# Mathematics Grade 11 Paper 1 Limpopo November 2019 Question Paper

> Grade 11 Mathematics Paper 1 question paper from the Limpopo November Exam 2019, 10 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/gr11-p1-nov-2019-limpopo/ca6cde76-f735-48cc-864c-9fcdc64670b9
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper
- Year: 2019
- Exam period: Limpopo November Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 10

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## About this document

Mathematics · Grade 11 · Limpopo November Exam · 2019. Question paper, 10 pages. Read online or download the PDF.

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

## Document text

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### Page 1

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LIMPOPO

PROVINCIAL GOVERNMENT
REPUBLIC OF SOUTH AFRICA

DEPARTMENT OF

EDUCATION

NATIONAL
SENIOR CERTIFICATE

GRADE 11

MATHEMATICS P1

NOVEMBER 2019

MARKS: 150

TIME: 3 hours

This question paper consists of 9 pages, an answersheet and an information sheet

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Mathematics P1 2 LimpopoDoE/November 2019
NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1. This question paper consists of 9 questions.

2. Answer ALL questions.

3. Answer Questions 5.2.1 and Question 7 on the DIAGRAM SHEET PROVIDED
4, Answer correctly according to the numbering system used in this question paper.

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

6. Answers only will not necessarily be awarded full marks.

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

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

10. Write neatly and legibly.

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Mathematics PI 3 LimpopoDoE/November 2019
NSC
QUESTION 1
ill Solve for x:
L.1.1 5x? -33x-14=0 Q)
1.1.2 x?+7x+4=0 (answer correct to TWO decimal places) (3)
ibe Given; V¥8-x =x-2

13

14

TS

1.2.1 Without soving the equation, show that the solution above will lie in

the interval 2<x <8. (3)
1.2.2 Solve the equation. (5)
1.2.3. Hence or otherwise, solvex if —V8-x =x-2, @)
Solve for x if x°+2x215 (4)

Solve for x and ¥ in the given equations:

2) =32* and y=x—2x-18 (6)
44 /74+3
The solution of a quadratic equation is: x= ofr eae where peR.
Determine the values of P so that:
1.5.1 The equation has equal roots (2)
1.5.2 The equation has non-real roots. (2)
[29]

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Mathematics P1 4 LimpopoDoE/November 2019
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QUESTION 2

2.1 Simplify without the use of a calculator:

511 W8+x8 °
lk 50 (4)
See nee 3) wie
Zale ene (4)
2.2 Solve for x without the use of a calculator:
3)’ =27
re nie lat ie )
2.2.2 4%_3.2%=40 (4)
[16]
QUESTION 3
During the 2019 Cricket World Cup the South African Captian Faf du Plessis hit a
ball with all his might. After the ball left his bat, the hight of the ball in metres was
expressed by the equation h(x) =-x’+4x after x seconds.
Calculate the maximum height of the ball? (4)
[4]
QUESTION 4
4.1 Consider the following number pattern: 4; 9; 14; ...
4.1.1 Write down the next two terms of the pattern. (2)
4.1.2 Determine the expression for the n™ term of the pattern. iC)
4.1.3 Determine if 1099 is a term of the number pattern? (3)

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Mathematics P1 5 LimpopoDoE/November 2019
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4.2 Consider the following quadratic number pattern: 6; 105 18:2.

4.2.1 Write down the following two terms of the pattern. (2)
4.2.2 Determine the equation of the general term in the form:

T, =an’ +bn+c (4)
4.2.3 Calculate the value of 7, (2)
42.4 What term of the pattern will have a value of 766? (4)

4.3. A certian number pattern has the following properties:

| ° [=k
. 7,=14
Bee
° £-7,=10 (5)

Determine the value of [.
[24]

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Mathematics P1 6 LimpopoDoE/November 2019
NSC

QUESTION 5

k
5.1 In the diagram below f(x) z ar +q where A(2;1) is the point of intersection of the
x-

asymptotes of fand B(0;—2) is the y-intercept.

Ay

ree
ie |
IB(0;— 2):
5.1.1 Write down the equations of the asymptotes of /. (2)
5.1.2 Determine the equation of f. (3)
5.1.3 Write down the domain of f (1)
5.14 Calculate the coordinates of D. (4)

5.1.5 Calculate the equation of the function h(x)=ax° +bx+¢which

goes through the point B, C and D, where are C and D are
the x-—intercepts of h. (5)

5.2 Given the graph of g defined by the equation: gia)= oe

5.2.1 Draw aneat sketch of gon the answer sheet provided. Show

the asymptote and intercept with the axis. (3)
5.2.2 Determine the equation of g(x-3). (2)
[20]

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LimpopoDoE/November 2019
NSC

QUESTION 6

The graph of f(x)=-x*?+bx+c and the straight line g are sketched below. A and
D are points of intersection of f and g. Point A is the turningpoint of f. Points D

and B (1 ; 0) are the x-intercepts of f. The axis of symmetry of f is x=—1.

6.1

Write the coordinates of D.
6.2 Show that b=—2 and c=3
6.3 Determine :
6.3.1 the range of f.
6.3.2 the equation of g in the form y=mx+c
6.4 For which values of x is :
x.f(x)>0
6.5 For which values of & will Hf (x) =k have non-real roots?
| 6.6 Tis a point on the x-axis and M isa point on f such that
TM x-axis. TM intersects 2 at P. Calculate the maximum length
| of PM.
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(1)
(4)

(2)

(3)

(4)

(3)

(4)
[21]

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Mathematics P1 8 LimpopoDoE/November 2019
NSC

QUESTION 7

The function f defined by f(x)= —* 144 has the following properties:
x+p

e Thedomain: xeR; x¥3
e y=-x+4 isa line of symmetry.
e a>0

Draw a neat graph of this function on the answer sheet provided. Your sketch must

include the asymptotes. (3)
[3]
QUESTION 8
8.1 Jaco bought a new car for R250 000. At the end of 6 years the value

of the car depreciates to R150 000. If the car depreciates in a reducing
balanced method
Calculate the rate of the depreciation.

8.2 Calculate the effective interest rate p.a. if the nominal rate
is 8,9% p.a., compounded monthly. (3)

p
8.3 Mary opened an investment account and deposited R35 000. The

account earns an interest of 8% per annum compounded half yearly

for the fisrt 18 months and after that 6,5% per annum compounded

monthly.

How much money will be in Mary’s account exactly 5 years after the

initial deposit? (5)

8.4 Donald deposited R15 000 into his new savings account at a rate of
16% p.a. compounded monthly. Exactly 3 years after his initial
deposit he deposited an additional ammount of R10 000 into the same
account. Exactly 5 years after his initial ammount was deposited he
withdrew an ammount of R8 000 from the account.

How much money will Donald have in his savings account
exactly 7 years after his initial deposit? (5)

[16]

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Mathematics P1 9 LimpopoDoE/November 2019
NSC
QUESTION 9
9.1 Given: P(A)=0,2
2 (B ) =0,5
P(Aand B)=0,1
Onl Are the events A and B mutually exclusive? Give reasons

for your answers.

] ee?) Are the events A and B independent? Give reasons for your
j answers.

9:2 The Venn-diagram below shows the probabilities of two independant
events A and B.

Determine the values of x and y. Show all calculations.

9.3 Kobus has a bag with 60 marbles, each of which is green, blue or red in

color. = of the marbles are green and 15% of the marbles are blue.

Kobus picks TWO marbles out of the bag, one at a time and without
putting the first one back.

OSL How many red marbles are there in the bag?
} 932 Draw a tree diagram to represent the situation above.
| 933 What is the probability that Kobus will pick a BLUE and
GREEN marble. (round off your answers to THREE decimal
places)

TOTAL:

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Q)

(3)

(4)

(2)
(3)

(3)
{17]

[150]

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11
NSC

Mathematics P1

LimpopoDoE/November 2019

Information Sheet Mathematics

-b+ Vb? —4ac

2a
A=Pil-tm) “A= Pd=ni) A=P(l-i)" A=P(+i)"
ft i I
Mian co tu T, =a+(n-l)d S, => Qa+(n-Dd)
i=l isl
Ta g -N a) , r#l 8, =; -1<47 21
i r-l St
pati -1 ptl=0+)""]
i i
wo S(xt+h)— f(x)
‘(x)= lim ————7—+
fe) h>0 h
X,+x J, =
d= G22), 1 )e M222 21272)
2 2
y=met+e y-y, =m(x-x,) a22e m=tand
ema
(x-a) +(y-4) =r?
InAdpe, = but of a* =b* +c2 —2be.cos A

sinA sinB  sinC
area ABC =— ab.sin C
sin(@ + B) = sin a.cos # +cosa.sin B
cos(a + )=cos@.cosf-sin a.sin B
cos’ a—sin® a
cos2a@ =41-2sin* @
2cos* a-1

(x; y) > (xcos6+ ysin @; ycos@ — xsin 0)

=
n
_ n(A)
P(A)= lS)
poatbx o>

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sin(a = A) = sin a.cos B —cosa.sin 3
cos(a — 8) = cosa.cos 8 +sin a.sin B

sin 2a = 2sin a.cosa@

(x3 y) > (xcosO- ysin@; ycos@ + xsin 6)
n 2
Dlx, -¥)

2 i=l

oO

An
P(A of B) = P(A) + P(B) — P(A and B)

XG-x)0-7)
Y@-x)

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