

9A
9.1.2

[16}

P(A) = 0,2 ¢ ‘
P(B) = 0,5
P(AorB)=0,6 where A and B ate two different events

Calculate P(A and B). (2)

Are the events A and B independent ? Show your calculations. (3)

9.2. A survey was conducted amongst 100 learners at a school to establish their
involvement in three codes of sport, soccer, netball and volleyball. The results are
shown below.

eensneee

55 learners play soccer (S)
21 learners play netball (N)
"7 learners play volleyball (V)
3 learners play netball only
2 learners play soccer and volleyball
1 learner plays all 3 sports

The Venn diagram below shows the information above. (

9.21
9.2.2

Copyright reserved

Determine the values of a, b, c, d and e. (6)

What is the probability that one of the learners chosen at random from
this group plays netball or volleyball? (2)

AM OETTINAN|Pseve

### Page 9

C)

Mathematics/P 1 9 DBE/November 2016
CAPS ~ Grade 11

9.3 The probability that the first answer in a maths quiz competition will be correct is 0,4.
If the first answer is correct, the probability of getting the next answer correct rises
to 0,5. However, if the first answer is wrong, the probability of getting the next
answer correct is only 0,3.

9.3.1 Represent the information on a tree diagram. Show the probabilities
associated with each branch as well as the possible outcomes. @)
9.3.2 Calculate the probability of getting the second answer correct. (3)
[18]

QUESTION 10
Bongani wants to start a small vegetable garden at his house. He wants to use an existing wall
and 14 m of fencing to enclose a rectangular area for the garden. Calculate the dimensions of :
the largest rectangular area that he can enclose. [4] |

TOTAL: 150

Conese | NILH

### Page 11

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Mathematios/PL/Wiskunde VE 3 DBENovenber 2016
*__ CAPS/KABY — Grade/Graad 11 ~Memorandura
113 Option/Opsie 1 OR/OF ‘Option/Opsie 2
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Mathematics/P1/Piskunde Vi 4 DBE/November 2016
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### Page 16

DBE/November 2016

Mathematics/P L/Wiskunde VI 7 DBE/November 2016
‘CAPS/KABV — Grade/Graad 11 ~Memorandum
a i r 12 x
NAN AON LON 4
3 7 IL 12
NZ N ZA NZ
4 #2 Vanswer/antw. — (1)
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nelson neh i)
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“Mathematics/P 1/Wiskunde VI
CAPS/KABV —' GradeKGraad li- Menor
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### Page 17

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### Page 18

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j DBE/November 2016

vihen / warmer rel ys-}

when/wanneer x =—4; y=—2

ae ed and D (-4;~2)

¥ x-values/waardes

Mathematics/P1/Wiskande V7 2
CAPS/KABY ~ Grade/Graad 1] ~Memorandom
7
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1 | ¥ substituton/vervanging.
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|
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|
|

¥ co-ordinates/kodrdinate C
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Mathematics UWiskunde V2 il DBE/November 2016
CAPS/KABY — Grade/Graad 11 ~Memorandum
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DBE/November 2016

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QUESTION/VRAAG 9
9.1 | Givew/Gegee: P(A)=02 |
P@)=05 |
P(A or B)=0,6
9.1.1 | P(A or B) = P(A) +P) —P(A and B) 70,6 =0,2+0,5 —P(A and B)
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