This Memorandum Consists of 12 Pages

Mathematics/P11DoE/Preparatory Examination 2008

NSC – Memorandum

MARKS: 150

TIME: 3 hours

This memorandum consists of 12 pages.

QUESTION 1

1.1 /
/ √ Standard form
√ Factors
√ Both solutions
(3)
1.2 / / √LCD: (x+1)
√Standard form
√Factors
√x = 0 and x = 3
Both values
(4)
1.3 / …….(1)
….(2)
From (1): (3)
Substitute (3) into (2)
/ √ substitution
√ standard form
√ simplification
√√ both x values
√√ both y values
(7)
1.4 /
or / √standard form
√factors
√√Solutions of x(1 mark each)
√correct inequality signs
OR must be stated
5
[19]

QUESTION 2

2.1 / /  formula
substitution
log
answer
4
2.2.1 / R650 000.00 /  Answer
1
2.2.2 /
/ √ formula
√ i
√ substitution
√ answer
(4)
2.2.3 /
/ √ formula
√ substitution
√ k = 50
√ answer
(4)

QUESTION 3

3.1 / 14 / √√ answer
2
3.2 / ThThe sum of 1's is given by

ThThe sum of the other numbers in the sequence is given by

=950
The required sum is 25 + 950 = 975 / √ sum of 1’s
√ formula
√ substitution
√ answer
(4)
QUESTION 4
4.1 / / √ √ 1 mark for each term
(2)
4.2 / Solution
1st differences: 5, 7, 9; 11, …
2nd differences: 2, 2, 2, …
Since the 2nd differences are constant

/ √ quadratic equation
√value of a
√ value of b
√ value of c
4
4.3 /

/ √ equation
√making the subject
√ two roots
√choosing the right answer
4
[10]

QUESTION 5

5.1.1 / Total amount = R511,50 / value of r
value of a
formula
substitute
answer
(5)
5.1.2 / Yes;
R511,50+R290=R801,50 he will have enough money to buy the boots. /  answer
reason CA
(2)
5.2.1 /
To converge:
/ √ value of r
√ statement
√√ both values and inequality signs correct
(4)
5.2.2 / /  formula
substitution
answer
(3)
[13]
QUESTION 6
6.1 / /  one value of a
1
6.2 / / y asymptote
x asymptote
2
6.3 /
asymptotes shape coordinate (3) [6]
QUESTION 7
7.1.1 / / x and y
Correct base
(2)
7.1.2 / Yes, only one corresponding y value for every x value / yes
reason
(2)
7.1.3 / / 

(2)
7.2 / / substitution of (1 ; 4)
value for a = 4
(2)
7.3 / / x –2
-1
(2)
7.4 / x-intercept
Is the y-intercept / √ Substitution
√ x-intercept
√ y-intercept
(3)
[13]]
8.1 / 2 / √answer
(1)
8.2 / or / √√ inequality
(2)
8.3 / / √√ answer
(2)

QUESTION 8

8.4 / / √√ Any two
(2)
[7]

QUESTION 9

9.1.1 / / √ Formula
√ Substitution
√ Simplification
√ Common factor
√ h = 0
(5)
9.1.2 /
h =3 – 1 = 2
Average gradient
/ formula
value of h
answer
(3)
9.2.1 /
/ expanding
 one per term
(4)
9.2.2 / / the two fractions
 1 per term
answer
(4)
[16]

QUESTION 10

10.1 / y intercept is (0;3)

So x intercepts are (1;0) and (-3;0) / y intercept
equation
each x intercept
(4)
10.2 /
Turning points: (1;0) and / derivative = zero
factors
both x values
each y value
(5)
10.3 /

shape
x intercepts
y intercept
Turning point
(4)
10.4 / / value of gradient
y value
equation
(3)
10.5 / Turning points: (2;0) and / 
One mark per coordinate
(2)
10.6 /

The concavity changes as x increases through
an inflection is at / √ = 0
√x value
√ statement
√conclusion
(4)
[22]

QUESTION 11

11.1 / Incorrect formula was given in Q paper
/ Incorrect formula was given in Q paper
RHS
simplification
(2)
11.2 /
Please consider the working with the incorrect formula /  derivative
 = 0
 answer
(3)
11.3 / /  Substitution
 answer
(2)

Mathematics/P11DoE/Preparatory Examination 2008

NSC – Memorandum

QUESTION 12

12.1 / <150
<120
>40
>10
200
/  constraint
 constraint
 constraint
 implicit constraint
(6)
Please consider alternatives for all questions.
12.2

√ feasible region
√√√√√ one mark per constraint CA
6
12.3 / (80 ;120)
80 Elegance and 120 Classic / √ search line
√ x value
√ y value
(3)
12.4 / P = 60x +100y / √ equation x and y
(1)
12.5 / P = 60(80)+100(120)
P = R16 800 / √substitute values from 11.3
√ R16 800
(2)
[18]