This Memorandum Consists of 16 Pages

Mathematics/P1 1 NW/September 2014

NSC– Memorandum

MARKS: 150

This memorandum consists of 16 pages.

NOTE:

If a candidate answered a question TWICE, mark the FIRST attempt ONLY.
If a candidate crossed out an attempt of a question and did not redo the question, mark the crossed out question.
Consistent accuracy (CA) applies in ALL aspects of the memorandum.

QUESTION 1
1.1
1.1.1 /

or
/ Factors


(3)
1.1.2 /

=
=
or / Standard form
Substitution into formula
Simplify
Each value of x
 (5)
1.1.3 /
Critical values: or

OR

Critical values: or

OR

Critical values: or

/ Critical values



Critical values



Critical values



1.2
1.2.1 /

/ Exponential law
Equate exponents
(2)
1.2.2 /
Substitute

or
or
or / Substitute
Standard form
Factors
Both values of a
Both values of b
(5)
1.3 /

= OR

/ Simplify
Answer
(2)
(If , penalise 1 mark)
1.4 /

OR

/ Squaring
Expand
Simplify
Expand
Bracket squared
Simplify
(3)
[23]
QUESTION 2
2.1 /

S18

/ Expansion
Substitute a and d into correct formula

Answer (4)
2.2
2.2.1 /
On 2nd day: T2 =
OR
Day 2: T2 /  of 216
Answer
(2)

Answer (2)
2.2.2 /
On the 7th day: Tn
T7

/ a
r
Answer(2 dec.)
(3)
2.3
2.3.1 /
Converge if

/ 

Answer
(3)
2.3.2 /

= 2 / Value of a
Value of r
Substitution into correct formula
Answer
(4)
2.4 / 2 ; x ; 12 ; y

2nd difference = 6

Substitute into

/ 2nd difference
Equation in terms of x

Substitute into 2nd equation

(5)
[21]
QUESTION 3
3.1 /
Vertical asymptote:
Horizontal asymptote:
y-intercept:
x-intercept:

/ Both asymptotes
Shape


(4)
3.2 / , / 


(3)
[7]
QUESTION 4
4.1
4.1.1 /
Turning point: OR f’(x) = 4x – 6
0 = 4x – 6
x =

OR = =
D OR D / Value of x
Value of y
(2)
4.1.2 /

or
A B / 
Factors
Both coordinates
(3)
4.1.3 /
Substitute :

/ Substitute
Answer (2)
4.1.4 /

OR

For non-real roots

OR
For no point of intersection f must be shifted more than 24,5 units upwards.y-intercept will move 20 + 4,5 units upwards.
/ Change to
Answer (2)

Answer (2)
Answer only

(2)
4.1.5 /
or / 

(2)
4.1.6 /

Tangent if roots are equal:

OR

/ Equate
Standard form

Answer
(4)




(4)
4.2
4.2.1 / and

Shift p 1 unit to the left and 2 units downwards.
(If you replace x with you are shifting the graph 1 unit to the left and when subtracting 2 you are shifting the graph 2 units down) / 

Explanation
(3)
4.2.2 /
OR
/ 
(1)
[19]
QUESTION 5
5.1 / or / Any one point
(1)
5.2 /
Substitute inverse point:
OR

,
OR
Substitute or into :
OR

, / Substitute correct coordinate
Equation

(3)
Substitute correct coordinates
Equation

(3)
5.3 /

/ Substitution into
Same base

(3)
5.4 / / 

(2)
[9]
QUESTION 6
6.1 / =
=
=
=
=
Quarterly rate = 14,16 % / Substitution into formula
Simplification
Answer
(3)
6.2 / R3500 + R5700 A

T0 T1 T2 T3 T4 T5
7% p.a. quarterly 8% p.a. monthly

/ 


Answer
(4)
[7]
QUESTION 7
7.1 / Calculate monthly payment for Option 1:
P= 950000
x x

T0 T1 T240
Option 1: = 0,01

Total cost for Option 1:
Option 1
/ Substitution into correct formula
 = 0,01

Simplify
Answer
Calculation
Answer
(7)
7.2 / Total cost for Option 2:
Option 2

Option 1 is the best. By choosing option 1 he will save R10281,60. / 
Answer
Conclusion
(3)
[10]
QUESTION 8
Note: Penalise only once for notation.
8.1 /

/ Formula
Substitution
Simplify
Factorise
Answer
(5)
8.2
8.2.1 /

/ 


(3)
8.2.2 /

/ Factorise LHS
Factorise RHS
Simplify
Answer
(4)
8.3 /

/ Multiply brackets


Answer
(4)
[16]
QUESTION 9
9.1
9.1.1 /
At turning point :

Substitute

- - - (i)
Substitute in

- - - (ii)
(i) + (ii):

Substitute into (ii):

/ 
Substitute
Equation (i)
Substitute
Equation (ii)


(7)
9.1.2 / At C:

But at A

OR touching point at A

C / 
 factor

(3)
9.1.3 / Turning point of k: / 

(2)
9.2 /
/ Shape


(3)
[15]
QUESTION 10
10.1 /
P and Q
QR
PQ
Area of PQRS = PQ QR
=
= / QR
PQ
Method
(3)
10.2 / For maximum area:

or
N/A
Maximum area
units2 / 


Answer
(4)
[7]
QUESTION 11
11.1 / C- correct W- wrong
C
0,7
C
0,6 0,3 W
C
0,4
0,4 W
0,6
W
P(2nd answer correct)
= P(CC) + P(WC)
=
=
= OR
/ Tree diagram
Sum of probabilities
Substitution
Answer (4)
11.2 /

/ 
Substitution
Value of x
Sum of probabilities is 1
Value of y (5)
11.3.1 /
/ 
Answer (2)
11.3.2 / 8 and 11 can be arranged in different ways. Consider 8 and 11 as an entity. 11 objects can be arranged in different ways.
Total arrangements

/ 

Answer (3)
11.3.3 / = = =
OR
= / 
Answer (2)
Answer only, full marks.
[16]

TOTAL: 150

ANALYSIS OF QUESTION PAPER: MATHEMATICS PAPER: 1 DATE: Sept 2014

Question
Nr / Concept / Level 1
Knowledge / Level 2
Routine Procedures / Level 3
Complex Procedures / Level 4
Problem Solving
1.1 / Equations
1.1.1 / Factorisation / 3
1.1.2 / Formula / 5
1.1.3 / Inequality / 3
1.2 / Simultaneous Equations
1.2.1 / Exponential Equation / 2
1.2.2 / Simultaneous Equations / 5
1.3 / Exponents / 2
1.4 / Surds / 3
2 / Sequences and Series
2.1 / Sigma notation / 4
2.2.1 / Geometric sequence / 2
2.2.2 / 3
2.3.1 / Infinite series / 3
2.3.2 / 4
2.4 / Quadratic number pattern / 5
3 / Hyperbola
3.1 / Sketch / 4
3.2 / Reflection / 3
4 / Quadratic function
4.1.1 / Turning point / 2
4.1.2 / X-intercept / 3
4.1.3 / Equation line / 2
4.1.4 / 2
4.1.5 / 2
4.1.6 / 4
4.2
4.2.1 / 3
4.2.2 / 1

Mathematics/P1 1 NW/September 2014

NSC– Memorandum

Question
Nr / Concept / Level 1
Knowledge / Level 2
Routine Procedures / Level 3
Complex Procedures / Level 4
Problem Solving
5 / Inverse
5.1 / 1
5.2 / 3
5.3 / 3
5.4 / 2
6 / Financial Mathematics
6.1 / 3
6.2 / 4
7.1 / Loans / 7
7.2 / 3
8 / Differential Calculus
8.1 / 5
8.2.1 / 3
8.2.2 / 4
8.3 / 4
9 / Cubic Function
9.1.1 / Equation / 7
9.1.2 / Coordinate / 3
9.1.3 / Transformation / 2
9.2 / Application / 3
10.1 / Application / 3
10.2 / 4
11 / Probability
11.1 / 4
11.2 / 5
11.3.1 / 2
11.3.2 / 3
11.3.3 / 2
TOTAL: / 26 / 52 / 51 / 21
% / 17,3 / 34,7 / 34 / 14