# Mathematics Grade 12 GP March 2023 Paper & Memo

> Grade 12 Mathematics question paper and memo from the GP March 2023, 15 pages. Read online or get the free PDF download.

- Page: https://www.hlayiso.com/library/gauteng-maths-grade-12-march-2023-qp-and-memo/883e015e-2060-4c56-9bc3-50ae28fbbef7
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper and memo
- Year: 2023
- Exam period: GP March
- Curriculum: CAPS
- Pages: 15

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## About this document

Mathematics · Grade 12 · GP March · 2023. Question paper and memorandum, 15 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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GAUTENG PROVINCE

EDUCATION
REPUBLIC OF SOUTH AFRICA

JOHANNESBURG WEST DISTRICT

MARKS: 50 DURATION: 1 HOUR

This question paper consists of 6 pages including the formula sheet.

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rade 12

INSTRUCTIONS AND INFORMATION

10.

This question paper consists of 6 questions.
Answer ALL the questions in your answer book.
Use the appropriate and correct numbering system as it is used on this 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.

An approved scientific calculator (non-programmable and non-graphical) may be used,
unless stated otherwise.

If necessary, answers should be rounded off 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 this paper.

It is in your own interest to write legibly and to present your work neatly.

Copyright reserved Please turn over

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rade 12
QUESTION 1
1.1 Solve for x.
11.1 -x(2x-3)=0 (2)
11.2  0=3x?-5x-11 (3)
1.1.3. x(8x + 4) —2(8x+ 4) <0 (3)
1.2 The roots of a quadratic equation, in terms of p, are given as:
4+/8—p3
ya we
Determine the value(s) of p for the roots fo be real. (3)
[11]
QUESTION 2
The first four (4) terms of a quadratic pattern are: 11; 20; 33; 50;...
2.1 Determine the general term of this pattern in the form T,, = an? +bn+c. (4)
2.2 Prove that the sum of the first n first-differences of this quadratic pattern can
be given by S, = 2n?+7n. (2)
[6]
QUESTION 3
A convergent geometric series is given by: 4 + Mev + a
3.1 Calculate the values of x. (3)
3.2 If x =1, calculate the sum to infinity, 5, . (2)
[5]

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rade 12

QUESTION 4

(1—x) ; (x+2) and (2x —5) are the first three (3) terms of an arithmetic sequence.

4.1 Determine the value of x . (3)
4.2 If the first three (3) terms of this pattern are: 9 ; —6 ; —21; ..., calculate
the numerical value of the sum of the first 100 terms, Syqq . (2)
4.3 Hence, or otherwise, calculate m if:
m-1
yy (24 — 15n) = Stop + 73 320 (4)
n=0
[9]
QUESTION 5
The graph of f(x) = ao +q_is sketched below:
Ay
| \f
i
< 30-1 Xx
i
1 | —______s
aaa --- eee poo fe
{ -1
\
|
v
5.1 Write down the values of p and q (2)
5.2 The straight line g(x) = —x +k is one of the axes of symmetry of the graph
of f . Determine the value of k. (2)
5.3 If h(x) = —2[g(x)], determine the equation of the inverse of A, A, in the
form h-4(x)=mxt+c. (3)
5.4 Draw aneat sketch of the graphs of h and h~1 on the same set of axes.
Clearly show all intercepts with axes, point of intersection and the axis of (4)
symmetry.
[11]
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rade 12

QUESTION 6

The graphs of f(x) = ax? and g(x) = b* are sketched on the same set of axes. Points
A(—1;2) and B are points of intersection of f and g . The graph of f has the turning
point at the origin:

A(-1;2)

A

6.1 Calculate the values of a and b. (2)

6.2 The inverse of f is NOT a function. Write down at least one condition which
can be used to restrict the domain of f such that its inverse will bea function. (1)

6.3. For which value(s) of x , where x € (—00;0], will g(x) S f(x)? (2)
6.4 If h(x) = g(x + 3) , write down the coordinates of ...

6.4.1 A’ , the new coordinates of A on the graph of h. (1)

6.4.2 A" , the new coordinates of A onthe graph of h-?, the inverse of h (2)

. [3]

TOTAL = 50 MARKS

Copyright reserved Please turn over

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INFORMATION SHEET
_-b4Vb? -4a0
2a
A=P(l+ni) A=P(-ni) A=P(-i)" A=P(+i)”
T, =a+(n—Nd Ss, =F a+ (nnd)
T, =ar"" s, = sea!) gr#l S.=jSs-ler<l
r- -r

patsy -1) pa2t-a+)"]
i i

‘¢¢) = Jim LAtM-FO)

i rr

y27-Y

y=mxte Y-yY =m(x—-x,) n= m=tan@
ae |
(x-a) +(y-by =r?
fading
sinA sinB sinC
a? =b? +c? —2be.cosA
area AABC = Sab sinc
sin(a + £)=sina.cosf+cosa.sinB sin(a—B)=sina.cosB —cosa.sinB
coda + £)=cosa.cos#—sina.sin cos(a — 8) =cosa.cosf# +sina.sinB
cos’ a —sin’ a
cos2e@ =41-2sin’? a sin2a = 2sina.cosa
2cos? a -1
: S (x, x)?
__>s# - 2 %)
x= ——
n n
n(A) =
P(A) = (5) P(A or B) = P(A) + P(B) - P(A and B)
n
pratbx p= 2-2)

De-%

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GAUTENG PROVINCE

EDUCATION
REPUBLIC OF SOUTH AFRICA

JOHANNESBURG WEST DISTRICT

GRADE 12

eee eee eee eee eee eee eee eee eee eee cee eee eee eee cece

MARKS: 50

This Marking Guidelines consists of 6 pages including this cover page.

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Marking Guidelines rade 12

IMPORTANT NOTES AND INFORMATION

+ Ifa candidate answers a question TWICE, only mark the FIRST attempt.

¢ Ifa candidate has crossed out an attempt of a question and not redone the question, mark the
crossed out version.

* Accept any other Mathematically valid attempt which yields a correct answer and credit full
marks.

* Consistent accuracy applies in ALL aspects of the marking memorandum.

« Assuming answers/values in order to solve a problem is NOT acceptable.

QUESTION 1
Q# Suggested Solutions Descriptors
11.1 x(2x — 3) =0 v¥x=0
x=O0orx=2 vx=2
2 2
(2)
1.1.2 0 = 3x*-—5x-11 Y correct substitution
__ -btvb?=4ac ¥x=-1,25
x= 2a ¥x=2,92
-(-5)tVC5)2-4@) C1)
oo) or OCD (3)
x =-1,25 or x = 2,92
11.3 x(3x + 4) — 2(3x +4) <0 ¥ factors/ method
(x-2)@x+4) <0 4 Y critical values
Critical values: x = 2; x = -3 ‘ ¥ solution
-f<xs<2 “3
3 (3)
1.2 For real roots: ¥8-p?>0
8-p>=0; p#0 ¥p#0
—p? =>-8 Yps2
piss8 (3)
ps2
Subtotal [11]
QUESTION 2
Q# Suggested Solutions Descriptors
21 11; 20 ; 33; 50 Ya=2
1% differences: 9; 13; 17 ¥b=3
2™ differences: 4; 4 ¥c=6
. 2a=4 3a+b=9 atb+c=11 |” In=2n?+3n+6
a=2 3(2)+b=9 24+34c=11
b=3 c=6 (4)
Ty = 2n? + 3n+6
2.2 1 differences: 9; 13; 17 Y correct substitution
a=9:d=4 ¥ simplification
S, = 5a + (n= 1d] (2)
= 51209) + (n~ 1)4]
= 5 {14 + 4n]
= 7n + 2n?
Subtotal [6]

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Bownleadedtfrom Stanmorephysics.com JW-GDE/ March 2023
Marking Guidelines rade 12
QUESTION 3
Q# Suggested Solutions Descriptors
3.1 = = Y-1< = <1
-1<*P<1
-3Se+1<3 yises? @)
—4<x<2, but x#—-1
3.2 Sa ye Y correct substitution
_ sey v answer
141
rae (2)
= 10
Subtotal [5]
QUESTION 4
Q# Suggested Solutions Descriptors
(2x —5) — («+ 2) = (x+2)-(1-x) v method
4.1 x-7=2x+1 ¥ simplification
-8=x ¥ x=-8 (3)
9;-6;-21 ¥ correct substitution
4.2 a=9,d =—15,n=100 y
n
Sy = 5 [2a + (n= 1d] answer °)
100
St00 = = BO) + (100 — 1)(—15)]
= —73 350
43 m=1 v RHS = —30
(24 — 15n) = Si99 + 73 320 ¥ F224) + (m= 1)(-15)]
n=0 ¥ standard form
= —73 350 + 73 320 ¥ m= 5 and rejection
(4)
= [2(24) + (m — 1)(—15)] = —30
m(48 — 15m +15) = —60
63m — 15m? = -60
0 = 15m? — 63m — 60
0 = 5m? — 21m — 20
0 = (5m+4)(m—-5)
m=5 0rm# -:
Subtotal [9]
QUESTION 5
Q# Suggested Solutions Descriptors
5.1 p=3 Yp=3
q=-1 ¥q=-l
(2)
5.2 gix)=-x+k ¥ correct substitution
-1=-(-3)+k _...at point (—3;-1) y¥ -4=k
—4=k (2)

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eserved

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Bownleadedtfrom Stanmorephysics.com JW-GDE/ March 2023
Marking Guidelines rade 12
5.3 h(x) = —2(—x - 4) ¥ h(x) = 2x +8
=2x+8 v swapping x and y
For inverse: Vv yan 4
x=2y+8 a)
x—8=2y (3)
x-85
“Fan
-yss-4 shl(x)=2+-4
5.4 y Y correct graph shapes
v x- and y-intercepts
interchanging
¥ correct point of
intersection
¥ axis of symmetry passes
through the correct point of
< intersection
(4)
Subtotal [11]
QUESTION 6
Q# _| Suggested Solutions Descriptors
6.1 | f(x) = ax? g(x) = b* Ya=2
2 =a(-1)? 2=b? il
na=2 b= 1 vb= 2
~2
(2)
6.2 |x<0 orx>0 ¥ any one of the correct
conditions
(1)
63 |x<-1 OR x€(—o;-1] OR -w<x<-1 Y correct critical value
Y correct notation
(2)
6.4.1 | A’ (—4; 2) ¥ (-4;2)
(1)
6.4.2 | A" (2; -4) ¥¥(2;-4)
(2)
Subtotal [8]

TOTAL = 50 MARKS

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### Page 11

Bownleadedtfrom Stanmorephysics.com JW-GDE/ March 2023
Marking Guidelines rade 12

QUESTION 1

1.1 Solve for x.

11.1  x(2x-—3)=0 (2)
11.2 0=3x?-5x-11 (3)
113 x(3x+4)-2@x+4 <0 (3)
1.2 The roots of a quadratic equation, in terms of p, are given as:
4+/8-p3
x=—~Y
fe (3)
Determine the value(s) of p for the roots to be real.
[11]
QUESTION 2
The first four (4) terms of a quadratic pattern are: 11; 20; 33; 50;...
2.1 Determine the general term of this pattern in the form T,, = an? + bn+c. (4)
2.2 Prove that the sum of the first n first-differences of this quadratic pattern can
be given by S, = 2n?+7n. (2)
[6]

QUESTION 3

a S(xt+1
A convergent geometric series is given by: ~ dy

5(x+1)? + 5(x+1)3
9 27

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Bownleadedtfrom Stanmorephysics.com JW-GDE/ March 2023

Marking Guidelines rade 12
3.1 Calculate the values of x. (3)
3.2. If x =1, calculate the sum to infinity, 5, . (2)
[5]
QUESTION 4
(1—x) ; (« +2) and (2x —5) are the first three (3) terms of an arithmetic sequence.
4.1 Determine the value of x. (3)
4.2 If the first three (3) terms of this pattern are: 9 ; —6 ; —21; ..., calculate
the numerical value of the sum of the first 100 terms, Sio9 . (2)
4.3 Hence, or otherwise, calculate m if:
> (24 — 15n) = Sip + 73 320 (4)
n=0

[9]
QUESTION 5

2

The graph of f(x) = vp +q_ is sketched below:

A

|
ay
xv

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Bownleadedtfrom Stanmorephysics.com JW-GDE/ March 2023

Marking Guidelines rade 12
5.1 Write down the values of p and q (2)
5.2 The straight line g(x) = —x + k is one of the axes of symmetry of the graph
of f . Determine the value of k. (2)
5.3 If h(x) = —2[g(x)] , determine the equation of the inverse of A, h~?, in the
form h-4(x) =mxt+c. (3)
5.4 Draw aneat sketch of the graphs of h and h~1 on the same set of axes.

Clearly show all intercepts with axes, point of intersection and the axis of (4)
symmetry.
[11]

Copyright reserved Please turn over

### Page 14

Bownleadedtfrom Stanmorephysics.com JW-GDE/ March 2023
Marking Guidelines rade 12

QUESTION 6

The graphs of f(x) = ax? and g(x) = b* are sketched on the same set of axes. Points
A(—1;2) and B are points of intersection of f and g . The graph of f has the turning
point at the origin:

A(-1;2)

A

6.1 Calculate the values of a and b. (2)

6.2 The inverse of f is NOT a function. Write down at least one condition which
can be used to restrict the domain of f such that its inverse will bea function. (1)

6.3. For which value(s) of x , where x € (—00;0], will g(x) S f(x)? (2)
6.4 If h(x) = g(x + 3) , write down the coordinates of ...

6.4.1 A’ , the new coordinates of A on the graph of h. (1)

6.4.2 A" , the new coordinates of A onthe graph of h-?, the inverse of h (2)

. [3]

TOTAL = 50 MARKS

Copyright reserved Please turn over

### Page 15

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INFORMATION SHEET
_-b4Vb? -4a0
2a
A=P(l+ni) A=P(-ni) A=P(-i)" A=P(+i)”
T, =a+(n—Nd Ss, =F a+ (nnd)
T, =ar"" s, = sea!) gr#l S.=jSs-ler<l
r- -r

patsy -1) pa2t-a+)"]
i i

‘¢¢) = Jim LAtM-FO)

i rr

y27-Y

y=mxte Y-yY =m(x—-x,) n= m=tan@
ae |
(x-a) +(y-by =r?
fading
sinA sinB sinC
a? =b? +c? —2be.cosA
area AABC = Sab sinc
sin(a + £)=sina.cosf+cosa.sinB sin(a—B)=sina.cosB —cosa.sinB
coda + £)=cosa.cos#—sina.sin cos(a — 8) =cosa.cosf# +sina.sinB
cos’ a —sin’ a
cos2e@ =41-2sin’? a sin2a = 2sina.cosa
2cos? a -1
: S (x, x)?
__>s# - 2 %)
x= ——
n n
n(A) =
P(A) = (5) P(A or B) = P(A) + P(B) - P(A and B)
n
pratbx p= 2-2)

De-%

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