# Mathematics Grade 10 KwaZulu Natal June 2017 Memo

> Grade 10 Mathematics memorandum from the KwaZulu Natal June 2017, 18 pages. Read online or get the free PDF download, question paper linked when available.

- Page: https://www.hlayiso.com/library/maths-2017-june-qp-memo/9870ea69-cc9c-4703-af3f-2068ef62f444
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 10
- Document type: Memorandum
- Year: 2017
- Exam period: KwaZulu Natal June
- Curriculum: CAPS
- Pages: 18

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## About this document

Mathematics · Grade 10 · KwaZulu Natal June · 2017. Memorandum, 18 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

KwaZulu-Natal Department of Education
REPUBLIC OF SOUTH AFRICA

Gen RGR R RR SRR RT Re

* MATHEMATICS =
nm COMMONTEST = 8

NATIONAL
SENIOR CERTIFICATE

MARKS: 100

TIME: 2 hours

This question paper consists of 10 pages and 2 DIAGRAM SHEETS.

### Page 2

Mathematics

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June 2017 Common Test
NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions:

L.

2.

10.

This question paper consists of 8 questions. -
Answer ALL the questions.

Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in
determining the 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,
TWO diagram sheets for answering QUESTION 7.1, QUESTION 7.2,

QUESTION 7.3, QUESTION 8.1 and QUESTION 8.2 are attached at the end of this
question paper. Write your name on these sheets in the spaces provided and insert the
sheets inside the back cover of your ANSWER BOOK.

Diagrams are NOT necessarily drawn to scale.

Number the answers correctly according to the numbering system used in this
question paper.

Write neatly and legibly.

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Mathematics 3 June 2017 Common Test
NSC
QUESTION 1
1.1 Factorise the following expressions fully:
y LLL 7414 ve (1)
1.1.2 2x? +2ax—3bx-3ab (3)
1.2 Determine the product of the following expression:
~2(x+D00? ~x +1) (3)
1.3 Calculate the value of the following expression without using a calculator:
(0,072)? ~ (0,028)? Lo (2)
14 — Simplify the following expression fully:
5x? + 14x —3 ;
x? -9 (3)
15 Evaluate the following expression:
get gx?
Gagat . Write your answer as a fraction in its simplest form, 6)
verre (17).

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Mathematics

QUESTION 2

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2.1 Solveform: 4% =1

2.2 Given: a+ Ss

5x

2.2.1 Solve for x.

2.2.2 Write the answer to QUESTION 2.2.1 in interval notation.

2.3 Solve simultaneously for x and y:

x-2y=3

37 where xeR

and = 4x+3y+10=0

(2)

(3)
68)

6)

24  Arectangular garden is made up of a square lawn of side x m and two paths 1,5 m

wide, as shown in the diagram below. The total area of the garden is 88 m_.
Write down an equation in terms of x and solve the equation to find the

dimensions of the lawn.

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1,5 m

i
I
I
a
[

I
I
I
[
I
I

+

I

15m

CT

[I

TT NOT
J TO
SCALE
T
I

(5)
[16]

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Mathematics 5 June 2017 Common Test
NSC

QUESTION 3

3.1 The nth term ofa pattern is given as T, =12n—~7.

3.1.1 Write down the first three terms of this pattern. (2)

3.1.2 Is 356 a term in this pattern? Explain your answer. Q)

3.2 Consider the following sequence of Es:

3.2.1 How many blocks are needed to make the next E? qd)

3.2.2 Write down the general term, T,,, for the number of blocks used in each E. (2)

3.2.3 Calculate how many blocks will be needed to make the 100" E, (2)
3.2.4 Calculate which E can be made from 116 blocks. (3)
[12]
QUESTION 4

The following functions are given: f(x) =x~-2 and g(x)= 4 ~2
x

Sketch the graphs of f and g on the same set of axes, clearly showing all intercepts
with the axes and asymptotes where applicable, [6]

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Mathematics June 2017 Common Test

NSC

QUESTION 5

Sketched below are the graphs of f(x)=-4x° +9 and g(x)=2x+3.

The graph of f intersects the x-axis at A and B. The graph of g intersects f at A and D
and the y-axis at C, DE // y-axis.

ty
g
Cc
A x
A N EB >
5.1 Write down the coordinates of C. qd)
5.2 Calculate the length of AB. Q)
5.3 Calculate the length of DE if AE =2 ; units. (2)
5.4 For which values of x will s(x) > g(x)? (2)
5.5 Calculate the length of AD. (2)
[10]

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Mathematics
NSC

QUESTION 6

Sketched below are the graphs of g and hf. g(x) =b* +c and A(x) = k :
x

A, the point of intersection of g and A, is (1; 1).

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Use the graphs and the information above to answer the following :
6.1 Write down the values of k, ¢ and d.

6.2 Write down the equation of the asymptote of g.

6.3. Write down the domain of h.

6.4 Determine the equation of f if f is the reflection of g in the y-axis,

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June 2017 Common Test

(4)
G)
(2)

(2)
19]

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Mathematics
NSC

QUESTION 7

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June 2017 Common Test

In this question, you must give a reason to justify each of your statements.

71. Inthe diagram below, the diagonals of parallelogram ABCD intersect in M.

AB = 13cm, ABC=76° and COM=28°.

13cm

28°
D Cc

7.1.1 Write down, giving a reason, the length of DC.

7.1.2 Calculate, giving reasons, the size of ADM

7.2 %n the diagram below, PR is a diagonal of square PORS. Point E lies on SR
and QE is drawn, PR and QE intersect at T. SET =120°.

P Q

1209
E

7.2.1 Giveareason why SPR = 45°,

7.2.2 Calculate, giving reasons, the size of PTE

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76°,

(2)
Q)

13)

Q)

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”

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Mathematics June 2017 Common Test

NSC

7.3 Inthe diagram below, ABCD is a kite having diagonals AC and BD intersecting at
O. AO = 8cm, BO = 2x cm and DO = 5x

A
8
Sx 2x
D B
ie)
Cc
cm,
7.3.1 Write down, giving a reason, the length of OC. (2)
7.3.2. Write down the area of ABCD in terms of x. (2)
7.3.3. Ifthe area of ABCD is 168cm’, calculate the value of x (2) -
73.4 Calculate, giving a reason, the length of AB. (3)
[16]
QUESTION 8
In this question, you must give a reason to justify each of your statements.
8.1 In the diagram below, ABCD is a quadrilateral having AB = DC and AB || DC.
A +4 B
D 1
2
mn 1
D or Cc
Use the diagram on the DIAGRAM SHEET to prove that ABCD is a parallelogram. (5)

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Mathematics June 2017 Common Test

NSC

8.2 In APQR, A is the midpoint of QR and B is the midpoint of PA. C and D are
points on PR such that QBC || AD. G is a point on QB such that GB = BC.

A
8.2.1 Give a reason why PGAC is a parallelogram. qd)
8.2.2 Prove that PC = CD = DR. (4)
8.2.3 Prove that GCDA is a parallelogram (4)

[4]

TOTAL MARKS: 100

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Mathematics June 2017 Common Test
NSC
| NAME:
! DIAGRAM SHEET 1
! QUESTION 7.1
A 13cm B
M
28°
: D i C
%| QUESTION 7.2
Bip —Q
5!
RY
é |
2!
E ' T
Be ' o
s 120' R
: E
! QUESTION 7.3
A
5x 2x
D r) B
C

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Mathematics June 2017 Common Test
NSC
: NAME:
| DIAGRAM SHEET 2
| QUESTION 8.1
A ~ B

No

QUESTION 8.2

PLEASE TEAR ON DOTTED LINES

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### Page 13

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Mathematics 3 June 2017 Common Test
GRADE 10
Marking Guideline
QUESTION 2
Zl 4 =]
4 =4 v1=4
x=0 ¥ answer
2
2.2.4 2415 sto
4 3
3x+180 <20x—24 vmultiplying by 12
-17x S-204 Y simplification
x212 v answer
@)
OR
x Sx
4° 15< 3 2
3% 445< 202 5 mom
RB 12” ¥ common denominator
Vix forx
aps Y simplification
x212 ¥ answer
@)
222 | xe [12;<) @
23 x—2y=
x=2yt3 VY x=2y43
A(2y +3) +3y +10 =0 Y substitution
8y+1243y+10=0 ~ multiplying out
lly =-22
yo v y—value
x= 2(-2)+3
ze] ¥ x~value
(5)
24 Area of rectangle = [xb
88 = x(x +3) Y x(x+3) ¥ equating to 88
x? +3x-88=0 Y standard form
(~-8)(x411) =0 Y factors
x=8vx#-11
- The lawn is 8 m by 8 m Y answer 6
[16]
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Mathematics 4 June 2017 Common Test
GRADE 10
Marking Guideline
QUESTION 3
3.11 ‘The sequence is: 5 ; 17; 29; ... v5 ¥17 and 29
(2)
3.12  )No v answer
12n-7=356
363 is not exactly divisible by 12 ¥ reason
OR
12 is not a multiple of 363 Q)
3.21 17 blocks au
ie)
322 | TL =3n+5 ¥3n
+5
(2)
3.23 | No. of blocks required to make the 100°E: 3(100)+3 j ¥ substitution
=305 Y answer
(2)
N.B. Answer only: full
marks.
3.24 3n+5=116 ¥ 3n+5=116
3n=111 Y simplification
n=37
The 37" E can be made from 116 blocks Y answer
G)
{12}
QUESTION 4

f)=x-2 and g(a)= 4-2

v x-intercepts of f (2; 0)

y-intercept of f: (0 ;-2)

v x-intercept of g: (2 : 0)
Y asymptote of g: y=~2
¥ another point ong eg.

(132), 43-0,
(2; 4), (1; 6), etc.

Please turn over

2;4)
Y shape of g ie.
hyperbola predominately
in quadrants 1 and 3.
[6t
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### Page 15

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### Page 16

Mathematics. 7 June 2017 Common Test
GRADE 10
72
P iQ
T
120)
(eo) 5 R
O E
© (721 _ J The diagonals of a square bisects the vertex angles. Y reason
12) @)
—~ 722 ) pfE+45°+90° +120°=360° (gum of angles in quad) vSIR
PTE =360°—255°
io} =i0s° Y answer,
= fp "
7.
A
fo} 8
; a bx on
Qu D ray B
TW
AY) Q
S °
© [734 [0C=8em (diagonals of @ kite) YSYR
t (2)
= 732 |p ceaof ite = (ACNBD)
1 g 120° 1
==(16)(7: R 1
B FOOT) E ¥ 50072)
= Y answer
= 56x
2)
733 | 36x=168 VS
x=3 Y answer
2)
734 [OB=6em VS
AOB =90° (diagonals of a kite) vse
AB’ =67 +8 ‘Theorem of Pytha;
=100 ‘ of Fythagorss) Y answer with
AB=10 reason.
(3)
[16]
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«

Mathematics 8 June 2017 Common Test
GRADE 10
Marking Guideline

QUESTION 8

8.1

A B
:
(NI
Y 2
D t 4

Constr: Draw diagonal AC

Proof: In AABC and ACDA
@ = ACis common

@  aB=DC (given)
Gi) AC, (alt angles AB {[ DC)
AABC=ACDA (8323S)
oA, =O,
‘These are alternate angles
<-AD || BC

:. ABCD isa parallelogram (both pairs of opp sides are
parallel)

Y constr

Y AABC=ACDA
(S;2;8)
YA, =¢,
“AD || BC

YR

G)

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### Page 17

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### Page 18

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