# Mathematics Grade 11 P1 Free State June 2025 Question Paper

> Grade 11 Mathematics Paper 1 question paper from the Free State June Exam 2025, 7 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/fs-maths-grade-11-june-2025-p1-only/82015d8f-bcc0-478e-ad47-d3b295dabb01
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper
- Year: 2025
- Exam period: Free State June Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 7

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## About this document

Mathematics · Grade 11 · Free State June Exam · 2025. Question paper, 7 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

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education

Department of
Education

FREE STATE PROVINCE

MARKS: 100

HOURS: 2 HOURS

This question paper consists of 7 pages and a formula sheet

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INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

I.

2:

This question paper consists of 6 questions. Answer all the questions.
Answer ALL the questions in the SPECIL ANSWER BOOK provided.

Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your
answers.

yarded full marks.

Answers only will NOT

)grammable and non-
tated.

An approved scientii ji
graphical) may be

If necessary, answers | ff to TWO decimal places, unless stated otherwise.
Diagrams are not necess ‘awn to scale.

An information sheet with formulae is included at the end of the question paper.

Write neatly and legibly.

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QUESTION 1

113 2. Art
grt

gros +e 2m
gions

1.2 Prove that ¥2..32-4

QUESTION 2

2.1 Solve for x:

(answer correct to two decimal places)

215. [eseavJe

2.2 Solve for n if dn =8
2.3 Solve for x and y:

x +4y? =2xy+7 and 3+x=2y

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FSDoE/June 2025

(2)

(3)

(3)

(4)

Q)
[15]

(2)
(3)

(3)
(4)
(5)

(3)

(6)

[26]

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QUESTION3

3.1. Determine the nature of the roots of the following equation, without solving
the equation: x° +5x-9=0. : (3)

3.2. The solutions of a quadratic equation are given by: x = (2)
For which value(s) of k will the equation have two real and equé
3.3. Given: S (x) =ax’ +bx-te. has equal roots, name = (5)
and it is further giver - ; termine the
[10]
QUESTION 4
imorephysics.com
Given; g(x)=——+2
x—
4.1. Write down the equation of the asymptotes of g. (2)
4.2 Calculate the intercepts with the axes of g. (3)
4.3. Draw a graph of g, indicating any intercepts with the axes and the asymptotes. (3)
4.4 Determine the value(s) of x where g(x) >0. (2)
4.5 Determine the equation of the axis of symmetry of g which has a positive gradient. (2)
4.6 Write down the domain of h if h(x)=g(x+l). 2)
[14]

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QUESTIONS

The graph of h(x)=—x* +x+2and k(x)=4x—2 are drawn below. A and B are the

x-intercepts of h. D and C are the y-intercepts of / and k respectively. P and Q are the points of
intersection of and k.

5.1 Calculate the coordinates of A and B. (4)
5.2. Determine the length of CD. (3)
5.3 Determine the range of h(x). (4)
5.4 Determine the maximum value of airs (2)

5.5. Write down the coordinates of the turning point of f, if f is the reflection of / in the x
axis. (2)

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5.6 If the coordinates of P and Q are (-4;—18) and (1; 2) respectively, determine for which
values(s) of x is:
5.6.1 h(x)-k(x)>0? (2)
5.6.2 xh(x)<0. (2)
5.7 Write down the value(s) of n for which h(x) =n will have equal roots? (4)
[23]
QUESTION 6
The graph of g(x v. T (1;2) is the point on the graph.
6.1 Determine the equation of (3)
6.2 Write down the equation of the asymptote of g. (1)
6.3. Write down the equation of f if f is the graph of g shifted 2 units to the right. (1)
6.4 Calculate the average gradient of g between point T and the origin. (2)
6.5 If the domain of g(x) is restricted to be x €[-2;3], write down the range of g. (3)
[10]

TOTAL: 100 MARKS

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INFORMATION SHEET/INLIGTINGSBLAD

_ =b£Nb? -4ac
2a
A=P(l+ni) A=P(I-ni) A=P(1-i)" A= P(1+i)"
T, =a+(n-l)d S, =F Ra+ (nna

m=tan0

ab c

In AABC: = a’ =b* +c? —2be.cos A

sind sinB sinC

area AABC = Sabin Cc

cos @—sin* a

cos2a ={1—2sin> @ sin 2a = 2sin a.cosa
2cos* a-l

P YG, -37

xa oa os
n n

n(A)
P(A) = n(S) P(A or B) = P(A) + P(B) — P(A and B)

n
peathx p= 2-0-9)

DY@-»x)
6

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