# Mathematics Grade 12 P1 NSC June 2022 Question Paper (Eng)

> Grade 12 Mathematics Paper 1 question paper from the NSC June Exam 2022 (English), 10 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/mathematics-p1-may-june-2022-eng/9006a0fa-3020-421f-914d-af8b3a910527
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper
- Year: 2022
- Exam period: NSC June Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 10

Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 12](https://www.hlayiso.com/library/grade-12) › [Mathematics](https://www.hlayiso.com/library/grade-12/mathematics) › [Mathematics Grade 12 P1 NSC June 2022 Question Paper (Eng)](https://www.hlayiso.com/library/mathematics-p1-may-june-2022-eng/9006a0fa-3020-421f-914d-af8b3a910527)

## About this document

Mathematics · Grade 12 · NSC June Exam · 2022. 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

Text extracted from the PDF. Layout, diagrams and tables may not survive extraction.

### Page 1

basic education

Department:
Basic Education
REPUBLIC OF SOUTH AFRICA

SENIOR CERTIFICATE EXAMINATIONS/
NATIONAL SENIOR CERTIFICATE EXAMINATIONS

MATHEMATICS Pi

2022

MARKS: 150

TIME: 3 hours

This question paper consists of 9 pages and 1 information sheet.

Copyright reserved Please turn over

### Page 2

Downloaded from hlayiso.com

Mathematics/P 1 2 DBE/2022

SC/NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1,

2.

10.

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, etc. 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.
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

Downloaded from hlayiso.com

Mathematics/P 1 3 DBE/2022
SC/NSC
QUESTION 1
11 Solve for x:
1A x? +2x-15=0 (3)
1.1.2 5x’?-x-9=0 (Leave your answer correct to TWO decimal places.) (3)
1.1.3 x? <3x (4)

1.2 Given: a+ tu16

a
1.2.1 Solve for a. G)
1.2.2 Hence, solve for x: 2" +2°* =16 (3)
i002 + 1006
13 Without using a calculator, calculate the value of |/———.3—
17(2) (4)
14 Solve for x and y simultaneously:
1
2x-y=2 and —-3y=l
y x y 6)
[26]
QUESTION 2
2.1 The first term of an arithmetic sequence is -1 and the 7” termis 35.
Determine:
2.1.1 The common difference of the sequence (2)
2.1.2 The number of terms in the sequence if the last term of the sequence
is 473 (3)
2.1.3 The sum of the first 40 terms in this sequence (2)
2.2 75 ;53;35;21;.., isa quadratic number pattern.
2.2.1 Write down the FIFTH term of the number pattern. (d)
2.2.2 Determine the n™ term of the number pattern. (4)
2.2.3 Determine the maximum value of the following number pattern:
-15;-3;-7;-21,
ar eee (4)
[16]

Copyright reserved Please turn over

### Page 4

Downloaded from hlayiso.com

Mathematics/P! 4 DBE/2022
SC/NSC

QUESTION 3
3.1 Consider the following geometric sequence: 1 024; 256; 64; ...
Calculate:

3.1.1 The 10" term of the sequence (2)

3.1.2 5.256(4"”)
=0

(4)
3.2 The first two terms of a geometric sequence are:
3 2
-P-61—9 and t?+9t° +27t+27
2
Determine the values of ¢ for which the sequence will converge. (5)
{1a}
QUESTION 4
The graph of g(x) = (3) +7 passes through point E(2 ; 10).
41 Calculate the value of a. (3)
42 Calculate the coordinates of the y-intercept of g. (2)
43 Consider: A(x) = (:)
4.3.1 Describe the translation from g to h. Q)
43.2 Determine the equation of the inverse of }, inthe form y=... (2)
[9]

Copyright reserved Please turn over

### Page 5

Downloaded from hlayiso.com

Mathematics/P 1 j DBE/2022
SC/NSC

QUESTION 5
. a
Consider: g(x) =——— +4
x+p

The following information of g is given:

e Domain: xeR; x#-2
e x-intercept at K(1 ; 0)

e y-intercept at n(a 7 3)

5.1 Show that the equation of g is given by: g(x)= 344
x+2 (6)
5.2 Write down the range of g. (1)
5.3 Determine the equation of h, the axis of symmetry of g, in the form y=mx+c,
where m> 0. (3)
5.4 Write down the coordinates of K’, the image of K reflected over h. (2)

[12]

Copyright reserved Please turn over

### Page 6

Downloaded from hlayiso.com

Mathematics/P1 6 DBE/2022
SC/NSC

QUESTION 6

The sketch below shows the graph of (x)= —x? —6x+7.
C is the y-intercept of f

A and B are the x-intercepts of

D(-5 ; 4) isapointon f

E ty
D(-5 ; k)
f Cc
A B +

6.1 Calculate the coordinates of E, the turning point of f (3)
6.2 Write down the value of &. (0)
6.3 Determine the equation of the straight line passing through C and D. (4)
6.4 A tangent, parallel to CD, touches f at P. Determine the coordinates of P. (4)
6.5 For which values of x will f(x)-12>0? (2)

[14]

Copyright reserved Please turn over

### Page 7

Downloaded from hlayiso.com

Mathematics/P 1 7 DBE/2022
SC/NSC
QUESTION 7
TA How many years will it take for an investment to double in value, if it earns interest at
arate of 8,5% p.a., compounded quarterly? (4)

72 A company purchased machinery for R500 000. After 5 years, the machinery was
sold for R180 000 and new machinery was bought.

721

7.2.2

7.2.3

QUESTION 8
8.1 Determine
8.2 Determine:

8.2.1

8.2.2

Copyright reserved

Calculate the rate of depreciation of the old machinery over the 5 years,
using the reducing-balance method. (4)

The rate of inflation for the cost of the new machinery is 6,3% p.a. over
the 5 years. What will the new machinery cost at the end of
5 years? (2)

The company set up a sinking fund and made the first payment into this
fund on the day the old machinery was bought. The last payment was
made three months before the new machinery was purchased at the end of
the 5 years. The interest earned on the sinking fund was 10,25% p.a.,
compounded monthly. The money from the sinking fund and the
R180 000 from the sale of the old machinery was used to pay for the new
machinery.

Calculate the monthly payment into the sinking fund. (5)
{15}
t ‘(x) from first principles if it is given that f(x) = —x?, (5)
f(x), ifit is given that f(x)=4x? — 5x7 (2)
63
>, 6 ils + |
* (4)
{11}

Please turn over

### Page 8

Downloaded from hlayiso.com

Mathematics/P] 8 DBE/2022
SC/NSC

QUESTION 9

Sketched below is the graph of f(x)=x* +ax? +bx+c.
The x-intercepts of f are at (3 ;0) and M, where M lies on the negative x-axis.

K(O ; -3) is the y-intercept of f
M and N are the turning points of 7

ty
M x
N

9.1 Show that the equation of f is given by f(x)=x°-x? -5x-3. G6)
9.2 Calculate the coordinates of N. (5)
93 For which values of x will:

93.1 f(x) <0 Q)

9.3.2 f be increasing (2)

9.33 f be concave up G3)
9.4 Determine the maximum vertical distance between the graphs of f and f ’ in the

interval -1<x<0. (6)

[23]

Copyright reserved Please turn over

### Page 9

Downloaded from hlayiso.com

Mathematics/P 1 9 DBE/2022
SC/NSC

QUESTION 10

10.1 Flags from four African countries and three European countries were displayed in a

10.2

10.3

row during the 2021 Olympics.
Determine:

10.1.1 The total number of possible ways in which all 7 flags from these
countries could be displayed

10.1.2 The probability that the flags from the African countries were displayed
next to each other

A and B are two independent events.

P(A) =0,4 and P(A or B)= 0,88

Calculate P(B).

There are 120 passengers on board an aeroplane. Passengers have a choice between a
meat sandwich or a cheese sandwich, but more passengers will choose a meat

sandwich. There are only 120 sandwiches available to choose from. The probability
that the first passenger chooses a meat sandwich and the second passenger chooses a

cheese sandwich is = . Calculate the probability that the first passenger will choose

a cheese sandwich.

TOTAL:

Copyright reserved

(2)

(3)

(3)

()
[13]

150

### Page 10

Downloaded from hlayiso.com

Mathematics/P I DBE/2022
SC/NSC
INFORMATION SHEET

abt Vb? ~Aae

2a
A= P(l+ni) A= P(-ni) A=P(-i)" A= P(1+i)"
T, =a+(n-l)d S, =F Pa+@-na]
T, =ar"! 5, a=) sr#l S, = s-l<r<l

r-1 l-r

pale a1 pawl Gsiy”

L qT
; a f(x+h)-f@

= lim LAT
Pee h
—= X, +X Wty.
d=\(%-m) +0r-H)° M2222)
yamx+e y-y=m(x—x) m= mtn’
X,—%

(x-a)l +(y-by =??
InaaBc; —2-=—2_=_£

sinA sinB sinc

a’ =b> +c? —2be.cos A
1 :

area AABC = 5 ab.sin Cc
sin(a + B)=sina.cos B + cosa.sin B
cos(a + f)=cosa.cos 8 -sina.sin B

cos’ a—sin’ a
cos2@ =41—2sin’ a

2cos* a -1

Copyright reserved

sin(a — £)=sina.cos B - cosa.sin 8

cos(a — 8) = cosa.cos f + sina.sin B

sin 2a = 2sina.cosa

Y(x, -3)°
o= isl

n

P(A or B) = P(A) + P(B) — P(A and B)

po ae OF)
Yi«-xy

## Related documents

- [Gr12 Mathematics P1 (English) SEP 2022 Question Paper](https://www.hlayiso.com/library/gr12-mathematics-p1-english-sep-2022-question-paper/14941e0e-8578-4c8c-ba9e-f87f93e33e32) — Mathematics · QP · 2022 · Eng
- [Mathematics P1 May June 2019 Eng](https://www.hlayiso.com/library/mathematics-p1-may-june-2019-eng/a645dde5-42e0-4a8d-85e6-9027775ee0b4) — Mathematics · QP · 2019 · Eng
- [Mathematics P1 May June 2016 Afr](https://www.hlayiso.com/library/mathematics-p1-may-june-2016-afr/3a87d204-17dd-4b6b-bcf2-7f6302fb5865) — Mathematics · QP · 2016 · Afr
- [MATHS P1 GR12 MEMO JUNE 2022 English Afrikaans](https://www.hlayiso.com/library/maths-p1-gr12-memo-june-2022-english-afrikaans/9b15b6bd-06b3-48e5-b6d7-c1e74e052ebf) — Mathematics · Memo · 2022 · Afr
- [Gr12 Mathematics P1 (Afrikaans) SEP 2022 Possible Answers](https://www.hlayiso.com/library/gr12-mathematics-p1-afrikaans-sep-2022-possible-answers/38fb7466-deff-4faa-9c6c-825fcf932aae) — Mathematics · Memo · 2022 · Afr
- [Limpopo Mathematics Grade 12 PreTrial 2022 P1 and Memo](https://www.hlayiso.com/library/limpopo-mathematics-grade-12-pretrial-2022-p1-and-memo/e06438a7-82ad-46b2-84d5-019105ff0d59) — Mathematics · Memo · 2022

## More from Grade 12 Mathematics

- [MATHS P1 ANSWER BOOK GR12 SEPT 2025 English Afrikaans watermark](https://www.hlayiso.com/library/maths-p1-answer-book-gr12-sept-2025-english-afrikaans-watermark/d78c3fd3-dcd5-4f3f-911b-e5635b4686cc) — Addendum · 2025 · Afr
- [MATHS P2 MEMO GR12 SEPT 2025 E+A watermark](https://www.hlayiso.com/library/maths-p2-memo-gr12-sept-2025-e-a-watermark/838d50ea-fdac-4e70-8d62-e365a012252f) — Memo · 2025
- [Maths Grade 12 NSC P2 MEMO September 2025 Eng Northern Cape](https://www.hlayiso.com/library/maths-grade-12-nsc-p2-memo-september-2025-eng-northern-cape/f00a552e-132c-4871-bf72-c887cfc67272) — Memo · 2025 · Eng
- [MATHS P2 ANSWER BOOK GR12 JUNE 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-answer-book-gr12-june-2024-afr-english/4a71e975-4ac4-4f55-8e23-0b8155a5b0c6) — Addendum · 2024 · Eng
- [MATHS P2 MEMO GR12 JUNE 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-memo-gr12-june-2024-afr-english/4a5f997e-e38d-4abb-b726-8b72e6672832) — Memo · 2024 · Eng
- [MATHS P1 GR 12 MEMO SEPT 2024 English+Afrikaans](https://www.hlayiso.com/library/maths-p1-gr-12-memo-sept-2024-english-afrikaans/f0eedb8f-ec6f-4f46-9885-3933cd274781) — Memo · 2024 · Afr

## Collection

- [Grade 12 past papers](https://www.hlayiso.com/grade-12/past-papers)

---

Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. When citing, link the page URL above, not a PDF or /api/ URL.