This Memorandum Consists of 16 Pages

MARKS: 150

This memorandum consists of 16 pages.

Copyright reserved Please turn over Mathematics/P1 2 NW/September 2014 NSC – Memorandum  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  Factors or  

(3) 1.1.2  Standard form  Substitution into formula = = or  Simplify  Each value of x  (5) 1.1.3 Critical values: or  Critical values

 

Critical values: or

 Critical values

  OR

Copyright reserved Please turn over Mathematics/P1 3 NW/September 2014 NSC – Memorandum

Critical values: or  Critical values

 

1.2 1.2.1  Exponential law  Equate exponents

(2) 1.2.2 Substitute  Substitute

 Standard form

 Factors

 Both values of a or or  Both values of b or (5) 1.3

= OR  Simplify

 Answer

(If , penalise 1 mark)

1.4  Squaring

 Expand

 Simplify

 Expand

 Bracket squared

 Simplify

QUESTION 2 2.1  Expansion

S18  Substitute a and d into correct formula 

 Answer (4) 2.2

nd On 2 day: T2 = 2.2.1  of 216  Answer OR

Day 2: T2 (2)

  Answer (2) 2.2.2 th On the 7 day: Tn  a T7  r

Copyright reserved Please turn over Mathematics/P1 5 NW/September 2014 NSC – Memorandum  Answer (2 dec.)

(3) 2.3 2.3.1 Converge if  

 Answer

(3) 2.3.2  Value of a  Value of r

 Substitution into correct formula = 2  Answer

(4) 2.4 2 ; x ; 12 ; y

 2nd difference

2nd difference = 6  Equation in terms of x

Substitute into  Substitute into 2nd

equation

QUESTION 3 3.1 Vertical asymptote: Horizontal asymptote: y-intercept: x-intercept:

 Both asymptotes  Shape

(4) 3.2 ,    (3)

QUESTION 4 4.1 4.1.1 Turning point: OR f’(x) = 4x – 6  Value of x

0 = 4x – 6  Value of y

x = (2)

OR = =

D OR D

4.1.2 

 Factors or A B  Both coordinates (3) 4.1.3 Substitute :  Substitute  Answer (2)

4.1.4  Change to

 Answer (2)

For non-real roots

 Answer (2)

OR  Answer only For no point of intersection f must be shifted more  than 24,5 units upwards. y-intercept will move 20 + 4,5

units upwards . (2)

4.1.5  or 

(2) 4.1.6  Equate  Standard form Tangent if roots are equal: 

 Answer OR (4)

  

(4) 4.2 and 4.2.1  

Shift p 1 unit to the left and 2 units downwards.  Explanation

(If you replace x with you are shifting the graph 1 unit to (3) the left and when subtracting 2 you are shifting the graph 2 units down)

4.2.2  OR (1)

QUESTION 5 5.1 or  Any one point

(1) 5.2 Substitute inverse point:  Substitute correct OR coordinate

 Equation , 

OR (3)

Substitute or into : OR  Substitute correct coordinates ,  Equation Copyright reserved Please turn over Mathematics/P1 9 NW/September 2014 NSC – Memorandum

(3) 5.3  Substitution into  Same base 

(3) 5.4  

[9] QUESTION 6 6.1 =  Substitution into formula =

=  Simplification =

Quarterly rate = 14,16 %

 Answer

(3) 6.2 R3 500 + R5 700 A

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

  

 Answer

(4) Copyright reserved Please turn over Mathematics/P1 10 NW/September 2014 NSC – Memorandum

QUESTION 7 7.1 Calculate monthly payment for Option 1: P= 950 000 x x

T0 T1 T240

Option 1: = 0,01

 Substitution into correct formula  = 0,01 

 Simplify

Total cost for Option 1: Option 1  Answer

 Calculation  Answer

7.2 Total cost for Option 2: Option 2 

Option 1 is the best. By choosing option 1 he will save  Answer R10 281,60.  Conclusion

QUESTION 8 Note: Penalise only once for notation. 8.1  Formula

 Substitution

 Simplify

 Factorise

 Answer

(5) 8.2 8.2.1

 Copyright reserved Please turn over Mathematics/P1 12 NW/September 2014 NSC – Memorandum 

(3) 8.2.2  Factorise LHS  Factorise RHS

 Simplify

 Answer

(4) 8.3  Multiply brackets  

 Answer

QUESTION 9 9.1 9.1.1 At turning point :  Substitute  Substitute  Equation (i) - - - (i)  Substitute Substitute in  Equation (ii)

- - - (ii)  (i) + (ii):

Substitute into (ii): 

9.1.2 At C: 

But at A  factor OR touching point at A Copyright reserved Please turn over Mathematics/P1 13 NW/September 2014 NSC – Memorandum

 C (3) 9.1.3 Turning point of k:  

(2) 9.2

 Shape  

QUESTION 10 10.1

P and Q QR  QR PQ  PQ Area of PQRS = PQ QR =  Method = (3) 10.2 For maximum area: Copyright reserved Please turn over Mathematics/P1 14 NW/September 2014 NSC – Memorandum

 or  N/A 

Maximum area units2  Answer

QUESTION 11 11.1 C- correct W- wrong C 0,7

C 0,6 0,3 W  Tree diagram C 0,4 0,4 W 0,6 W

nd  Sum of P(2 answer correct) probabilities = P(CC) + P(WC)  Substitution = =  Answer (4) = OR

Copyright reserved Please turn over Mathematics/P1 15 NW/September 2014 NSC – Memorandum 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.

TOTAL: 150

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

Question Concept Level 1 Level 2 Level 3 Level 4 Nr Knowledge Routine Complex Problem Procedures Procedures 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

Copyright reserved Please turn over Mathematics/P1 16 NW/September 2014 NSC – Memorandum 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

Question Concept Level 1 Level 2 Level 3 Level 4 Nr Knowledge Routine Complex Problem Procedures Procedures 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

Copyright reserved Please turn over Mathematics/P1 17 NW/September 2014 NSC – Memorandum 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

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