# Mathematics Grade 12 P2 North West Mock 2025 Question Paper

> Grade 12 Mathematics Paper 2 question paper from the North West Mock Exam 2025, 13 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/maths-grade-12-nsc-p2-qp-september-2025-north-west/74afb2dd-ef77-4d09-97fb-bff56d51eb8c
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper
- Year: 2025
- Exam period: North West Mock Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 13

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## About this document

Mathematics · Grade 12 · North West Mock Exam · 2025. Question paper, 13 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

education

Department:

Education
North West Provincial Government
REPUBLIC OF SOUTH AFRICA

{ NATIONAL SENIOR CERTIFICATE }

GRADE 12

MATHEMATICS P2
SEPTEMBER 2025

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MARKS: 150
TIME: 3 hours

This question paper consists 12 pages, 1 information sheet
and an answer book of 22 pages.

Please turn over

Copyright reserved

### Page 2

Mathematics/P2 2

NW/September 2025

NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1,

2

This paper consists of 10 questions.

Answer ALL the questions in the SPECIAL ANSWER BOOK provided.

: sadetecmini
Clearly show ALL calculations, diagrams, graphs etc. which 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.
An information sheet with formulae is included at the end of the question paper.

Write neatly and legibly.

Copyright reserved

Please turn over

### Page 3

Mathematics/P2 3

: NW/September 2025
NSC

QUESTION 1

A survey was done under 100 members of a gymnasium about the cost of their annual
membership contract,

Results showed an average annual payment of R3 240.

AMOUNT (R) FREQUENCY
0<x<1000 8
1000 <x <2000 12
2000 < x <3000 P
3000 <x <4000 30
4000< x <5000 Q
5000 < x <6000 12
1.1 How many members payed less than R2 000 for their annual contract? (1)
1.2 Proof by calculation that P = 20 and Q = 18. (5)
1.3. Hence, complete the cumulative frequency table in the ANSWER BOOK. (2)
1.4 Use the cumulative frequency table to draw an ogive to illustrate the information
above. GB)
1.5 Use the ogive to determine how many members spent more than R4 200
annually on their contracts. (ql)
[12]

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### Page 4

Mathematics/P2 4
NSC

QUESTION 2

Eight couples entered a dance competition. Two judges gave marks for their
performances. The marks (out of 20) are shown in the table below.

COUPLE 1 7 aad Peach bee il (eed pea fel et
JUDGE 1 185 |0 42 | 65/8. [25s] al2 | 10: [14
JUDGE 2 1535[4,024|5:3) 4] 5 [214s|..8° 15

2.1 Determine the equation of the least squares regression line of the marks given by
the two judges.

2.2. A ninth couple had a late entry in the competition and received a mark of 15 by
JUDGE 1. Calculate to the nearest integer, the mark they possibly would have
received from JUDGE 2.

2.3. Are the judges consistent when allocating marks?
Motivate your answer with appropriate calculations.

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NW/September 2025

(G3)

(2)

(3)
[8]

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### Page 5

Mathematics/P2 3 NW/September 2025
NSC

QUESTION 3
In the diagram below PQRS is a quadrilateral with vertices P(3 ; 6), Q(9 ; ), R(8 ; 1)

and S(5 ; 0). PQ || SR.
AB is a straight line that touches the quadrilateral at P. QPB=50°

QI 59

S(5; 0) ar
3.1 Calculate the gradient of SR. (2)
3.2 Determine the equation of PQ in the form y= mx+c. (3)
3.3 Calculate the value of ¢. 2)
3.4 Calculate the length of PQ if r=8. Q)
3.5 Proof that PS is perpendicular to SR. (B)
3.6 IfPQ=PS, calculate the area of PQRS. (6)
3.7. Calculate the value of @, the angle of inclination of SR. (2)
3.8 Calculate the equation of AB, Show ALL working, ©)
6

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### Page 6

NW/September 2025
Mathematics/P2 6

NSC
QUESTION 4

. 2 2 -
In the diagram below the circle with centre A has the equation (x +1) + (¥ + 1) oe
FG is a chord of circle A. AD bisects chord FG.
FGC is a tangent to the circle with centre B(3 ; 2) at point c(4 Ae

Ay
C(4;1)
< >x
G
D
F
4.1 Write down the coordinates of A. (1)
4.2 Determine the equation of tangent FC, in the form y = mx+c. (4)
vio
4.3 Given: AD= a units, Calculate the length of FG,
(4)
4.4 Determine the length of AB. Q)
4,5 Another circle with centre B, touches the circle with centre A at K.
Determine the equation of the new circle. GB)
(t4]

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P: Please turn over

### Page 7

Mathematics/P2 7

NW/September 2025
NSC

QUESTION 5

5.1 Inthe diagram below, line OP is given with P(4;-5). KOP =@

Calculate, without using a calculator, the numerical value of the following:

5.1.1 sin?(180°+8)

(4)
5:12 tan(-0) @)
5.2 Calculate, without using a calculator, the value of the following:
52:1 cos 15° (6)
5.2.2 cos(90°+x).cos(180°—x)
cos’ (180° + x).tan(180°—~x) (5)
sin20+2cos@-2cos' 0.
5.3. Given: m =sin20
1+sin0
5.3.1 Proof the identity. (5)
5.3.2 For which values of @ in the interval [-360°;360°] is the identity in
QUESTION 5.3.1 undefined? (2)
5.4 Calculate the maximum value of eee a
[26]

Please a
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### Page 8

NW/September 2025
Mathematics/P2 8

NSC
QUESTION 6

In the diagram below, the graphs of f(x) = cos(x+ 60°) and g (x)=sin scribed

for the interval x €[—90°;180°].

|

Oe OF —30° 0°

6.1 Calculate the values of x, in the interval xe[-90°; 180°] for which

f(x) = g(x). (7)
6.2. Write down the period of g(x). qa)
6.3 Use your answer in question 6.1 to determine the value(s) of x where
alx)2/(2). -
6.4 Describe the transformation from h to p if h(x) =sinx and
p(x) =sin(x-30°). @)
[13]

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pyrig! Please turn over

### Page 9

Mathematics/P2 9 NW/September 2025
NSC

QUESTION 7

7.1 In the diagram below, AABCis 90° < C <180°.

A

|CO 3 0) Bia; 0)

Proof: c?=a? +b? —2abcosC. (4)

7.2 Inthe diagram below, A, B and C are three points in the same horizontal
plane.

¢ P is the image of a balloon vertically above C
e The angle of elevation to P from A is 6
© ABC=90°-a@

e BC= taB
2
e AB=dunits

d.tanO.V5-4sina
2

7.2.1 Prove that h= , where A is the height of the balloon above
the ground. (4)
7.2.2 Determine the value of h if d=300m, a =32° and 0 = 63°. @)

4 Please turn over
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### Page 10

NW/September 2025
Mathematics/P2 10
NSC
Provide reasons for your statements in QUESTION 8, 9 and 10.

QUESTION 8
In the diagram below PQBR is a cyclic quadrilateral.

¢ BP isa diameter of the circle. PR is produced to S, and PB to T
¢ PBT intersects QR at A and the circle at B

¢ RT bisects QRS, TS LSP

e PQ=PR
2
mn BIA As}2 2N\P
2 TK2 1]2 1
3] 4
R

1-5) Eee fe O= 55°, calculate with reasons the size of:

8.1.1 R, (2)

2 (2)

8.13 pap @)

ois: a (3)

8.2 Give areason why AQ = AR, ()
8.3 Prove that AT=TS, (4)
[14]

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### Page 11

Mathematics/P2 il NW/September 2025

QUESTION 9

In the diagram O is the centre of the circle, with CEG a tangent to the circle.

7
Ne
E

re) G

9.1 Prove the theorem that states that CED = F. (5)

9.2 In the diagram below, ABCD is a cyclic quadrilateral. EF || BD.
ACG and DCE are straight lines.

A

E
Prove that:
9.2.1 8,=A, a
9.2.2 EFisa tangent to the circle EAC (ty
9.2.3. AABC ||| AEDF 4)
92:43! BEAL: ED.BC
GH DF OF

ed Please turn over
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### Page 12

NW/September 2025
Mathematics/P2 12 :

NSC

QUESTION 10

In the diagram below, AB is a diameter of the circle. CB is a tangent to the circle at B.
AC intersect the circle at D.

e DC=%

|
e DC=—AD
2

BD
10.1 Prove that —— = J2
DC

(4)
10.2 Calculate the perimeter of AABCif AD = 10 mm.

GQ)
(7

TOTAL: 150

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### Page 13

Mathematics/P2

NW/September 2025
Nsc
INFORMATION SHEET
ea b+ yb? = 4ac
: 2a
A=P(l+ni
(1+ ni) A= P(1=ni) A=P(i-i)" A=P(i+i)"
T, =a+(n-1)d Si
(n-1) S, = 5[2a+(n-1)d]
T= ar"! _a(r" 1)
Feri. S, = s-lersl
Pie -1] naa]
n i
f(x) = tim£@ +9) =F) ea Dt Vb" = ae
> h 2a
d= (x, x) +(2-n) M[AtS ed
2 y}
yemx+e y-y,=m(x-%,) a m= tanO
Fea

(x= a) +(y-ay =P

Ge OTE Ree

In AABC:

sinA sinB_ sinC

a =b? +c? —2becos A

area AABC = 5absinc
sin(a + B) =sina.cos B + cosa.sin B
cos(a + f) = cosa.cos f — sina.sin B

cos’ a — sin’ a
cos2a = 4] — 2sin’ a

2cos’ a -1

Copyright reserved

sin(@ — B) = sina.cos B — cosa.sin B

cos(a ~ B) = cosa.cos B + sina.sin B

sin2a@ = 2sina.cosa@

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