# Mathematics Grade 12 GP March 2022 Paper & Memo

> Grade 12 Mathematics question paper and memo from the GP March 2022, 27 pages. Read online or get the free PDF download.

- Page: https://www.hlayiso.com/library/jnorth-maths-gr12-march-2022-qp-and-memo/a4fe76a7-1158-4c29-aa2a-a2656e5a966d
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper and memo
- Year: 2022
- Exam period: GP March
- Curriculum: CAPS
- Pages: 27

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## About this document

Mathematics · Grade 12 · GP March · 2022. Question paper and memorandum, 27 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

JN/2022

GAUTENG DEPARTMENT OF EDUCATION

                                                       � ,
                                                        ♦

     JOHANNESBURG NORT... .-.__....,TRICT

                             202
                        G
                   co                   EST

                              EMATICS
                             ERM1

: 2 hours

            This questions paper consist of 14 pages

                              Page 1                           P.T.O

### Page 2

Mathe                                                                                            JN/2022

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.
1. This question paper consists of 8 questions.

2. Answer ALL the questions.

3. Clearly show ALL calculations, diagrams, graphs, etc. which was used in detennining the answers.

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

5. You may use an approved scientific calculator (non-programmable and non-graphi�nless stated
   otherwise.

6. Where necessary, answers should be rounded off to TWO decimal pla�less stated otherwise.

7. Diagrams are NOT necessarily drawn to scale.

8. Tear off page 11 till page 14. AND SUBMIT theses              \th your answer scripts.
                                                            �

9. An information sheet is on page IO of the questi&r.

10. Number the questions correctly according       e'i?umbering used in the question paper.
                                               �
                                            0
11. Write neatly and legibly.

                                                   Page 2                                             P.T.O

### Page 3

JN/2022

QUESTION 1

1.1   Solve for x:

      1.1.1   x2 - 7X + 10 = 0                                             (2)

      1.1.2   3x2 + 2x + 6 = 10 (correct to two decimal places)            (4)

               I      I
      1.1.3 x2 + 3x4-28 = 0                                                (4)

      1.1.4 �=x-2                                                          (5)

1.2   Given: 3x2 + kx -3x-k = 0.
                                                                       ♦
      For which values of k will the equation have real roots?             (4)

1.3   Solve for x and y:

      3y + x = 5 and x 2 + y 2 = 100 + Sy                                  (6)

                                                                           [2 5]

QUESTION 2

2.1   Consider the seque 'c)��; 11; 22; 37; ....
                        �
      2.1.1   Calcul�� n th term.                                          (4)

      2.1.2   W�erm in the sequence has a value of 407?                    (4)

2.2   How many terms are there in the following arithmetic sequence.

      40; 46; 52; 58; ...... 202                                           (3)

                                                                           [11]

                                                Page 3                             P.T.O

### Page 4

Mathe                                                                                        JN/2022

QUESTION 3

3.1     The 4th term ofan arithmetic sequence is -3 and the 20th term is -35.

        Determine the common difference and the first term.                            (5)

                         20
                              3k-2
                        L
3.2     Evaluate:                                                                      (4)
                        k=l

3.3     The following sequence forms a convergent geometric sequence:

           3          1    1 (x - 1)
                  +--- +- +--- + ...
        (x - 1 )2  (x - l) 3    9

        3.3.1 Determine the possible values of x.                                      (3)

        3.3.2 If x = 2, calculate S00 •                                                (2)

                                                                                       [14)

QUESTION 4

4.1     Given sin24° = m and cos35 ° = n. Determine the following in terms ofm or n.

        4.1.1 tan66 °                                                                  (3)

        4.1.2 sin70°                                                                   (3)

                                                       cos2x
4.2     Prove that:     sin(45 ° + x). sin(45 ° - x) = --                              (5)
                                                         2

4.3     Given cos(x + 42° ) = sin2x. Solve for x if x E [-180°,180° ].                 (6)

                                                                                       [17]

                                                    Page 4                                     P.T.O

### Page 5

JN/2022

QUESTION 5

A mountain climber wants to determine the height PQ of a mountain. The climber is standing atRon a
flat ground.Rand Sare in the same horizontal plane as the foot of the mountain Q.

FromR, he measures the following angles:

  •    The angle of elevation of the top of the mountain P is w•.

  •    PRSisx'

He then walks z metres to point Sand measures R SP which is y·

                        s
                         zsiny. sinw
5.1    Show that PQ = ---­                                                                  (4)
                      sin(x + y)

5.2    Determine PQ, if z = IO00m, w = 90° - x and x = y                                    (4)

                                                                                             [8]

                                                   Page 5                                            P.T.O

### Page 6

Mathentaawmdanadad from Stanmorephysics.com JN/2022
Give reasons for your statements in Question 6, 7 and 8.

Use the Annexure A provided to answer Question 6, 7 and 8

QUESTION 6

Given /A\ ABC with DE || BC as shown in the figure below:

A

AD AE

Prove that: —— = [5]
DB EC

Page 6 P.T.O

### Page 7

Mathenlaamudanaded From Stanmorephysics.com

QUESTION 7

In the diagram below, AC and CE are tangents to the circle with centre O.

B, D, G and H are points on the circumference of the circle.

HG is produced to F. BD = BH D, = Dy = x.

71

7.2

7.3

Find four other angles equal to x.
Hence or otherwise prove that BD || HG.

Show that G, = 180° — 2x.

Page 7

(4)
(2)
(2)

[8]

JN/2022

P.T.O

### Page 8

Mathenaawmnadad From Stanmorephysics.com JN/2022

QUESTION 8

8.1 In the diagram below, AB lies on circle with centre O, and is produced to C which lies on circle

with centre P. Similarly, FE is produced to D.. BE || CD.

Prove that ACDF is a cyclic quadrilateral. (4)

Page 8 P.T.O

### Page 9

Mathenaawmnadad From Stanmorephysics.com JN/2022

8.2 In the diagram below, AB is the diameter of circle with centre P, EP L AB.

8.2.1 Prove that /\ BPE/// \ BDA (4)
PE?.BA.BD
8.2.2 Hence, prove that BE = ———————. (4)
BP
[12]
TOTAL 100

Page 9 P.T.O

### Page 10

Mathenlaamudanaded From Stanmorephysics.com JN/2022
INFORMATION SHEET: MATHEMATICS

—b + Vb? — 4ac
x = ——__—_
2a
A= P(1+ni) A= P(1—ni) A=P(1-i)" A=P(i+i)"
n n
+1 n
Yiten yiatety T, =at(n—Dd Sy =5 (2a + (n— 1d)
i=1 i=1
a(r” — 1) Seo
Ty = ar™-1 rn :r#l __4 ; -l<r<l
1-r
14+i"-1 1-(1+i)™
p awl +9 ] pail a+) ]
i i
vox FH) = fF)
F') = mS
= — x,)? —y,)? XatXe , Vato
d= VG2- 1)? + 02-1) m2; 222)
y27—V1
y=mxt+c y-Y. = m(x — x,) m= ——— m = tan@
Xy—Xy

(xa)? + (y—b)? = 1?

In AABC:
a b c

1
= = 2 = b? +c*—2bc.cosA ==ab.si
snd sin ainG a c ic .COS areaAABC 3 ab.sinC

sin(a + B) =sina.cosB +cosa.sinp sin(a — B) = sina.cos B —cosa.sinB
cos(a + 8) = cosa.cos 8 — sina.sinB cos(a — 8) = cosa.cosfB + sina.sinB
cos* a — sin? a
cos 2a = 41-—2sin?a@ sin2a = 2sina.cosa
2cos?a—-1

(x;y) > (xcos 6 — ysin@; ycos@ + xsin@)

paix ot = D4 - 9?
n i=1
n
(A) = n(A) P(A or B) = P(A) + P(B) — P(A and B)
n(S)
a _Y@-HDO-y)
J=atbx b= Ta-p

Page 10 P.T.O

### Page 11

Mathenlaamudanaded From Stanmorephysics.com JN/2022

Name: Class:

ANNEXTURE A

QUESTION 6

A

(5)

Page 11 P.T.O

### Page 12

Mathenlaamudanaded From Stanmorephysics.com JN/2022
QUESTION 7
71 (4)
72 (2)
73 (2)
Page 12 P.T.O

### Page 13

Mathentaamudnated From Stanmorephysics.com

JN/2022

QUESTION 8

8.1

(4)

Page 13

P.T.O

### Page 14

Mathenlaamudnated From Stanmorephysics.com JN/2022
8.2
A
8.2.1 (4)
8.2.2 (4)
Page 14 P.T.O

### Page 15

Downloaded f rom St anmorephysics. com

        GAUTENG DEPARTMENT OF EDUCATION

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                                                  m
                                            si c
                           st
             JOHANNESBURG NORTH DISTRICT
                              an
                                mor
                          2022
                        GRADE 12    ep
                      CONTROL TEST    hy
                        om
                     fr
                oa      MATHEMATICS
                  de       TERM1
                    d
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           MARKING GUIDELINES
MARKS   : 100
TIME    : 2 hours

                             Page 1

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