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
QuestionNr / 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
Copyright reservedPlease turn over
Mathematics/P1 1 NW/September 2014
NSC– Memorandum
QuestionNr / 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
Copyright reservedPlease turn over