COMMON TEST JUNE GRADE 12 MEMO - 2018 · Mathematics !12 NSC Memo June Comm Test 2018 QUESTION 9...

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MATHEMATICS

COMMON TEST

JUNE 2018

MEMORANDUM

NATIONAL SENIOR CERTIFICATE

GRADE 12

Mathematics ! NSC Memo June Comm Test 20182MARKS: 125

TIME: 2.5 hours

This memorandum consists of 11 pages.

Copyright reserved Please Turn Over

Mathematics ! NSC Memo June Comm Test 20183QUESTION 1

1.1.1 A✓ 0 A✓ 6 (2)

1.1.2A✓formula

CA✓substitution

CACA✓✓answers

[Penalise for rounding off here only in the entire paper]

(4)

1.1.3A✓Isolating surd term

CA✓ squaring both sides

CA✓standard form

CA✓factors

CA✓answers and rejecting

(5)

1.2A✓y / x the subject

CA✓substitution

CA✓standard form

CA✓factors

CA✓ x – values

CA✓ y – values

(6)

……(1) and ! ….(2)

01 =+− xy 32 =+ xyx

( )( )

221

123

013203233)1(

)2(into)3(ngSubstituti)3......(1:)1(From

2

22

2

−==

−==

=+−

=−−

=−+

=−+

−=

yory

xorx

xxxxxxx

xxx

xy

58,858,0)1(2

)5)(1(4)8()8(2

4

058

2

2

2

−=

−−±−=

−±−=

=−+

or

aacbbx

xx

( )( )

an

xorx

xxxx

xxxxx

xx

/491

0941095410144

1012

1102

2

2

=−=

=−+

=−−

+=+−

+=−

=+−

60 or


Mathematics ! NSC Memo June Comm Test 20184

QUESTION 2

1.4A✓factorization

A✓reasoning

A✓ conclusion (3)

[20]

The graph y = ! has its x – intercept at x = 0 and the graph y = – 33x2 has its maximum value at x = 0. Therefore the equation has only one solution

( )( )

2

2

2

3

3313033130

033130333.

xxorx

xxxxx

x

x

x

x

−=−

=+−=

=+−

=+−

13 −x

2.1 x 4 8

y

T1 T2 T3

T4

1D 4-x 4

y-8

2D x y-12

x = 4 and y = 16

A✓ x – value

A✓ y – value (2)

2.2 CA✓ a value

CA✓b value

CA✓ c value

CA✓answer

(4) 862

84

603242

2 +−=

=

=++

−==+

==

nnTc

cbabba

aa

n


Mathematics ! NSC Memo June Comm Test 201852.3

A✓quadratic

CA✓factors

CA✓ answer (3)

[9]

( )( )79820798206478301295662

12964862

2

2

2

≠=∴

=+−

=−−

=−−

=+−=

nornnn

nnnn

nnTn



3.1

(5)

3.2 A✓correct formula

A✓substitution

CA✓ answer(3)

3.3 A✓condition

A✓substitution of r value

CA✓answer(3)

[11]

1228512)12(3

1)1(

12

12

=−

−=

−

−=

S

rraSn

n

A✓ !

CA✓a – d = 0

A✓

CA✓ a + d = 4

CA✓a – value

)3(27 dada +=+

122 =++++ dadaa

28353

1351

11

−<<−

<+<−

<+

<−

<<−

xx

xr

242:)2()1()2(4

1233122

)1(0627)3(27

.......;)2(;)(;

=⇒=+

→=+

=+

=++++

→=−

+=+

+=+

++

aadada

dadaada

dadadadadadaa



QUESTION 4

4.1(2)

4.2 A✓ y – intercept value

A✓ x – intercept value

(2)

4.3

A✓ shape

CA✓ x – intercept

CA✓ y – intercept

CA✓ asymptotes(4)

[8]

A✓ !

A✓

1−=x

3−=y

31 −=−= yandx

35:intercept

5:intercept

−=−

−=−

xx

yy



5.1 A✓ axis if symmetry value

CA✓y – value

CA✓answer [coordinate form](3)

5.2CACA✓✓answer (2)

5.3A✓equation equal to 0

CA✓factors

CA✓x – values

CA✓answer(4)

5.4 A✓equating

CA✓standard form

CA✓factors

CA✓x – values

CA✓answer

(5)

5.5 A✓substituting (x – 3 )

CA✓ x – value

CA✓y – value (3)

[17]

( )( )

⎟⎠

⎞⎜⎝

⎛ −

=−=

=−+

=−−

+−=++−

+−=++−

814;

43P

243

02340654

631224

32362

2

2

2

xorx

xxxx

xxx

xxx

816≤y

New turning point

( )24132

69623)3()3(2)(

2

2

2

−+−=

−++−−=

−−+−−=

xxxxx

xxxh

⎟⎠

⎞⎜⎝

⎛816;

413A

( )( )

units213BC

223

0232062062

2

2

=

=−=

=−+

=−−

=++−

xorx

xxxxxx

⎟⎠

⎞⎜⎝

⎛

=+⎟⎠

⎞⎜⎝

⎛+⎟⎠

⎞⎜⎝

⎛−=

816;

41A

8166

41

412

2

y



6.1A✓ substitution of the point A

CA✓ answer (2)

6.2 CACA✓✓ answer (2)

6.3 AA✓ ✓answer or any other point

that satisfies the equation. (2)

6.4

A✓ x – value

CA✓ answer(2)

6.5

CACA✓✓ answer (2)

[10]

910

913

2log2)(

2

3

1

≤<

==

−=

−≤

−

−

x

x

xxh

xy 3log=

⎟⎠

⎞⎜⎝

⎛=

⎟⎠

⎞⎜⎝

⎛= −

2log

2)(

3

1

x

xhxf

⎟⎠

⎞⎜⎝

⎛− 2;

91

3391)(

22

2

=

=

=

=

−−

−

aa

a

axh x



7.1 A✓formula

A✓substitution into formula

CA✓answer(3)

7.2.1A✓substitution into formula

CA✓value

CA✓answer (3)

7.2.2 A✓formula

A✓ substitution of F

A✓substitution of i

A✓substitution of n

CA✓answer

(5)

7.2.3 A✓formula

A✓substitution of F and i values

A✓substitution of n value

CA✓ R630,79

(4)

[15]

New monthly deposit = R 13337,73

79,6301212,0

11212,01

8000

]1)1[(

12

R

x

iixFn

v

=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠

⎞⎜⎝

⎛+

=

−+=

He will pay R1337771,79 – R300 000

=R1037771,79

( )79,77711330825,01000900

)1(5

R

iPA n

=

+=

+=

94,127061212,0

11212,01

79,1037771

]1)1[(

60

R

x

iixFn

v

=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠

⎞⎜⎝

⎛+

=

−+=

42,452253)0925,01(000500

)1(7

R

iPA n

=

−=

−=


Mathematics ! NSC Memo June Comm Test 201811QUESTION 8 [Penalise once only in questions 8 and 9 for notational error]

8.1 A✓formula

A✓substitution

CA✓ simplification of numerator

CA✓factors

CA✓answer

(5)

8.2.1

(4)

8.2.2

(4)

[13]

2/

1

2

41)(4

4)(

−

−

+=

−=

−=

xxfxx

xxxf

A✓ A ✓

CA✓answer CA✓answer

34

x2

91 −x

331

/

234

23 4

92

34)(

91

)3()(

−

−

−

−=

+=

+=

xxxg

xx

xxxg

( ) ( )

( )

56

536

536

5355363

)53()(5)(3

)(

lim

lim

lim

lim

lim

0

2

0

222

0

22

0

0

−=

−+=

−+=

+−−−++=

−−+−+=

−+=ʹ

→

→

→

→

→

xhhxhh

hhxhh

xxhxhxhxh

xxhxhxh

xfhxfxf

h

h

h

h

h

A✓x A✓

CA✓answer CA✓answer

14 −− x



9.1 AA✓✓x – intercepts / point form

A✓y – intercept /point form (3)

9.2

A✓derivative and equal to 0

CA✓standard form

CA✓factors

CA✓x – values

CA✓y – values (5)

9.3

A✓shape

CA✓ x – intercepts

CA✓ y – intercept

CA✓ turning points

(4)

9.4CA✓second derivative

CA✓answer (2)

( )( )

)0;3()32;1(03231

031032

0963)(2793)(

2

2/

23

−−

=−=

=−=

=−+

=−−

=++−=

−++−=

yoryxorx

xxxx

xxxfxxxxf

11

066)(963)(

//

2/

>

=

=+−=

++−=

xx

xxfxxxf

2733

−=

=−=

yxorx



Total Marks : 125

9.5A✓substituting x = 0 into derivative

CA✓gradient value

CA✓equation (3)

9.6(3)

9.7(2)

[22]

032 <<− k

A✓

CA✓substitution of ! into f

)3( +xf

)3( +x 27)3(9)3(3)3()3()(

23 −+++++−=

+=

xxxxfxt

2799)0(

963)(/

2/

−=

=

++−=

xyf

xxxf

CA✓ 32

CA✓0

A✓inequality

−


COMMON TEST JUNE GRADE 12 MEMO - 2018 · Mathematics !12 NSC Memo June Comm Test 2018 QUESTION 9...

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