Symbol 

Explanation

M 

Method

M/A 

Method with accuracy

CA 

Consistent accuracy

A 

Accuracy

C 

Conversion

S 

Simplification

RT/RG/RD 

Reading from table/graph/diagram

SF 

Correct substitution in formula

O 

Opinion/Example

P 

Penalty, e.g. for no units, incorrect rounding off, etc.

R 

Rounding off

AO 

Answer only full marks

NPR 

No penalty for rounding

J 

Justification

QUESTION 1 [31 marks] 

Ques 

Solution 

Explanation 

Level

1.1.1 

World population = 65,3 million × 113  ✔M 
 = 7 378,9 million  ✔S 
 = 74 hundred million    ✔R
 = 7 400 million = 7 400 000 000 
= 7,4 billion 

1M multiplying 
1S simplification in  millions 
1R answer in hundred  million (3)

L2 

D

1.1.2 

✔M 
% Europe = 100% – ( 12% + 29% + 14% + 39%) 
= 6 %    ✔A 
Total displaced people = (65,3 + 21,3 + 10) million 
= 96,6 million   ✔A 
Number of people distributed in Europe  
= 6% × 96,6 million  ✔M 

= 5,796 million OR 5 796 000   ✔CA 

OR 

Total displaced people = (65,3 + 21,3 + 10) million 
= 96,6 million  ✔A 
12% + 29% + 14% + 39% = 94%   ✔A 
94% × 96,6 million = 90,804 million  ✔M 
Number of people in Europe  
= 96,6 million – 90,804 million  ✔M 
= 5,796 million    ✔CA

1M adding to get 94% 
1A percentage for Europe 
1A total 
1M percentage calculation 1CA number in Europe

OR 

1A total 
1A adding to get 94% 
1M percentage calculation 
1M subtracting from total
1CA number in Europe (5)

L3 

D

1.1.3 

Number of persons from the three countries given 
= (1,1 + 2,7 + 4,9) million 
= 8,7 million   ✔A
% of refugees =  8,7 million  ×    100%  ✔M
                           21,3million  ✔RT 
 = 40,8 %     ✔CA 
∴The statement is not valid.  ✔O 

OR 

Number of refugees from the three countries 
               ✔RT
= 21,3 million × 54%  ✔M 
= 11,5 million    ✔A 
Total number at the three countries 
= (1,1 + 2,7 + 4,9) million 
= 8,7 million   ✔A 
∴The statement is not valid.✔O 

1A total persons  
1RT total of refugees 
1M % calculation 
1CA percentage 
1O verification 

OR 

1RT total refugees 
1M % calculation 
1A number 
1A total persons 
1O deduction 
NP for omitting millions (5)

L4 

D

L2 

P

This age group covers the largest range of ages.  ✔✔O 

OR 

This age group is a workforce. They might not have work  in their own country.  ✔✔O

OR 

They are physically fit and able to migrate.  ✔✔O

OR 

Adults fleeing to protect their children/ poltical climate of  country.    ✔✔O 

OR

Any other valid reason 

L4 

D

L2 

D

1M calculating mean 
1A sum of the number of  refugees 
1CA mean 
NPR 
_{(No mode or median  calculated correctly full  marks)} 

(3)

L2 

D

          ✔O                                                       ✔O
For both years the number of refugees increase from  January to June  ✔O 

OR 

           ✔O                                                             ✔O 
For 2014 the number of refugees increase from January to  June and for 2015 the number of refugees increase from  January to June  ✔O 

OR 

            ✔O                                                     ✔O 
For both years the number of refugees increase  substantially in April and June.  ✔O 

OR 

                 ✔O                              ✔O                     ✔O 
Month to month there are an increase form 2014 to 2015 

OR 

                             ✔O                    ✔O 
Compared to 2014, 2015 has more refugees entering  Europe per month. ✔O 

OR  

                                          ✔O                           ✔O 
There was a significant increase from March to April in  both years  ✔O 

1O both years 
1O increase  
1O months 

OR 

1O for year 
1O increase 
1O months  

OR 

1O both years 
1O increase substantially
1O months 

OR 

1O both years 
1O increase substantially
1O months 

OR 

1O both years 
1O increase substantially
1O months 

OR 

1O both years 
1O increase substantially
1O months  (3)

L4 

D

Budget amount for 2016 
                                       ✔A 
= US$ 5 300 million × 118,7%  ✔M   or (1,187) 
= US$ 6 291,1 million  ✔CA 
= US$ 6 291 100 000  ✔C
Factor increase = 6 291100 000   or  6 291,1 
                                   300 000              0,3
 = 20 970,3333 ✔CA 

OR 

Increase from 2015 
18,7% × US$ 5 300 million  ✔M 
= US$ 991,1   ✔A 
Budget amount for 2016 
= US$ 5 300 million + US$ 991,1 million 
= US$ 6 291,1 million  ✔CA 
= US$ 6 291 100 000  ✔C 
Factor increase = 6 291100 000 
                                 300 000 
 = 20 970,3333  ✔CA

1M increase % 
1A 118,7% 
1CA increased amount 
1C value in millions or 
1950 budget to 0,3 
1CA factor 
NPR 

OR 

1M calculating % 
1A amount 
1CA increase amount 
1C value in millions 
1CA factor 
NPR    (5)

L3 

F

QUESTION 2 [40 marks] 

Ques 

Solution 

Explanation 

Level

2.1.1

Density =  39 000  ✔SF 
              13,5acres 
                                            ✔CA 
 = 2 888,88 persons per acre 
            ✔R
 ≈ 2 889 persons per acre 

1SF substitution of correct  values 
1CA simplification 
1R rounding  (3)

L2 

M&P

2.1.2 

P =  11393      ✔RT 
       39000       ✔M 
 ≈ 0,29 or 29,21%  ✔CA

1RT reading values 
1M probability concept
1CA correct rounded  probability  
AO    (3)

L2 

P

2.1.3 

(a)

            ✔RT         ✔M
15 000 – 14 979 = 21 ✔CA 

1RT values 
1M subtracting 
1CA number of seats    (3)

2.1.3 

(b)

There are provisions made for disabled spectators who  don't require seats.  ✔✔O

OR 

Some people can be standing .  ✔✔O 

OR  

Staff , line judges, officials, coaches, media personnel.   ✔✔O

2O reason (2)

L4 

M&P

2.1.4 

(a) 

✔RT
Width of the screen =  40 m²    ✔ M 
                                     5 m 
 = 8 m✔ A 

1RT value 
1M dividing 
1A width     (3)

2.1.4 

(b) 

Measured width of screen 6 mm 
Scale: 6 mm : 8 m  ✔ A
 6 mm : 8 000 mm  ✔C
 1 : 1333,33 ✔CA 

1A scale 
1C converting 
1CA unit scale     (3)

L3 

M&P

2.2.1 

12 ✔✔A

2A correct number  (2)

L2 

M&P

2.2.2 

F ✔✔A

2A correct number   (2)

L2 

M&P

Ques 

Solution 

Explanation 

Level

2.2.3 

Area of the court = 41 m × 22 m 
 = 902 m²  ✔A 
Seed needed = 902 m² × 245 g/m²  ✔M 
 = 220 990 g 
 = 220,99 kg  ✔C 

Fescue seed = ³/₁₀ × 220,99 kg ✔M 
 = 66,297 kg  ✔CA 
The statement is not valid.  ✔O 

OR 

Area of the court = 41 m × 22 m   
 = 902 m^{2   ✔A} 
 = ³/₁₀ of area of the court = 103 × 902 m²  ✔M 
 = 270,6 m² 

Fescue seed = 270,6 m² × 245 g/m²  ✔M 
 = 66 297 g  ✔CA 
 = 66,297 kg    ✔C 
The statement is not valid.  ✔O 

OR 

Area =902 m²  ✔A 
Ratio 7 : 3 
                   ✔M 
= ³/₁₀ × 245 g = 73,5 g fescue/ m²  
             ✔M 
73,5g/ m²× 902 m²= 66 297g  ✔CA
 = 66,297kg ✔C 
Not valid ✔O 

1A area 
1M multiply with spread rate 
1C converting to kg 
1M working with ratio 
1CA mass of red fescue seed
1O conclusion 

1A area 
1M working with ratio 
1M multiply with spread rate
1CA mass of red fescue seed 
1C converting to kg 
1O conclusion 

OR 

1A area 
1M working with ratio 
1M multiply with spread rate
1CA mass of seed 
1C converting to kg 
1O conclusion  (6)

L4 

M

Ques 

Solution 

Explanation 

Level

2.3.1 

                                                          ✔RT 
Percentage increase =  £2,50 -  £1,70 ×  100%  ✔SF 
                                            £1,70 
 = 47,0588…%  ✔CA 
% increase per year = 47,0588   ✔A
                                         21 
 ≈ 2,24 %  ✔CA 

1RT reading values from  graph 
1SF substitution 
1CA simplification 
1A dividing by 21 
1CA simplification 
NPR   (5)

L3 

F

2.3.2 

                              ✔M 
Income = 142 000 × £2,50  ✔RT 
 = £355 000   ✔CA

1M multiplying 
1RT price from graph 
1CA income 
 AO     (3)

L2 

F

2.3.3 

The average inflation rate remained unchanged / constant  ✔✔A 

OR 

The annual inflation rate change for the UK would have  been 0%  ✔✔A 

2A comment 
_{(if the answer only refers to  the price of strawberries max  1 mark)}   (2)

L4 

F

[40]

QUESTION 3 [36 marks] 

Ques 

Solution 

Explanation 

Level 

3.1.1 

                   ✔RT
35°C – (–3°C) = 35°C + 3°C 
 = 38°C✔CA 

1RT reading values from  table 
1CA difference 
AO   (2)

M 

L2

3.1.2

✔M
Range = 29°C – 9°C = 20°C  ✔A 
Month: September  ✔A 

1M concept of range 
1A range in °C 
1A September  (3)

D 

L2

3.1.3

1A × 6 for each two points plotted correctly 
1CA joining the points    (7) 

D 

L2

3.1.4 

Inner band  ✔✔A

OR 

          ✔A        ✔A 
25 to 75 percentile band. 

OR 

                  ✔A                                ✔A 
Above the mean but below the 75^th percentile 

2A band 

OR 

1A interpreting the starting  point of the percentile band 1A end point of percentile  band
_{(accept 50 to 75 percentile  band)}      (2)

D 

L4

Ques 

Solution 

Explanation

3.1.5

ºF = (ºC × ⁹/₅) + 32 
119,1ºF = (ºC × ⁹/₅) + 32  ✔SF 
(ºC × ⁹/₅) = 119,1 – 32 ✔S
ºC = 87,1 ÷ ⁹/₅  ✔S
 = 48,3888 
 ≈ 48,4 ºC    ✔CA

1SF substituting values 
1S simplification 
1S simplification 
1CA Celsius value  (4) 

M 

L3

3.2.1 

North ✔✔RT

2RT modal wind direction. (2)

D 

L3

3.2.2 

P(westerly) = 16% + 11% + 9% ✔RT 
 = 36% ✔CA

1RT reading all W values
1CA probability 
AO (2)

P 

L2

3.2.3 

                                       ✔✔O 
The percentages do not add up to 100%.  

OR 

Too many sectors needed  ✔✔O

2O explanation (2)

D 

L4

Ques 

Solution 

Explanation 

T&L

3.3.1 

Accommodation per person = R850 ✔A
                                                  3 
 = R283,33   ✔CA 
Kz 100 000 = R9 173,05 
                                                                       ✔A 
Amount Kwanza =    R283,33    ×  Kz100000  ✔M
                                R9173,05 
 ≈ Kz 3 088,76 ✔CA 

OR 

R9 173,05 = Kz 100 000 
 R1 =  100 000 
          9173,05    ✔M 
 = Kz 10,9014995 
∴ R850 = Kz 10, 9014995 × 850   ✔A 
 ≈ Kz 9 266,27  ✔CA 

Cost per person = 9 266,27  ✔A
                                   3 
 ≈ Kz 3 088,76  ✔CA 

1A divide by 3 
1CA accommodation per  person in R 
1A multiply by 100 000 
1M divide by 9 173,05 
1CA amount per person 

OR 

1M divide by 9 173,05 
1A multiply by 850 
1CA total amount 
1A divide by 3 
1CA accommodation per  person in Kz 
^{(using R850 per person max 5  marks. 
Multiplying R850 by 3 max 4  marks)} 

(5)

F 

L3

3.3.2 

$1 = Kz 169,27344 
                                                                      ✔M 
Average disposable salary = $ 1 760,41 × Kz 169,27344/$ 
≈ Kz 297 990,66   ✔A 
Angola: 
Rent as a % of income =   145 990     ×   100%    ✔M 
                                       297 990,66 
 = 48,99%  ✔CA 
South Africa:
Rent as a % of income = 4 430   ×   100%   ✔M 
                                       16 500 
 = 26,85%  ✔CA 
Not valid .It is much cheaper in SA but not double.  ✔O

1M multiplying 
1A Disposable salary in Kz
1M percentage calculation 
1CA percentage 
1M percentage calculation 
1CA percentage 
1O conclusion     (7)

F 

L4

[36]

QUESTION 4 [43 marks] 

Ques 

Solution 

Explanation 

Levels

4.1.1

                                                                      ✔SF 
Volumetric mass = 43 cm × 30,5 cm × 14,5 cm  ✔C 
                                                  5 000          ✔RT 
 = 3,8 kg   ✔CA 

OR 

Volume (in mm³) = 430 × 305 × 145  ✔SF 
 = 19 016 750 
Volumetric mass = 19 016 750 
                                   5 000        ✔RT 
= 3 803,35g ÷ 1 000  ✔C
 = 3,8 kg    ✔CA 

1SF substitution mm/cm
1C conversion to cm
1RT correct mass factor
1CA volumetric mass AO 

OR 

1SF substitution in  volume formula 
1RT correct mass factor
1C conversion  
1CA volumetric mass (4)

L2 

M

4.1.2

Volumetric mass = volume of the parcel in cm³ 
                                       mass factor 
2 kg = 20cm × 25cm × 15cm  ✔SF 
                  mass factor 
Mass factor = 7500cm³   ✔S 
                         2 kg        ✔S 
= 3 750 cm³/kg  ✔S 
 ≈ 4 000 cm³/kg   ✔R 

OR 

Volumetric mass (using 5000) = 20 cm × 25 cm ×15 cm   ✔SF  
                                                                5 000 
 = 1,5kg  ✔S

Volumetric mass (using 4000) = 20 cm × 25 cm ×15 cm   ✔SF 
                                                               4 000 
 = 1,875kg  ✔S 
Hence 4000cm³/kg  ✔O

1SF substitution 
1S volume 
1S change formula 
1S simplification 
1R rounding 

OR 

1SF substitution 
1S simplification 
1SF substitution 
1S simplification 
1O conclusion  (5)

L3 

M

Ques 

Solution 

Explanation 

Level

4.1.3  

Surface area of a rectangular-based box  
                                                ✔A           ✔SF 
= 2(575 mm × 375 mm + 575 mm × 400 mm + 375 mm ×  400 mm) 
= 1 191 250 mm²  ✔CA
Surface area of a square based box  
                 ✔A             ✔SF 
= 2 × 410 mm (2 × 600 mm + 410 mm)  
= 1 320 200 mm²  ✔CA
The statement is not valid.  ✔O

OR 

Surface area of a square based box  
                ✔SF                                    ✔A 
= 4 × 410 mm × 600 mm + 2 × (410 mm)²  
= 1 320 200 mm²  ✔CA 
The statement is not valid.  ✔O

1SF substitute into  formula 
1A correct values 
1CA simplification 
1SF substitution  
1A using the squared side  (410) 
1CA simplification 
1O conclusion (7)

L4 

M

4.2.1

These places are far from Mbombela.  ✔✔O 

OR 

There might not be many parcels to deliver to those places.  ✔✔O 

OR 

From Mbombela parcels might go to a central depot to be  delivered from there. ✔✔O 

2O reason (2)

L4 

M&P

Ques 

Solution 

Explanation 

Level

4.2.2 

(a)

Package to Graskop: Less than 30 kg @ R70,00  ✔A 
Package to Klerksdorp: 18 kg 
                                        ✔ A 
 15 kg + 1 excess of 5 kg 
                             ✔A                            ✔CA 
Delivery cost R106,00 + R15,00 = R121,00 
Package to Port Alfred: 18 kg 
                          ✔A 
 10 kg + 2 excess of 5kg 
                              ✔A                       ✔CA 
Delivery cost R160,00 + 2 × R15 = R190 
Total cost = R70 + R121 + R190 = R381  ✔M 
 VAT = R381 × 14%   ✔M 
 = R53,34 
Total cost including VAT = R434,34  ✔CA 

OR 

Prices with VAT 
Local: R70 ×114% = R79,80 
Klerksdorp: R106 ×114% = R120,84  ✔M 
Shaded areas:R160 ×114% = R182,40 
Excess label: R15×114% = R17,10 

To Graskop cost = R79,80  ✔A 
                                          ✔A           ✔A        ✔CA 
To Klerksdorp cost = R120,84 + R17,10 = 137,94 
                                          ✔A            ✔A              ✔CA 
To Port Alfred cost = R182,40 + 2 × R17,10 =  R216,60 
Total cost = R79,80 + R137,94 + R216,60  ✔M 
 = R434,34  ✔CA

1A Graskop R70 
1A splitting mass to  Klerksdorp 
1A R106 
1CA cost  
1A splitting mass to PA 
1A R160 
1CA cost 
1M adding  
1M VAT 
1CA total cost incl. VAT
_{(For Port Alfred max 3  marks if cost is calculated  using R106 - Cost R121 or R117 - Cost 132 )} 

OR 

1M adding VAT to costs 
1A Graskop cost 
Klerksdorp: 
1A basic cost 
1A one excess label 
1CA cost 
Port Alfred 
1A basic cost 
1A two excess labels 
1CA cost 
1M adding 
1CA total cost incl. VAT  (10)

L3 

F

Ques 

Solution 

Explanation 

Level

4.2.2 

(b) 

30 April from 14:50 to 24:00 is 9 hours 10 min ✔A 
1 May                 is 24 hours  ✔A
2 May from 00:00 to 8:15 is 8 hours 15 min  ✔A 
Total elapsed time = 41 hours 25 min  ✔CA 
This is within the 48 hour service.  ✔O 

OR 

30 April from 14:50 
To 1 May 14:50 ( 24 hours / 1st day)  ✔A 
To 2 May 14:50 ( 48 hours / 2nd day)  ✔A
But 2 May 8:15 is before 48 hours.  ✔A 
It is within 48 hours   ✔O

1A time 30 April 
1A time 1 and 2 May
1CA adding time 
1O opinion based on  CA from 4.2.2 (a) 

OR 

1A 1st day 
1A 2nd day 
1A conclusion 
1O conclusion   (4)

L4 

M

4.2.3 

(a)

Box size A: 
Number of boxes =  650  = 92,857 ✔M 
                                  7
≈ 93   ✔R 
Mass of box = 7 × 2 kg = 14 kg 
                    ✔A
Cost = R117,00 × 93  
 = R10 881  ✔CA 

1M dividing 
1R rounding up 
1A rate to George 
1CA cost   (4)

L3 

F

Ques 

Solution 

Explanation 

Level

4.2.3 

(b)

Box size B: 
Number of boxes =  650  = 43,333  ✔MA
                                 15
43 boxes packed with 15 parts, mass 30 kg each  ✔R 
Number of parts left = 650 – 43 × 15 = 5  ✔CA 
Mass of the parts = 5 × 2 kg 
 = 10 kg 
1 box packed with the remaining 5 parts, mass 10 kg 
Cost per 30 kg box = R117 + 3 × R15 = R162  ✔A 
Cost = R162 × 43 + R117  ✔M 
 = R7 083  ✔CA 
Box size B is more economical.  ✔O 
OR (for the first part) 
Mass of all the parts = 650 x 2kg = 1 300 kg 
Mass of a box with 15 parts = 30 kg 

Number of boxes needed = 1300 = 43,33 
                                               30 

1MA dividing 
1R rounding down 
1CA extra smaller box 
1A cost per box 
1M multiply and adding
1CA cost 
1O advice  (7)

L4 

F 

[43]

TOTAL 

150