Mathematics 1 Practice Test/ feb-mar 2025

NSC-KZN

Basic Education
KwaZulu-Natal Department of Basic Education
REPUBLIC OF SOUTH AFRICA

MATHEMATICS

PRACTICE TEST

FEBRUARY/MARCH 2025

NATIONAL
SENIOR CERTIFICATE

GRADE 12

Marks: 100

Time: 2 hours

N.B: This question paper consists of 10 pages and 1 information sheet

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Mathematics 2 Practice Test/ feb-mar 2025
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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, et cetera that you have used in
determining your answers.

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

5. An approved scientific calculator (non-programmable and non-graphical) may be

used, unless stated otherwise.

6. If necessary, answers should be rounded off to TWO decimal places, unless stated
otherwise.

7. Diagrams are NOT necessarily drawn to scale.

8. Number the answers correctly according to the numbering system used in this
question paper. Write neatly and legibly.

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Mathematics 3 Practice Test/ feb-mar 2025
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QUESTION 1

5 ; 12 ; 21; 32;... is a Quadratic Sequence.

1.1 Write down the next term of the sequence. (1)

1.2 Determine the n th term of the sequence. (4)

1.3 Which term of the above sequence is 1152? (4)

1.4 Prove that none of the terms in sequence are perfect square (3)
[12]

QUESTION 2

2 ; 5 ; 8; 11;... is an Arithmetic Sequence.

2.1 Determine the first term that will be greater than 2012 (2)

2.2 Calculate the sum of the first 671 terms of the series (3)

2.3 n
If the Sum formula of the sequence: 2 ; 5 ; 8; 11;... is S n   3n  1 : (4)
2
th
Determine the 12 term, by using the Sum formula.

[9]

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Mathematics 4 Practice Test/ feb-mar 2025
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QUESTION 3

a 1  r n 
3.1 Prove that the sum to n terms of a Geometric series is given by S n  (4)
1 r

3.2 3 (6)
The first term of a geometric series is 12, the last term is and the sum of
256
6141
the series is .Determine the common ratio and the number of term of the series.
256
[10]

QUESTION 4

 
4.1
16 53
p
Find the value of . (4)
p 1

4.2 For what values of x will the series 2(1  x)  4(1  x) 2  8(1  x)3  ... be (3)
convergent?
[7]

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Mathematics 5 Practice Test/ feb-mar 2025
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QUESTION 5

1 1
The graphs below are f ( x)  x 2 and g ( x)    3. A  a; b  and B  c; d  are points
3 x 1
of intersection f and g.

5.1 Write down the equations of the asymptotes of g. (2)

5.2 If y  x  c is a line of symmetry to the graph of g , calculate the value(s) of c. (2)

5.3 Write down the range of f . (1)

5.4 Write down the x  value(s) for which f ( x)  g ( x) , x  1 . (4)

5.5 Determine the value(s) x if f ( x)  g ( x) , for the interval x  1. (2)

5.6 If h( x)   f  x  2   1, then write down the new equation of h in the form of (2)

h( x)  a  x  p   q.
2

5.7
Use your graph to determine the maximum value of 3h(x)  3 (2)

5.8 1 (2)
 x  5   k has one root equal to 0.
2
Determine the value(s) of k for which
3
[19]

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Mathematics 6 Practice Test/ feb-mar 2025
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QUESTION 6

6.1 Sketch the graph of f ( x)  3 x on the set of axes in your answer book (2)

6.2 Write down the equation of the INVERSE of f ( x)  3 x in form of y  ..... (2)

6.3 Sketch f 1 on the same set of axes indicating the intercepts with the axes and (3)
the line of symmetry with the graph of f .

1
6.4 Write down the equation of g ( x)  f ( x) . (2)

1
6.5 Determine the value(s) x for which f ( x)  1 (4)

[13]

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Mathematics 7 Practice Test/ feb-mar 2025
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QUESTION 7

7.1 If 4tan a  3  0 and 900    3600 ,determine without the use of a calculator the (5)
value of cos 2   sin  .

7.2 Simplify without using a calculator:

sin 610.cos  900  2  (4)

7.2.1
cos 290.sin  900   

7.2.2 cos150.sin150 (3)

7.3 Prove the following identity:

sin a  cos b sin a  cos b 2 (6)

 
sin a  cos b sin a  cos b cos 2a

7.4 Determine the general solution of cos 2x  cos x  2  0 (5)

[18]

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Mathematics 8 Practice Test/ feb-mar 2025
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QUESTION 8

The sketch below, shows the graphs of:

 f ( x)  sin p.x
 g ( x)  cos  x  q  ;

 1
A  450 ;1 and B 1650 ;   are two points of intersection of f and g ,where x  1800 ;1800  .
 2

8.1 Determine the value(s) of p and q. (4)

8.2 Determine the period of g. (1)

8.3 Write the coordinates of C, the turning point of the curve g. (1)

8.4 Write the coordinates of D, a point of the intersection of f and g. (1)

[8]

[100]

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Mathematics 9 Practice Test/ feb-mar 2025
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INFORMATION SHEET: MATHEMATICS

 b  b 2  4ac
x
2a
A  P(1  ni) A  P(1  ni) A  P(1  i ) n A  P(1  i ) n

Tn  a  (n  1)d Sn 
n
2a  (n  1)d 
2

Tn  ar n1 a r n  1 ; r 1 S 
a
; 1  r  1
Sn 
r 1 1 r

F

x 1  i   1
n
 P
x[1  (1  i)n ]
i i
f ( x  h)  f ( x )
f ' ( x)  lim
h 0 h
 x  x 2 y1  y 2 
d  ( x 2  x1 ) 2  ( y 2  y1 ) 2 M  1 ; 
 2 2 
y 2  y1
y  mx  c y  y1  m( x  x1 ) m m  tan 
x 2  x1

x  a2   y  b2  r 2
a b c 1
In ABC:   a 2  b 2  c 2  2bc. cos A area ABC  ab. sin C
sin A sin B sin C 2
sin     sin . cos   cos .sin  sin     sin . cos   cos .sin 
cos     cos . cos   sin . sin  cos     cos . cos   sin . sin 

cos2   sin 2 

cos 2  1  2 sin 2  sin 2  2 sin. cos
2 cos2   1

n 2

x  x  x i
x   2 i 1
n n
n( A )
P( A)  P(A or B) = P(A) + P(B) - P(A and B)
nS

yˆ  a  bx b
 x  x ( y  y )
 (x  x) 2

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Mathematics 10 Practice Test/ feb-mar 2025
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NAME:

SCHOOL:

DIAGRAM SHEET

QUESTION 6.1 and 6.3

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