Symbol

Explanation

M

Method

M/A

Method with accuracy

MCA

Method with consistent accuracy

CA

Consistent accuracy

A

Accuracy

C

Conversion

S

Simplification

RT/RG/RM

Reading from a table OR Reading from a graph OR Read from map

F

Choosing the correct formula

SF

Substitution in a formula

J

Justification

P

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

R

Rounding off OR Reason

AO

Answer only

NPR

No penalty for rounding

QUESTION 1 [37]

Ques.

Solution

Explanation

Level

1.1.1

Amount used for 3 batches = 3 × 125         MA
= 375 mℓ
Number of cups = 375 MA
                             250
= 1,5 cups OR 1½ cups        A

• 1MA Multiplying correct values
• 1MA Dividing by 250
• 1A Number of cups  (3)

M L2

1.1.2

Price of 3 eggs = 14,99 M
                               12
= R1,249166667 × 3M
= R3,7475 S
≈ R3,75 CA

• 1M Dividing by 12
• 1M Multiply by 3
• 1S Simplification
• 1CA Cost (4)

F L3

1.1.3

°Fahrenheit = 1,8 × °Celsius + 32°
= 1,8 × 180° + 32°SF
= 356°F – 330°FM
= 26°F

• 1SF Substitute correct °C
• 1M Subtract correct values  (2)

M L2

1.1.4

Time taken for 9 batches = 25 min + 45 min  
               MA
=  70 min ×   9
= 630 min   CA
Time in hours and minutes = 10 hours 30 min      C
Time completed = 09 hours 15 min + 10 hours 30 min     M
= 19:45     CA
Not valid   O

• 1MA Total time for preparation and baking
• 1CA Total time for 9 batches
• 1C Convert to hours and minutes
• 1M Adding time 1CA Time completed
• 1O Not valid   (6)

M L4

1.1.5

Cake flour = 3 × 250 = 150 grams
                    5
Cost of cake flour in grams = 21,99 M
                                               2500 
= 0,008796 × 50 × 9
= R11,87 
Cost of oil in millilitres = 35,99
                                       2000
= 0,017995 × 125 × 9
= R20,24 
Cost of eggs = 14,99
                          12
= 1,249166667 × 3 × 9
= R33,73CA
Total cost = R11,87 + R20,24 + R33,73
= R65,84 CA

Invalid O

OR

Cake flour = 3 × 250 = 150 grams 
                    5
Cost for cake flour in kg = 21,99 M
                                            2,5
= 8,796 × 0,15 × 9 M
= R11,87 CA
Cost of oil in litre = 35,99
                                 2
= 17,995 × 0,125 × 9
= R20,24 
Cost of eggs = 14,99
                          12
= 1,249166667 × 3 × 9
= R33,73 
Total cost = R11,87 + R20,24 + R33,73
= R65,84 

Invalid O

• 1C mℓ to gram
• 1M Dividing
• 1C kg to g
• 1MCA Multiply by 150 and 9

• 1CA Cost of flour
• 1CA Cost of oil
• 1CA Cost of eggs CA from 1.1.2
• 1CA Total cost
• 1O Invalid

• 1C mℓ to gram
• 1M Dividing 1C g to kg
• 1M Multiply by 0,15 and 9
• 1CA Cost of flour
• 1CA Cost of oil
• 1CA Cost of eggs CA from 1.1.2
• 1CA Total cost 1O Invalid      (9)

F&M L4

1.2.1

7 feet 8 inches = (7 × 0,3048)  + (8 × 0,0254) C
= 2,1336 m + 0,2032 m S
= 2,3368 mCA

6 feet 6 inches = (6 × 0,3048) + (6 × 0,0254)
= 1,8288 m + 0,1524 m
= 1,9812 mCA

Length = 2,3368 m + 1,9812 m
= 4,318 m CA

OR

Total feet in metres = 7 feet + 6 feet M
= 13 feet × 0,3048 M
= 3,9624 mCA
Total inches in metres = 8 inches + 6 inches
= 14 inches × 0,0254 C
= 0,3556 m CA
Length = 3,9624 m + 0,3556 m
= 4,318 m CA

• 1C cm to m
• 1M Multiplying and adding
• 1S Simplification
• 1CA Answer
• 1CA Answer
• 1CA Length
• 1M Adding
• 1M Multiply
• 1CA Answer
• 1C cm to m
• 1CA Answer
• 1CA Length    (6)

M L3

1.2.2

Top view A
All features clearly visible R

• 1A View
• 2A Reason (3)

M& P
L4

1.2.3

• People preparing meals in the kitchen.
• People helping to prepare meals.
• People in and out of the kitchen.
• It is frequently visited by all. A

• 2A First reason
• 2A Second reason

M& P L4

QUESTION 2 [39]

Ques.

Solution

Explanation

Level

2.1.1

Simple Interest    
Interest = 280 000 × 0,0975 × 2,916666667 SF
= R79 625 CA

• 1SF Substitution
• 1A Number of years
• 1CA Interest  (3)

F L2

2.1.2

Compound Interest
First year = 280 000 + (280 000 × 0,0825) M
= R303 100 CA
Second year = 303 100 + (303100 × 0,0825)
= R328 105,75 
11 months = R328 105,75 + (R328 105,75 × 0,075625)
= R352 918,75 CA

OR

Amount after 35 months
= 280 000 × 1,0825 × 1,0825 × 1,075625
= R352 918,75
Interest = R352 918,75 – R280 000
= R72 918, 75 CA

She will pay less interest on Option 2 (compound interest)

• 1M Adding and Multiplying
• 1CA Amt 1^st year
• 1CA Amt 2^nd year
• 1A Interest rate for 11 months
• 1CA Total amount
• 1CA Interest
• 1O Option 2
• CA from 2.1.1 (7)

F
L3(6)

L4(1)

2.2.1

Factory 1       M
IQR = 75 000 – 40 000 RD
= 35 000 CA
Median = 60 000

Factory 2
IQR = 80 000 – 35 000 RD
= 50 000 CA
Median = 50 000
Factory 2 performed worse because their IQR is greater and their median is lower O

• 1RD Q1 and Q3
• 1M Concept of IQR
• 1CA IQR
• 1RD Q1 and Q3
• 1CA IQR
• 1A Factory 2
• 1O Comparing median
• 1O Comparing
• IQR’s   (8)

D

L3(5)

L4(3)

2.2.2

No, factory 2 is still new A

• CA from 2.2.1
• 2A No with reason  (2)

D L4

2.3.1

Percentage = 94 MA   ×   100%
                     150 
= 62,7%

• 1MA Dividing correct values
• 1M Multiply by 100 (2)

M L2

2.3.2

Over the length = 310 𝑚𝑚       
                            78 𝑚𝑚 
= 3,97…
≈ 3 coffee mugs 
Over the width = 220 𝑚𝑚
                           78 𝑚𝑚
= 2,8…
≈ 2 coffee mugs CA
Over the height = 150 𝑚𝑚
                             94 𝑚𝑚
= 1,6…
≈ 1 coffee mug CA
Number of mugs in 1 box = 3 × 2 × 1
= 6 coffee mugs CA
Number of boxes = 66
                                6
= 11 boxes CA
Statement invalid O

• 1A Correct diameter
• 1M Divide correct values
• 1A Number of mugs (length)
• 1CA Number of mugs (width)
• 1CA Number of mugs (height)
• 1CA Total
• 1CA Number of boxes
• 1O Invalid   (8)

M

L4

2.4.1

Northeast 
North

• 2A Northeast
• 2A North (4)

M&P L2

2.4.2

Probability = 1A
                     4A

• 1A Numerator
• 1A Denominator (2)

P L2

2.4.3

• Turn left on the N6 in East London to Queenstown A
• Turn right on the R56 to Kokstad A
• Turn left on the N2 A

• 1A Left on N6
• 1A Right on R56
• 1A Left on N2    (3)

M&P L4

QUESTION 3 [36]

Ques.

Solution              A

Explanation

Level

3.1.1

Initial tax = 0,18 × 1958A50
= R35 253

• 1A Use correct %
• 1A Use correct amount     (2)

F L2

3.1.2

Pension = 7,5 × 37 537,75 MA
               100
= R2 815,33125 × 12 MA
= R33 783,98CA
Donation = 575 × 12
= R6 900 A
Total = R33 783,98 + R6 900
= R40 683,98 CA

• 1MA 7,5% of correct value
• 1MA Multiply by 12
• 1CA Pension amount
• 1A Donation amount
• 1CA Total amount  (5)

F L3

3.1.3

Taxable income = (37 537,75 × 12) – R40 683,98
= R450 453 – R40 683,98
= R409 769,02 CA

• CA from 3.1.2
• 1M Multiply by 12
• 1MCA Subtract pension and donations
• 1CA Taxable income  (3)

F L2

3.1.4

Tax payable = 63 853 + 31% of taxable income above 305 850
= 63 853 + 0,31 × (409 769,02 – 305 850)
= 63 853 + 0,31 × 103 919,02
= 63 853 + 32 214,8962
= R96 067,8962 – R14 220
= 81 847,8962 M
           12
= R6 820,66 CA
Invalid OR less than R6 850 O

• CA from 3.1.3
• 1A Correct tax bracket
• 1MCA Amount above
• 1S Simplification
• 1M Subtract rebate
• 1M Divide by 12
• 1CA Monthly tax
• 1O Invalid or Less than    (7)

F L3&4

3.1.5

They receive 3 rebates
OR
Their rebate is higher

• 2A Explanation  (2)

F L4

3.1.6

Gross monthly salary in 2018/2019 = 37 537,75        A
                                                             1,064          MA
= R35 279,84A
OR
A Gross monthly salary in 2018 = 450 453
                                                       1,064 
= R35 279,84A

• 1A Correct gross salary
• 1MA Divide by 1,064
• 1A Gross salary
• CA from 3.1.3
• 1A Correct gross salary
• 1MA Divide by 1,064
• 1A Gross salary      (3)

F V2

3.2.1

Value of A = 90 – (8 + 13 + 30 + 15 + 10)
= 90 – 76 MA
= 14 M
    2
= 7 CA

• 1MA Subtract from 90
• 1M Divide by 2
• 1CA Value of A  (3)

D L2

3.2.2

16 years A

• 2A Age              (2)

D L2

3.2.3

Average age       MCA
= (13 × 8) + (14 × 7)+ (15 × 13)+(16 × 30)+(17 × 15)+(18 × 7)+(19× 10)
                                                      90
= 104 + 98 +195 + 480 + 255 + 126 + 190
                                    90
= 1 448 M
       90
= 16,088… years CA
Statement invalid O

• CA from 3.2.1
• 1MCA Adding correct values
• 1M Dividing
• 1CA Average age
• 1O Not valid         (4)

D L3

3.2.4

Number of boys = 13 + 30 + 15 + 7
Probability = 65 MCA
                     90
= 0,722 R

• CA from 3.2.1
• 1MCA Numerator
• 1CA Denominator
• 1R 3 decimal places   (3)

P L2

3.2.5

The weight of the boys should also be taken into account.A

• 2A Reason         (2)

D L2

QUESTION 4 [38]

Ques.

Solution

Explanation

Level

4.1.1

14,202957 A        R

The lower the value, the stronger the Rand

• 1A Correct value
• 1R Reason  (2)

D L2&4

4.1.2

Amount after exchange fee = 40 830 – (40 830 × 0,045)
= 40 830 – 1837,35 MA
= R38 992,65 CA

At 14,983385 = 38 992,65 MCA
                         14,983385
= $2 602,39 CA
At 14,398064 = 38 992,65
                         14,398064
= $2 708,18CA
Difference = $2 708,18 – $2 602,39
= $105,79 CA
Statement invalidO

OR

At 14,983385 =   40 830     MA
                         14,983385 
= $2 725,018412 (2 725,018412 × 0,045)
= 2 725,018412 – 122,6258285 MCA
= $2 602,39 MCA
At 14,398064 =   40 830
                         14,398064
= $2 835,797924 – (2 835,797924 × 0,045)
= 2 835,797924 – (127,6109066)
= $2 708,18 CA
Difference = $2 708,18 – $2 602,39
= $105,79MCA
Statement invalid O

• 1MA Subtract 4,5%
• 1CA Value
• 1MCA Dividing correct values
• 1CA Dollar value
• 1CA Dollar value
• 1MCA Difference
• 1O Invalid
• 1MA Dividing correct values
• 1CA Value
• 1MCA Subtract 4,5%
• 1CA Dollar Value
• 1CA Dollar value
• 1MCA Difference
• 1O Invalid    (7)

F L3&4

4.1.3

• Political factors A
  OR
• Economic factors A
  OR
• Supply and demand of countries A
  OR
• Inflation rate A

Accept any other relevant responses

• 2A 1^st reason
• 2A 2^nd reason   (4)

D L4

4.2.1

Enlargement:
Northern Line (A) = 7,2 cm A (Accept 7,2 cm – 7,4 cm)
Scale is 4,2cAm = 300 km    (Accept 4,1 cm – 4,4cm)
Distance = 7,2 𝑐𝑚 × 300 km M
                 4,2 𝑐𝑚
= 514,286 kmCA

Map:
Northern Line (A) = 1,5 cmA (Accept 1,4 cm – 1,6 cm)
Scale is A  4,2 cm  = 1 500 km  (Accept 4,1 cm – 4,4 cm)
Distance = 1,5 𝑐𝑚 × 1 500 km
                 4,2 𝑐𝑚
= 535,714 km CA

• 1A Measure A
• 1A Measure scale
• 1M Ratio
• 1CA Kilometres
• 1A Measure line
• 1A Measure scale
• 1CA Kilometres      (7)

L4

4.2.2

Traveller 1 and 2 = $670,36 × 2
= $1 340,72 MA
Traveller 3 and 4 = 0,239 × 670,36 M
= $160,22 × 2
= $320,44 CA
Tax Amount = $188,64 × 4
= $754,56 MA
Total amount = $1 340,72 + $320,44 + $754,56MCA
= $2 415,72 CA

• 1MA Amount for 2 travellers
• 1M 23,9% of 670,36
• 1CA Amount
• 1MA Tax amount
• 1MCA Adding amount
• 1CA Total amount  (6)

F
L3

4.3.1

Range = Highest value – Lowest value
34°F = A - 54°F          M
A = 54°F + 34°F
= 88°F CA

• 1M Concept of range
• 1CA Value of A  (2)

D L2

4.3.2

Probability = 5 A
                    12 A
= 0,416… × 100
= 41,6…
≈ 42% CA

• 1A Numerator
• 1A Denominator
• 1CA Nearest %  (3)

D L2

4.3.3

°Celsius = (°F – 32) ÷ 1,8
= (34°F – 32) ÷ 1,8SF
= 2 ÷ 1,8 S
= 1,1…°C CA
Statement not valid O

• 1SF Substitution
• 1S Simplification
• 1CA °C
• 1O Not valid  (4)

M L2&4

• 1A Jan – Apr
• 1A Jan – Apr
• 1CA May – Aug from 4.3.1
• 1A Sept – Dec