Symbol

Explanation

M

Method

MA

Method with accuracy

CA

Consistent accuracy

A

Accuracy

C

Conversion

S

Simplification

RT

Reading from a table/a graph/document/diagram

SF

Correct substitution in a formula

O

Opinion/Explanation/Opinie

P

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

R

Rounding off

NPR

No penalty for rounding

AO

Answer only

MCA

Method with constant accuracy

QUESTON/1 [35 MARKS]

Q/V

Solution

Explanation

T&L

1.1.1

A = 367 × 3      ✓M
= 1 101      ✓A
B = 15 726 ÷ 3    ✓M  
= 5 242 ✓A
OR
                         ✓M
A = 367 × 2700 = 1 101      ✓A
            900
                         ✓ M
B = 900 × 15726 = 5 242 ✓A
           2700

1M multiplying
1A simplification
1M dividing
1A simplification

OR

1M working with ratio
1A simplification
1M working with ratio
1A simplification AO        (4)

D

L2

1.1.2

1 Teacher + 3 learners = 4 persons ✓A
                  ✓MA
Number of schools = 32 712 ÷ 4
= 8 178 ✓ CA

1A total persons
1MA dividing by 4
1CA simplification
AO      (3)

D

L2

1.2.1

             ✓RT  ✓RT
Median% = 58+62  ✓M
                       2
= 60 ✓CA

2RT correct values
1M median concept
1CA simplification 
AO         (4)

D

L2

1.2.2

Mean %
= 36+42+48+58+60+61+62+76+86 ✓ MA
                        9 ✓A
= 529  ≈ 58,78    ✓CA
    9

1MA adding correct values
1A dividing by 9
1CA simplification
AO
NPR        (3)

D

L2

Q/V

Solution

Explanation

T&L

1.2.3

IQR = Upper quartile - Lower quartile  ✓A
16% = 68% - C ✓SF
C = 52% ✓CA

1A value of Q3
1SF substituting 16% and Q3
1CA simplification (3)

D

L3

1.2.4

                           ✓✓O
Matuli's mean is higher than Bianca's.
OR
Bianca's mean is lower.
The range of Matuli'spercentages (86 - 48 = 38) is smaller than Bianca's (86 - 36 = 50) ✓✓O
OR
Bianca's range is bigger.
OR
                ✓✓O

The minimum Matuli scored was 48% which is better than Bianca's 36%.
OR
Bianca's minimum is lower than Matuli's.

2O comparing mean marks
2O comparing range or minimum marks (4)

D

L4

1.3.1

Probability of randomly choosing an Indian
                   ✓A
=       171        × 100% ✓M
   4 500 000    ✓A
                ✓CA
≈ 0,0038% < 0,004%
He is correct.  ✓O

1A numerator
1A denominator
1M percentage
1CA simplification
1O verification (5)

P

L4

Q/V

Solution

Explanation

T&L

1.3.2

Difference = Rs40 000        ✓A
                                 ✓MA
Rs40 000 = 40000  US Dollar
                     63,41
40 000 US dollar = 40000  ÷ 0,081 SA rand
  63,41                     63,41
          ✓S            ✓MA
= R 630,8153… ÷ 0,081
≈ R7 787,84        ✓CA

OR

                    ✓MA                                        ✓MA
Rs50 000 = 50000  USD = 788,51916…÷ 0,081 SA rand
                     63,41
≈ R9 734,80  ✓S
Rs 10 000 = 10000  USD = 157,7038…÷ 0,081 SA rand
                      63,41
≈ R1 946,96  ✓S
Difference = R9 734,80 - R1 946,96
= R7 787,84          ✓CA

OR

R1 ÷ 0,081 = R12,35    ✓A
Rs50 000 x R12,35 ÷ 63,45 ✓MA
= R9 732,07      ✓S
Rs10 000 x R12,35 ÷ 63,45 
= R1 946,41  ✓S
R9 732,07 - R1 946,41
= R7 785,66              ✓CA

1A difference
1MA convert to dollars
1S simplification
1MA convert to rand
1CA simplification in rand

OR

1MA convert to dollars
1MA convert to rand
1S simplification
1S simplification
1CA difference in rand

OR

1A rand per dollar ratio
1MA converting
1S simplification
1S simplification
1CA difference in rand
NPR (5)

F

L3

1.3.3

Change received 
= Rs4 000 - Rs2 440 = Rs1 560    ✓MA
3 × Rs500 = Rs1 500
1 × Rs50 = Rs 50    ✓MA
1 × Rs10 = Rs 10
5 notes      = Rs1 560
          ✓A        ✓O
NOT VALID, 5 is the minimum

1MA difference
1MA breakdown of the change
1A five

1O not valid (4)

F

L4

[35]

QUESTION 2 [38MARKS]

Q/V

Solution

Explanation

T&L

2.1.1

Right-hand side OR Western side  ✓✓A

2A correct side(2)

M&P

L2

2.1.2

(a)

140 mm : 3 500 mm        ✓MA
1 : 3 500 ÷ 140    ✓M
= 1 :25          ✓A

1MA values in correct order
1M dividing by 140
1A simplification (3)

M&P

L3

2.1.2

(b)

Length/Lengte = 6 000 ÷ 25    ✓MCA
= 240 mm ✓CA
= 24 cm ✓C

OR

140 : 3 500
✓M
x : 6 000
3 500 x = 840 000
              ✓CA
x = 240 mm
= 24 cm                  ✓C

CA from 2.1.2(a)
1MCA dividing by scale factor 
1CA length in mm
1C converting to cm

OR

1M concept of proportion
1CA length in mm
1C converting to cm (3)

M&P

L3

2.1.3

Side door area
= 2 000 mm  × 800 mm      ✓SF
= 1 600 000 mm²        ✓A
Garage door area
=  2 400 mm  × 2 100 mm
                      ✓A
= 5 040 000 mm²
Window area = 1 500 mm × 900 mm
= 1 350 000 mm²    ✓A
Total area      ✓M
= (1 600 000 + 5 040 000 + 1 350 000) mm²
= 7 990 000 mm²          ✓MCA

1SF substitution
1A side door area
1A garage door area
1A  window area
1M adding 3 areas
1MCA simplification (6)

M

L2

Q/V

Solution

Explanation

T&L

2.1.4

41 410 000 mm² = 41,410 m²      ✓C
Number of bricks = 41,41 × 68        ✓M
= 2 815,88    ✓CA
Number of pallets = 2 815,88 ÷ 500 ✓M
= 5,63176        ✓S
≈ 6            ✓R

OR

41 410 000 mm² = 41,410 m² ✓C
Area covered by bricks of 1 pallet  ✓M
= 500  = 7,35 m²    ✓CA
    68
Number of pallets = 41,41      ✓M
                                 7,35
= 5,63    ✓S
≈ 6        ✓R

OR

                             ✓C
68 bricks for 1 000 000 mm²
∴41 410 000 mm²  = 41410000 × 68   ✓ M
                                        1000000
             ✓CA
= 2 815,88 bricks
Number of pallets = 2 815,88 ÷ 500 ✓M
= 5,63176    ✓S
≈ 6            ✓R

1C converting to m²
1M multiplying
1CA simplifaction
1M dividing
1S simplification
1R rounding up

OR

1C converting to m²
1M dividing
1CA area
1M dividing
1S simplification
1R number of pallets

OR

1C converting to mm²
1M multiplying
1CA simplifaction
1M dividing
1S simplification
1R rounding up (6)

M

L3

2.1.5

Cost
                           ✓MCA                            ✓M
= R1 685 × 6 + R1 575 + R629,95 + R1 119,95
= R13 434,90              ✓CA
Not valid                        ✓O

CA from Q2.1.4
1MCA brick cost
1M adding 4 values
1CA simplification
1O conclusion
NPR                                  (4)

F

L4

Q/V

Solution

Explanation

T&L

2.1.6

SI = Principal amount × interest rate × time in years
= R35 000 × 8% ×  7   ✓SF
                             12
= R1 633,33        ✓CA
Total to be paid back
= R35 000 + R1 633,33
= R36 633,33        ✓CA
OR
A = P(1 + in)
= R35 000 [ 1 + 8% ×  7 ]   ✓SF
                                 12✓
= R35 000(1,04666…)
≈ R36 633,33        ✓✓ CA

1SF substituting correct values
1CA simplification
1CA simplification

OR

1SF substitution
2CA total amount (3)

F

L3

2.2.1

1 foot = 12 inches
= 12 × 25,4 mm      ✓M
= 304,8 mm
= 0,3048 m      ✓C
∴ 6 m =     6       foot
             0,3048
≈ 19,685 feet   ✓CA
10 feet slopes ½inch
∴D =  19,685 ×  1   ✓ M
              10        2
= 0,98425 inches                 ✓CA
= 0,98425 × 25,4 mm
≈ 25 mm    ✓CA

OR

6 m = 6 000 mm
25,4 mm = 1 inch
6 000 mm = x inches
x × 25,4 = 6 000
                      ✓M
x = 6000  ≈ 236,22 inches  ✓ C
      25,4
236,22 inches
= 236,22  feet  = 19,685 feet     ✓CA
      12
Slope ½ inch for 10 feet
∴D =  19,685 ×  1  ✓M
               10       2
= 0,98425 inches  ✓ CA
= 0,98425 × 25,4 mm ✓CA
≈ 25 mm

OR

½ inch = 12,7mm✓MA
1 foot = 12 inches
∴10 feet  = 120 inches ✓A
               ✓M
∴ 120 × 25,4 = 3 048 mm ✓C
∴ 12,7 mm : 3 048mm
x : 6 000 mm
x  =12,7 × 6000    ✓M
           3048
x = 25 mm ✓ CA

OR

             ✓A
120 inches: 1 inch
                   2
=240:1  ✓S
∴ 6m : D✓M
         ✓M        ✓S
D = 6m  = 0,025m
      240
= 25 mm  ✓C

1M multiplying
1C convert to m
1CA convert to feet
1M dividing and multiplying
1CA simplification
1CA simplification

OR

1M divide
1C convert to inches
1CA convert to feet
1M dividing and multiplying
1CA convert to inches
1CA simplification

OR

1MA use of proportion
1A feet to inches
1M multiply
1C conversion to mm
1M use of proportion
1CA simplification (6)

M

L4

2.2.2

                              ✓A
Volume = 3,142 × (40 cm)² × 1,20 m ✓SF
                      ✓C
= 3,142 × (40 cm)² × 120 cm  ✓S
= 603 264 cm³    ✓C
= 603, 264 ℓ

1A radius
1SF substituting
1C converting height to cm
1S simplification
1C converting to litres (5)

M

L3

[38]

QUESTION [38MARKS]

Q/V

Solution

Explanation

T&L

3.1.1

Local share 
= R410,6 × 20,12%      ✓MA
= R82,61272    ✓CA
E = R453,4 + R410,6 + R82,61272 ✓MCA
≈ R946,6      ✓CA

1MA calculating 20,12%
1CA simplification
1MCA adding
1CA simplification
NPR (4)

F

L2

3.1.2

Percentage increase
                            ✓RT
=  R546,1 − R490,00 ×100%    ✓M
            R490,00
= 11,4489…% ≈ 11,45%  ✓CA

OR

Percentage  ✓RT
R546,10 ÷  R490× 100% = 111,45%
Increase
             ✓M
111,45% - 100% = 11,45%    ✓MCA

1RT reading correct values
1M % increase
1CA simplification

OR

1RT correct values
1M subtracting 100%
1MCA simplification (3)

F

L2

3.1.3

National government sector services the whole country and not just one province. ✓✓O
OR
National government sector assist provinces when the need arises like during drought, or wild fires  ✓✓O
OR
National government sector has more expenses. ✓✓O
OR
National government sector employs more people. ✓✓O

2O explanation (2)

F

L4

Q/V

Solution

Explanation

T&L

3.1.4

Total ratio
= 1 +  4,784 + 5,246 = 11,03    ✓MA
Local sector
           ✓A              ✓MCA
=     1     × R1 240,5billion
   11,03
= R112,466…billion or R112 466 001 800    ✓S
≈ R112,5 billion or  R112 500 000 000

1MA adding ratio values
1A fraction
1MCA multiplying
1S simplification in billions
NPR final answer   (4)

F

L3

3.2

Annual taxable income
= 12 × R46 308,50= R555 702        ✓A
Tax due
                       ✓RT
= R149 475 + 39% (R555 702 - R555 600)        ✓SF
= R149 475 + 39%(R102 )
= R149 514,78      ✓S
Tax payable
= R149 514,78 - R13 500    ✓M
= R136 014,78      ✓CA
Monthly tax
= R136 014,78 ÷ 12
= R11334,565  ≈ R11 334,57    ✓CA

1A annual taxable income
1RT correct tax bracket
1SF substitution or R102
1S simplification
1M subtracting rebate
1CA simplification
1CA monthly tax (7)

F

L3

Q/V

Solution

Explanation

T&L

3.3.1

4 ✓✓A

2A number of boxes (2)

MP

L2

3.3.2

Number of sheets = 2750 ✓M
                                   4
= 687,5        ✓CA
∴ Not enough    ✓O

OR

Number of boxes = 687 × 4 ✓M
= 2 748        ✓CA
∴ Not enough ✓O

OR

Number of boxes per sheet   
= 2750 ✓M
   687    ✓CA
= 4,002911208 > 4

∴ Not enough ✓O

CA from 3.3.1
1M dividing
1CA number of sheets
1O conclusion

OR

1M multiplying
1CA number of boxes
1O conclusion

OR

1M dividing
1CA number of boxes/sheet
1O conclusion (3)

MP

L4

3.3.3

(a)

Income per box 
= R860 000 ✓RT 
       2 000      ✓M
= R430      ✓CA

1RT reading correct value
1M division by 2 000
1CA income per box
[Accept R400 - R430] (3)

F

L2

3.3.3

(b)

                    ✓✓RT
1 280 boxes/kaste

2RT estimation
[Accept  1 250 - 1 300]
[Accept answer by calculation] (2)

F

L3

Q/V

Solution/Oplossing

Explanation/Verduideliking

T&L

3.3.3

(c)

Variable cost per box
= (R680 000 - R320 000) ÷ 2 000
=  R360000     ✓CA
      2 000
= R180    ✓CA
Total Cost = Variable cost + Fixed cost
                                    ✓ MCA
= (R180 × 2750) + R320 000
= R815 000                ✓CA

Income  = R430 × 2750        ✓M
= R1 182 500              ✓CA
Profit  = R1 182 500 - R815 000
= R367 500 ✓CA
Her projection is VALID      ✓O

1CA using ANY TWO cost values or from Q3.3.3.(a)/(b)
1CA value
1MCA multiplying and adding
1 CA calculating cost
1M multiplying by 2 750
1CA income
1CA profit
1O conclusion  (CA from Q3.3.3.(a)/(b)) (8)

F

L4

[38]

QUESTION 4 [39MARKS]

Q/V

Solution

Explanation

T&L

4.1.1

Staff working at the gates need to go home. ✓✓O
The wild animals in the park makes it unsafe to travel or be in unprotected parts during the night.
OR
Animals are not visible in the dark, park/camp gates open when people can see the animals.  ✓✓O 
OR
To avoid overcrowding.  ✓✓O
OR
Access control  ✓✓O 
OR
Security reasons  ✓✓O 
OR
So that people travelling from far or within the Kruger National Park, can plan ahead.  ✓✓O
OR
Accept any other valid answer.  ✓✓O

2O 1^st reason
2O 2^nd reason (4)

D

L4

4.1.2

Skukuza ✓✓A

2A correct camp (2)

MP

L2

4.1.3

Orpen to/na Satara 48 k✓RT
Satara to Lower Sabie  93 km ✓RT
Total distance = 48 km + 93 km = 141 km ✓A

1RT distance to Satara
1RT distance to Sabie
1A total distance (3)

MP

L3

4.1.4

Main camps = 7 ✓RT
Other camps = 5
Difference = 7 - 5 = 2 ✓CA

1RT number of both camps
1CA difference with 1 correct camp
AO                                    (2)

MP

L2

Q/V

Solution

Explanation

T&L

4.1.5

Distance = speed × time
            ✓RT             ✓SF
64 km = 40 km/h × time
Time on gravel road
=  64 km ✓✓S
   40 km/h
= 1,6 h            ✓CA
= 1h36 min    ✓C
Time he will arrive at the gate is
17:03 + 1h36 min
= 18:39        ✓CA

1RT distance
1SF substitution with 40 km/h
1S change the formula
1CA time
1C conversion
1CA arrival time (6)

M

L3

4.1.6

The roads are not so busy / people drive slower / more animals are visible.      ✓✓O
OR
It is the scenic route
OR
The route blends in with nature and gives a more authentic bushveld experience.
OR
Gravel roads gives you more access (short cut) to different parts of the park.
OR
To experience a sense of adventure
Accept any other reasonable answer.

2O reason (2)

MP

L4

4.2.1

                        ✓A
P_Indian/=          6         or  0,00147   or  0,147%
                4 081  ✓A

1A numerator
1A denominator (2)

P

L2

Q/V

Solution/Oplossing

Explanation/Verduideliking

T&L

4.2.2

Coloured Employees 
                          ✓MA
622 - 80 - 141 = 401  or/of 2 111 - (49 + 4 + 1 657) = 401
P_{Coloured level B}
              ✓CA
=    401     or  0,18995   or    19%
    2 111   ✓A

1MA finding the missing value
1CA numerator
1A denominator (3)

P

L3

4.3.1

                            ✓RT            ✓RT
Difference= 260 USD - 80 USD
= 180 USD    ✓CA

1RT Jimbaran  (255 - 265)
1RT Kula (70 - 85)
1CA difference (3)

F

L2

4.3.2

                                 ✓O                    ✓O
The percentage occupancy decreased from 2011 to 2013 but increased again in 2014

1O decrease
1O years
1O increase
1O year (4)

D

L4

4.3.3

The average daily rates in Ubud had a increase. ✓✓O
It affected the occupancy negatively or the occupancy percentage went down.    ✓✓O

2O magnitude of the increase
2O effect on the occupancy percentage (4)

D

L4

4.3.4

The first part of the graph represents the years 2010 to 2014/ or number of years.    ✓✓O
The second part of the graph represents Year to Date of September 2014 and September 2015 or the second part represents only ONE year from September to September the next year. ✓✓O

2O explanation of the first part
2O explanation of the second part.
[Accept There is no relationship between the two parts of the graphs but Max 2 marks] (4)

D

L4

[39]

TOTAL :150