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GRADE 12 MATHEMATICAL LITERACY PAPER 2 MEMORANDUM - NSC PAST PAPERS AND MEMOS SEPTEMBER 2016

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MATHEMATICAL LITERACY P2
GRADE 12
MEMORANDUM
NATIONAL SENIOR CERTIFICATE
SEPTEMBER 2016

Symbol Explanation
M Method
MA Method with Accuracy
CA Consistent accuracy
A Accuracy
C Conversion
SF Substitution in a formula
F Choosing the correct formula
RT/RG/RM Reading from a table/Reading from a graph/Reading from map
S Simplifications
J Justification
P Penalty (no units, incorrect rounding off etc.)
R Rounding



QUESTION 1 [21]

Ques  Solution  Explanation  Level 
1.1  Two bedroomed flats in 1 block = 2 × 3
= 6
Total no of flats in 8 blocks = 6 × 8
= 48
One bedroomed flats = 2 × 3
= 6 ✓M
Total no of one bedroomed flats = 6 × 8
= 48
Total no of flats 48 + 48
= 96 ✓CA
1M Calculating no
of both flats
1CA Total no of
flat (2)
L2 
1.2  Income for 2 bedroomed flats
=107,5 x 3200 M
    100
= 3440 ×48
= R 165 120 ✓M
Income for 1 bedroomed flats= 2300 × 48
= R110 400 ✓M
Total income =165 120 + 110 400
= R275 520 ✓CA
1M Increasing by
7,5%
1M For 2
bedroomed flats
1M For 1 bedroomed flats
1CA Total (4) 
L3 
1.3  If 1 Ghanaian cedi = 3,77 South African Rand
415 = 3,77 × 415 ✓M
=R 1 564,55 ✓CA
Amount outstanding = 2 300 – 1 564,55 ✓M
= R735,45
= R735  ✓CA
1C Using 3,77
1CA
1M Difference
1CA Answer (4) 
L2 
1.4  If all occupied :
48 × 3 440 = 165 120 ✓M
93,75% × 48 = 45
93,75% occupied = 45 × 3 440
= 154 800 ✓CA
Money lost = 165 120 – 154 800
= R 10 320
OR
93,75% × 165 120 ✓M
= 154 800
Money lost = 165 120 – 154 800 ✓M/A ✓M
= R 10 320
OR
93,75% × 48 = 45
48 – 45 = 3 × 3 440 ✓CA ✓M
= R 10 320 ✓CA
OR
0,0625 × 48 = 3 M ✓CA
3 × 3 440✓ M 
= R 10 320 ✓CA
OR
100 – 93,75% = 6,25% ✓M/A
= 6,25% × 165 120 ✓M/A
= R 10 320 ✓CA
CA from 1.1.1
1M Total income
1CA
1M getting the
difference
1CA
1M Calculating
93,75%
1CA Answer
1M Subtracting
1CA
MA For 45
1CA Difference
1M Multiplying by
3440
1CA Answer
1M Calculating
6,25%
1CA
1M Multiplying by
3440
1CA
1MA Difference
between 100%
and 93,75%
2M
1CA (4)
 L4
1.5  People in 8 blocks
36 × 8 = 288 ✓M/A
37,5 × 288
100 ✓CA
= 108
Children = 288 – 108
= 180 ✓CA ✓MA
OR
62,5 × 288 = 108 ✓M ✓MA
100
Children = 288 – 108 ✓M
= 180 ✓CA
1MA Calculating
the number of
people
1CA
1M Subtraction
1CA Answer
2M Using 62,5%
1CA
1M Subtraction
1CA Answer (5)

L2  
1.6  Probability = ✓A
                    96 ✓A
CA from 1.1.1
1A numerator
1A denominator
(2) 
L2


QUESTION 2 [29]

2.1  2.1.1  Range = max – min
78 = 132 – A (min) ✓M
A = 132 – 78 ✓M
= 54  ✓CA
1M Concept of range
1M Subtracting
1CA (3) 
L2 
  2.1.2  Mean = sum of the numbers
                           14
90 =65+79+B+98+54+68+90+76+84+102+132+121+B+B
                                             14
90 × 14 =969 + 3B ✓S
1260= 969 + 3B ✓M
1260 – 969 = ✓3B
291= ✓3B
  3
= B
Mode = 97 ✓ CA
CA From 2.1.1
1MA Sum of values divided by 14
1S
1M Multiplying and adding B’s
1A (4) 
L4 
  2.1.3  54 65 68 76 79 84 90 97 97 97 98 102 121 132 ✓MA
Q2 (median) = 90+97 ✓A
                            2     ✓M
= 93,5 ✓CA
Q1 (lower Quartile) = 76 ✓CA
Q3 (upper Quartile) = 98 ✓CA
CA from 2.1.1 and 2.1.2
1MA Arranging in ascending order
1M Adding the 2 values
1M Dividing by 2
1CA Median
1CA Q1
1CA Q2 (6) 
L3 
  2.1.4  In paper 2 the mean is lower than in paper 1 therefore paper 1 was performed better than 2✓ R
OR
Paper 2 was more difficult ✓R
OR
Paper 1 was more easier ✓ R
2R
2R
2R (2) 
L4 
  2.1.5  Probability = 3 A
                    14 A

CA from 2.1.1, 2.1.2 and 2.1.3
1A numerator
1A denominator (2) 
L2 
2.2  2.2.1  Costs for venue ✓A
= R1 500+R1 200+(R150 × 66) ✓M
= R12 600 ✓CA
Costs for venue B = R 1 000 + 220 × 66
= R 15 520 ✓CA
Difference = 15 520 – 12 600
= R 2 920 ✓CA
1M Multiply by 66
1CA Cost for venue A
1CA Cost for venue B
1CA Difference in cost (5) 
L3 
  2.2.2  Graph to show costs of venues A and B
No. of learners 
1M Plotting 0 and 1000
1M For every 3 values plotted correctly
1CA Joining points to form a line
1CA Breakeven point
(6) 
L3 
  2.2.3  Breakeven point is where the cost of Venue A is equal to the cost of venue B ✓O for the same number of learners ✓O
Number of learners = 20
Cost = R5 700 ✓RG
1A Same cost
1A Same number of learners
1RG For reading the cost and the number of learners
(3) 
L3 


QUESTION 3 [30]

3.1  3.1.1  Annual income =368 450
Tax bracket from table=284 101 – 393 200 ✓RT
Tax = 59 314 + 31% of the amount above
= 284 100 ✓SF
= 59 314 + 0,31(368 450 – 284 100)
= 59 314 + 0,31 x 84 350
= 59 314 + 26 148,50 – [(270 × 2) + 181 × 12] ✓M
= 85 462,50 – 13 257 - 8652✓M 
=R63552,50  
       12         ✓M
= R5 296,04 ✓M
Monthly = 368 450 ÷ 12
= R30 704,17
% =5296,94 × 100
      30704,17
= 17,25% Accep17,3% ✓CA
1RT Correct tax bracket
1SF
1S
1M Subtracting rebates
1M Subtracting medical aid credits
1M dividing by 12
1M Monthly Income
1CA % (8) 
L4 
  3.1.2  Tax payable
= 85 462,50 – (13 257 + 7 407 + 2 466) ✓M
=85 462,50 – 23 130
= 62 332,50 – 8 652 ✓M
= 52 680,50
= R 4 473,38
Tax would be less  ✓J
1M Adding rebates
1M subtracting rebates
1J (3) 
L4 
  3.1.3  Option 1 = 30 704,17 × 6,9 × 3
                                     100
= 6 355,76 ✓M/A
Amount = R 30 704,17 + 6 355,76 ✓M/A
= R 37 059,93✓ CA
Option 2:
Year 1 = 106 × 30 704,17 ✓M
              100
= 32 546,42 ✓CA
Year 2 = 106 × 32 546,42
              100 
= 34 499,20 ✓CA
Year 3 = 106 × 34 499,20
              100
= R 36 569,16 ✓CA
Advise to use option 1 because there is more money in the investment at the end of the period  ✓O
1MA Multiply by 6,9% and 3
1MA adding
interest
1CA
1M Multiply by 10,6%
1CA
1CA Year 2
1CA Year 3
1O (8) 
L4 
3.2  3.2.1  50 ℓ model:
Surface area = (2 × π × r × l) + (π × r2 × 2) ✓SF
= (2 × 3,142 × 225 × 610) + (3,142 × 225 × 225 × 2)
= 862 479 + 318 127,5 S
= 1 180 606,5 mm2 ✓CA
100 ℓ model:
Surface area = (2 × π × r × l) + (π × r2 × 2)
=(2 × 3,142 × 275 × 840) + (3,142 × 275 × 275 × 2)
= 1 451 604 + 475 227,5 S
= 1 926 831,50 ✓CA
1926831,50 ✓M
          2
= 963 415,75
Not equal to the surface area of the 50 ml geyser ✓ O
2SF Substitution in the formula
1S Simplification
1CA Surface Area
1S Simplification
1CA Surface Area
1M Dividing by 2
1O (8)
L4 
  3.2.2  Length using a ruler = 50 mm ✓A
Actual length 840 mm
Scale is 50:840 ✓A
=1:16,8 ✓CA
1A Measure 50 mm
1A Scale
1CA
Accept 49 – 51 mm (answers will be
1:17,1 – 1:16,5) (3) 
L3 


QUESTION 4 [31]

4.1  4.1.1  Arrival 8:00
Depart at = 8:00 + 3h 45min
=11:45 ✓M/A
Time taken at 90km per hour
Average Speed = distance travelled
                                  time taken
90 = 86              ✓ SF
    time taken
Time taken = 86
                      90
= 0,955555 × 60
= 57,3 minutes
Arrival = 11:45 + 57,3 minutes ✓CA 
= 12:42 ✓CA ✓M
Will be late by 12 minutes ✓ O
1MA Time
1SF Substitution in the formula
1CA Calculating minutes
1CA Addition
1A Time of arrival
1O CA (6) 
L3 
  4.1.2  Costs:
Hiring =R2 800
Ferry = 70 × 2 (return)
= 140 ✓M/A
= 140 × 2 (for two days)
= R280 ✓CA
Accommodation = 543 × 2 × 3
=R 3 258
Total = 2 800 + 280 + 3 258
= R6 338 ✓M/A
Available = 700 × 14,391
= R10 073,70 ✓C
Therefore it will be enough 
1MA Calculating return cost
1CA Cost for 2 days
1MA Calculate accommodation
1MA Total
1C Conversion
1O (6)
L3 
  4.1.3  No ferry rides because it can be swept away by heavy currents ✓O
OR
Can cause ferry to capsize ✓CA
OR
Accept any other relevant reason  ✓CA
2O Reason
(2) 
L4 
4.2  4.2.1  The % of aids related deaths is decreasing from 2007 to 2014 ✓A
Reasons – people more educated about HIV
- People are taking medication✓ A
- Practising safe sex ✓O
(Accept any other TWO relevant reasons)
2A Explaining the trend
2R 1Reason
(4) 
L4 
  4.2.2  Total number of births
= 1 125 755 + 1 132 500 + 1 141 468 +
1 152 319 + 1 163 629 + 1 173 164 + 1 184
867 + 1 196 395 + 1 207 711 ✓M
= 10 477 808 ✓CA
Total number of Aids related deaths
= 343 194 + 297 659 + 257 504 + 228 051 + 213 864 + 211 839 + 203 293 + 189 376 +
171 733
= 2 116 513 ✓CA
Difference = 10 477 808 - 2 116 513
= 8 361 295  ✓CA
1M Addition
1CA Total (births)
1CA Total (deaths)
1CA Difference (4) 
L2 
  4.2.3  1207711 - 1196395 x 100 ✓M
       1196395  ✓M
= 0,95% ✓CA
Incorrect ✓O
Accept 0,9% 
1M Difference
1M Correct denominator
1CA Finding %
1O
(4) 
L2 
  4.2.4  Bar graph to show percentage Aids related deaths over a period of years  5M
1mark for each
correct bar
(5)
L2 

 

QUESTION 5 [37]

5.1 5.1.1 To allow allowance for opening the doors
If the doors are the same size, they will be too big and won’t fit. ✓O
2O
(2)
L4
  5.1.2 Front doors = 2 700 ÷ 39,7
= 6 doors ✓M
= 1 830 ÷ 716
= 2 doors ✓CA
No. of doors = 6 × 2
= 12 doors in 1 board ✓CA
Doors needed = 20
2 boards needed ✓A
Sides = 2700 ÷ 540
= 5 ✓M
1 830 ÷ 720 = 2
No. of sides = 5 × 2 = 10
Boards needed = 2 ✓CA
Back = 2 200 ÷ 720 = 3
1 200 ÷ 800 = 1
3 in 1 board ✓M
 ∴ For 10 backs = 4 boards
Bottom = 2 700 ÷ 54
= 5
1830 ÷ 716 = 2
5 × 2 = 10
No. of boards = 2 ✓CA
Top = 3 400 ÷ 780 = 4
For ten cupboards = 3 tops✓ M
1M Number of doors - length
1M Number of doors - width
1CA Total doors
1A Number of boards
1M Number of sides
1CA Boards needed for sides
1M Calculating the backs
1CA Number of boards
1CA Number of boards
1M Number of tops
(10)
L3
  5.1.3 Cost of material : 2 × cherry, 4 × melamine, × Masonite, 3 tops
4 × 390 + 2 (390 + 90) + 4 x 90 + 800 × 3 ✓M✓ M
= 1 560 + 960 + 360 + 2 400 ✓CA
= 5 280
5 280 × 114 ✓CA
             100
= R 6 019,20 ✓CA
CA from 5.1.2
1M Using R90
1M Multiplying
1M Addition
1CA Total
1M Using 14% VAT
1CA Price including VAT (6)
L3
  5.1.4 Dimensions = 3m × 4m
= 3 000mm × 4 000mm ✓C
Using 780mm by 600mm ✓A
= 4000 x 3000
    780      600
= 5 × 5
= 25 cupboards ✓M
10 will fit ✓CA
1C Conversion to
mm
1A Using correct
values
1M Calculating
number of
cupboards
1O Conclusion (4)
L4
5.2 5.2.1

17+19+20+22+26+28+29+30+31+32+33+2(34)+ 5(35)+2(36)
= 602
No. of people= 1/3 × (602 – 2 wheelchairs)
= 200 ✓M/A
2Men + 3men = 2 : 3
∴ Men = 200 x 2
               80
             =  5
                80  ✓CA

OR
Women = 3 x 200 ✓MA
                 5
= 120 ✓CA
Men = 200 – 120
= 80 ✓CA

1MA Number of
people in hall
1M Using concept
of ratio
1CA Number of
men
1M Concept of ratio
1CA Number of
women
1CA number of
men (3)
L3
  5.2.2 Row A15
Row B17 ✓A
Row V33
1A First row
1A Second row
1A Third row (3)
L3
  5.2.3  32   ✓A
602  ✓A
= 0,053156146
=0,053 ✓CA
1A numerator
1A denominator
1CA 3 decimal
places (3)
L3
  5.2.4 Enter through door 4, turn right and go straight to the end of the seats. Turn left and go straight past 8 rows. On the 9th row turn left. The seats are in row M seat numbers 2 and 3  3A for clear
directions to their
seats
(3)
L4
  5.2.5 Short-sighted person will be on D1 ✓A
Farsighted person will be on T12 ✓A
Short-sighted people can see things which are closer whereas longsighted people can see things which are far ✓A
1A Correct seat
number
1A Correct Seat
number
1O Reason (3)
L4

TOTAL: 150

Last modified on Tuesday, 15 June 2021 07:19