Maths Literacy Paper 2. Maps, plans, measurement.

Read this first

This guide is built from the Grade 12 Mathematical Literacy Paper 2 preparation broadcast of 4 September 2026, presented by the Gauteng Department of Education in collaboration with the Sci-Bono Discovery Centre. It went out the afternoon after learners wrote Paper 1, and its purpose was narrow and practical: make sure nobody walks into Paper 2 having revised the wrong topics.

It does three things. It sets out which topics Paper 2 actually tests and how the paper is built, it drills the conversions the presenter called the foundation of the whole paper, and it works six exam-type questions end to end.

On the memos. Every memorandum on the Exam paper tab is the solution as it was worked in the broadcast. It is a worked solution, not an official DBE memorandum, and the mark allocations shown are typical rather than official, since the presenter did not state them.

What Paper 2 actually tests

Paper 2 is out of 150 marks. Two topics carry almost all of it.

Topic	Share of the paper	Roughly
Maps, plans and other representations of the physical world, or just maps and plans	about 40%	about 60 marks
Measurement	about 55%	about 82 marks
Probability	about 5%	7 to 8 marks
Finance, if the examiner includes it	about 5%	a handful of marks

A note on those percentages. As stated in the broadcast they add up to more than 100%, so treat them as the presenter's working estimates rather than a strict split. The two figures that matter and that do reconcile against 150 are maps and plans at roughly 60 marks and measurement at roughly 82. The message underneath is not arithmetic: maps and plans plus measurement is where essentially the whole paper lives.

How the paper is built

The presenter's advice was to look at any recent Paper 2, final, prelim or June, because the shape barely changes:

Question	What it holds
Question 1	The easiest questions in the whole paper, about 30 marks. Percentages, ratios, counting off a plan, straightforward conversions.
Question 2	Maps and plans.
Question 3	Measurement.
Question 4	A combination of maps and plans with measurement.
Question 5, if there is one	Also a combination of the two.

The single most useful target in the lesson. Question 1 is roughly 30 marks of the easiest material in the paper. You should be walking away with at least 90% of question 1, which is 27 marks or better, and ideally all 30. Marks dropped in question 1 are the most expensive marks in the paper, because they were free.

Two extra notes on scope. Probability was already revised for Paper 1 and the concept does not change, so it needs no separate study. The same goes for finance. And growth charts can appear in either paper: the two papers are set by different panels who do not know what the other has set, so a growth chart in Paper 1 does not rule one out in Paper 2.

Maps and plans: the types you must name

The examiner can simply ask you to name the type of map or plan shown. That is a free two marks if you know the list.

Type	What it shows
National map	The whole country: national roads, all the provinces.
Provincial or regional map	One province lifted out of the national map: its towns, its capital, the national and regional roads running through it. Provincial and regional often mean the same thing in practice.
Strip chart	A route drawn as though it were straight, showing the distance between any two towns along it.
Street map	A town or city showing street names and well-known places.
Elevation map	The ups and downs of a road. Heights are given as altitude above sea level, because the sea is level everywhere and so makes a fair reference point.
Seating plan	How seats are arranged, for example the desk arrangement in an exam room.
Layout plan	How furniture and fittings are arranged in a room: where the bed faces, where the couches sit, which way the bathroom tap points. It is decided when the plan is designed, not on moving day.

Reading roads off a map

The letter tells you the class of road:

• N followed by a number, for example N1: a national road.
• R followed by a number, for example R21: a regional road.
• M followed by a number, for example M1: a municipal road.

The maps and plans skills checklist

• Explain the meaning of a given scale in words, and in context.
• Identify the type of scale: a number scale such as 1 : 100, or a bar scale.
• Identify and name national, regional and municipal roads.
• Name the route to travel between two locations, and the towns along that route.
• Measure and calculate the distance between two towns.
• Explain the terms floor plan, elevation plan and layout plan.
• Read dimensions, meaning lengths and breadths, straight off a plan.
• Measure with a ruler in millimetres or centimetres, then convert to a real distance.

The ruler trap. Start measuring at the zero mark, not at the physical end of the ruler. On many rulers the zero sits a small distance in from the edge, and starting at the edge puts every measurement out by the same amount.

The unit trap. You measure in millimetres or centimetres, but the answer is almost never in those units. For a map the actual distance is usually kilometres, sometimes metres. For a house plan it is metres.

Conversions: the foundation of Paper 2

The presenter said this more plainly than anything else in the lesson: if you struggle with conversions, you will find Paper 2 very challenging. Conversions are not a topic in Paper 2, they run underneath every other topic in it.

Metric to metric: know these by heart

These are never given. Whatever method you use, King Henry, Kilimanjaro or your own, it has to be automatic before you sit down.

Quantity	Relationship	Going up in size	Going down in size
Length	1 cm = 10 mm	mm to cm: divide by 10	cm to mm: multiply by 10
	1 m = 100 cm	cm to m: divide by 100	m to cm: multiply by 100
	1 m = 1 000 mm	mm to m: divide by 1 000	m to mm: multiply by 1 000
	1 km = 1 000 m	m to km: divide by 1 000	km to m: multiply by 1 000
Mass or weight	1 g = 1 000 mg	mg to g: divide by 1 000	g to mg: multiply by 1 000
	1 kg = 1 000 g	g to kg: divide by 1 000	kg to g: multiply by 1 000
	1 t = 1 000 kg	kg to t: divide by 1 000	t to kg: multiply by 1 000
Capacity	1 l = 1 000 ml	ml to l: divide by 1 000	l to ml: multiply by 1 000
	1 kl = 1 000 l	l to kl: divide by 1 000	kl to l: multiply by 1 000

In Mathematical Literacy mass and weight mean the same thing.

What you do NOT have to memorise. Every imperial and cooking conversion factor is given in the paper: feet and inches, yards, pounds and ounces, fluid ounces, cups, teaspoons and tablespoons. You are not expected to know that 1 inch is 25.4 mm. You are expected to know how to use a factor you are handed. Do not waste tonight memorising them.

Volume, capacity and mass of water: the chain that catches people

This chain turns up whenever a tank or container is involved, and every step is a one-to-one swap with no arithmetic at all:

1 cm³ = 1 ml, and for water 1 ml = 1 g, then 1 000 g = 1 kg.

So a volume in cm³ is the same number in ml, and the same number in grams, and only the final step to kilograms involves dividing.

Time

Unit	Equals	Unit	Equals
1 minute	60 seconds	1 year	12 months, 365 days
1 hour	60 minutes	1 leap year	366 days
1 day	24 hours	1 decade	10 years
1 week	7 days	1 century	100 years
1 fortnight	2 weeks	1 millennium	1 000 years
1 month	about 4 weeks	1 school week	5 days, but only if the examiner says so

Clocks

• Analogue clock: hands. You cannot tell 12-hour from 24-hour format on it.
• Digital clock: numbers. You can tell the format.
• 12-hour format carries a.m. or p.m. So 10:23 p.m.
• 24-hour format never carries a.m. or p.m., because the number already says it. The same time is written 22:23. After midday the hours run 13, 14, 15 and on to 23.

Elapsed time

The time difference, also called elapsed time, is ending time minus starting time. From 07:45 to 10:30 you subtract 07:45 from 10:30.

Temperature

The conversion formula between degrees Celsius and degrees Fahrenheit is given. The trap is that examiners will hand you the formula written one way round and then ask for the conversion the other way round. Do not assume the formula points in the direction of the question. Read what is asked, then rearrange the given formula if you have to.

Measurement

You must be able to calculate perimeter, area, total surface area and volume. The good news is that the formulas are given in almost every case, so the marks are in the substitution rather than in recall.

The one rule that governs every measurement question. Everything you substitute into a formula must be in the same unit, and that unit is dictated by the unit the answer must be in. If the answer must be in m², every value you substitute must be in metres. If the answer must be in cm³, everything goes in as centimetres. A length in metres and a breadth in centimetres cannot go into the same formula as they stand.

Radius and diameter

Simple, and constantly confused in both directions:

• Radius to diameter: multiply by 2.
• Diameter to radius: divide by 2.

Speed, distance and time

Speed = distance ÷ time. The examiner may give you the formula arranged as time = distance ÷ speed and then ask for the distance, so be ready to rearrange to distance = speed × time.

Rounding

• Look at the digit after the place you are rounding to. If it is 5 or more the digit goes up; if it is 4 or less it stays.
• When a conversion factor is given to four decimal places, use all four. Never round the factor before you calculate. Round once, at the end.
• Quantities you have to buy are rounded up, whatever the digit says. If a job needs 1.267 litres of paint you buy 2 litres, because 1 litre is not enough.

The calculator

Take the same calculator you practised on, the same model. An unfamiliar machine in an exam costs time and accuracy.

Activity diagrams

The figures for the worked questions, redrawn. These are reconstructions built to the numbers given in the broadcast, not copies of the original exam figures. Work the questions on the Exam paper tab with these in front of you.

The curved dashed line is the swing of the door, which is what tells you whether it opens clockwise or anticlockwise.

The rubber band runs all the way around the edge, so its length is the circumference of the mirror.

Because the bottom is not painted, the surface area is one circle plus the curved side, not two circles.

Convert the dimensions before you substitute, not after. It is far less work.

Altitudes are given above sea level. The change from one point to the next is what "uphill" and "downhill" mean on the table beside the map.

Question 1 worked: the layout plan

A layout plan of a classroom used for examinations. Desks are marked with the grade sitting at them. This is the "giving away marks" question: four sub-questions, and none of them needs anything beyond counting, a ratio and one conversion.

1.1 Determine the number of learners writing in this room. (2)

Count the occupied desks. One desk is empty, so it does not count.

21 learners

That is all. Two marks for careful counting.

1.2 Write the number of Grade 8 learners to the number of Grade 11 learners as a ratio in simplified form. (2)

Count each grade first: 9 Grade 8 and 12 Grade 11. Check against the total: 9 + 12 = 21, which matches 1.1.

Unsimplified ratio: 9 : 12

Divide both parts by the highest number that goes into both, which is 3:

3 : 4

If the question had asked for a unit ratio instead, one of the two numbers must become 1. Divide both parts by whichever side must become 1:

• Divide by 9: 9 : 12 becomes 1 : 1,33
• Divide by 12: 9 : 12 becomes 0,75 : 1

If the examiner specifies which side carries the 1, divide by that side. If not, either is acceptable. Simplified form and unit ratio are not the same thing: stop at 3 : 4 unless the words "unit ratio" appear.

1.3 Is the door opening clockwise or anticlockwise? (2)

Think of an analogue clock. Hands moving left to right across the top are moving clockwise; the opposite direction is anticlockwise.

On a plan the door is drawn with a quarter-circle arc showing its swing. Follow the arc from the hinge and compare it with the direction of a clock hand.

Clockwise, for the plan in the broadcast.

Read the swing on your own diagram rather than memorising the answer. Which way the door opens depends entirely on which side the hinge sits and which way the arc curls.

1.4 Convert the longer side of the classroom wall to millimetres. (2)

The two sides given are 8,5 m and 7,9 m, so the longer one is 8,5 m.

1 m = 1 000 mm, so metres to millimetres means multiply by 1 000.

8,5 × 1 000 = 8 500 mm

If you prefer to set it out as cross multiplication: 1 m is to 1 000 mm as 8,5 m is to ?, giving ? = 8,5 × 1 000.

Question 2 worked: the circular mirror

Circular mirrors are being installed in a staff bathroom, edged with a black rubber band to make them safer. The drawing is to a scale of 1 : 5 and the radius is 15,35 cm.

2.1 Explain the meaning of the scale in this context. (2)

A number scale of 1 : 5 means one unit on the drawing stands for five units in real life. Because the question says in this context, you must name the object:

One unit on the picture of the mirror represents 5 units of the actual mirror in reality.

Without "in context" you could stop at "one unit on the picture is the same as five units in reality". The word context is what forces you to mention the mirror. Note that a scale is unitless: it holds whether you measure in millimetres or centimetres.

2.2 Determine the diameter of the mirror to the nearest cm. (3)

You are given the radius, not the diameter. Radius to diameter means multiply by 2.

d = 15,35 × 2 = 30,7 cm

"To the nearest cm" means round to a whole number. The digit after the comma is 7, which is 5 or more, so the 30 goes up.

31 cm

2.3 Calculate the length of the black rubber band. (3)

The band runs around the edge of the mirror, so its length is the circumference. The formula is given: circumference = 2 × π × radius, with π = 3,142.

C = 2 × 3,142 × 15,35

C = 96,4594 cm

The examiner specified neither a unit nor a rounding here, so leaving the full answer in centimetres is correct. If you do round, round correctly: 96,5 to one decimal place, 96,46 to two. A carelessly rounded answer can be penalised where an unrounded one would not.

2.4 Hence define the term circumference in this context. (2)

In general, circumference is the total length around a circle or circular shape. Again the question says in context, so name the object:

The total distance around the edge of the mirror.

The pattern is worth learning because it repeats: take the general definition, then swap the generic noun for the object in the question.

Question 3 worked: the hiking trail map

A group hikes the Medicine Route Trail at a resort. The information board gives the round trip as 7,5 miles. A map shows the trails as dotted lines, the roads, and symbols for facilities.

3.1 Identify the trail that crosses Old Northeast Road. (2)

Trace each dotted trail and see which one actually crosses the road rather than stopping at it. The Medicine Route Trail ends at the road; the other continues over it.

Castle Trail

Naming it "Castle" is enough. This is a reading question, not a calculation.

3.2 Convert the round trip distance to kilometres, rounded to two decimal places. (3)

The conversion factor is given: 1 km = 0,6214 miles. It is given to four decimal places, so use all four. Never round a given factor before calculating.

Set it up: 1 km is to 0,6214 miles as ? km is to 7,5 miles.

? = 7,5 ÷ 0,6214 = 12,0695…

Two decimal places: look at the third decimal, which is 9, so the second decimal goes up from 6 to 7.

12,07 km

3.3 Determine the probability of finding a restroom on the Medicine Route Trail. (2)

Follow the Medicine Route Trail on the map and look for the restroom symbol along it. There is none.

0, or equivalently 0%.

A probability of 0 means the event is impossible. Note how little probability there is in Paper 2: this is the kind of thing the 7 or 8 marks are spent on.

Question 4 worked: the steel drum

A cylindrical steel drum stores oil and must be painted red. The bottom will not be painted. The diameter is 0,584 m and the height is 89 cm. One litre of paint covers 3 m².

4.1 Determine the radius of the drum. (2)

Diameter to radius means divide by 2.

r = 0,584 ÷ 2 = 0,292 m

This is the single most commonly reversed step in the topic. Diameter divided by two gives the radius; radius times two gives the diameter.

4.2 Two coats will be applied. Calculate, to the nearest litre, the paint needed. (5)

Step 1, get the units to agree. The radius is in metres and the height is in centimetres, and the paint coverage is per square metre, so everything must be in metres.

89 cm ÷ 100 = 0,89 m

Step 2, surface area. The bottom is not painted, so it is one circle plus the curved side: SA = πr² + 2πrh.

First part: 3,142 × 0,292² = 0,267899488

Second part: 2 × 3,142 × 0,292 × 0,89 = 1,63308592

SA = 1,900985408 m². Do not round yet; this is not the final answer.

Step 3, two coats. 1,900985408 × 2 = 3,801970816 m²

Step 4, paint needed. 1 litre covers 3 m², so divide:

3,801970816 ÷ 3 = 1,267… litres

Step 5, round. 2 litres.

This is the step that catches people. Normal rounding would give 1, because 1,267 is nearer to 1 than to 2. But you cannot paint the drum with 1 litre: you need more than 1, so you must buy 2. Quantities you have to purchase always round up. The presenter corrected himself on air on exactly this point.

2 litres

4.3 Verify whether the claim that the volume is 238 430,5 cm³ is correct. (4)

Read the unit of the answer first. It is cm³, so everything substituted must be in centimetres, not metres.

Radius: 0,292 m × 100 = 29,2 cm. Height: 89 cm, already correct.

V = πr²h = 3,142 × 29,2² × 89

V = 238 430,5443… cm³

Rounded to one decimal place that is 238 430,5 cm³, which matches the claim.

The claim is correct.

Write the conclusion down. On a "verify" question there is a mark specifically for the concluding statement. Doing the arithmetic and stopping loses it.

Question 5 worked: body mass index

BMI is calculated with a given formula, and a table classifies weight status. The person has a mass of 90 kg and a height of 173 cm.

5.1 Determine the BMI, rounded to one decimal place. (3)

The formula is given: BMI = mass in kg ÷ (height in m)². The formula itself states that the height must be in metres, so the examiner is expecting a conversion.

173 cm ÷ 100 = 1,73 m

BMI = 90 ÷ 1,73² = 30,0711…

One decimal place: the next digit is 7, which is 5 or more, so the 0 goes up to 1.

30,1 kg/m²

5.2 Write down the weight status of this person. (2)

Read 30,1 against the classification table. It sits just above 30.

Obesity

5.3 Explain why it is important to know your weight status. (2)

So that you can monitor your health. A status outside the normal band of 18,5 to 24,9 is a signal to act: underweight may point to illness, and overweight or obese carries its own health risks. Knowing where you sit is what lets you do something about it.

Explanation questions like this want a reason, not a restatement. "Because it tells you your weight status" scores nothing.

Question 6 worked: the backup water tank

A household on municipal water installs a backup tank. Available sizes are 707 l, 950 l, 1 000 l, about 2 050 l, 2 450 l and 2 500 l. Global water usage is 173 l per person per day. The tank considered is 1 400 mm in diameter and 1 800 mm high.

One figure to check. The fourth tank size was garbled in the auto-generated transcript. It has to be a size below 2 076 l for the presenter's conclusion in 6.2 to hold, so it is shown here as about 2 050 l. Check it against your own paper.

6.1 Determine the maximum water two people would use in a day without exceeding the global usage. (2)

173 l per person per day, for two people:

173 × 2 = 346 litres

6.2 Verify the claim that the smallest suitable tank for at least 6 days is the 2 450 l tank. (4)

Water needed for 6 days at 346 l per day:

346 × 6 = 2 076 litres

Now test the available sizes against 2 076 l. The sizes below it, 707, 950, 1 000 and about 2 050, are all too small. The smallest size that holds at least 2 076 l is the 2 450 l tank.

The claim is correct.

Again, say so explicitly. A verify question wants the conclusion stated.

6.3.1 Determine the volume of the water tank in cm³. (4)

Convert first, substitute second. The answer must be in cm³, so get the radius and the height into centimetres before touching the formula. It is far less work than converting a volume afterwards.

Radius: 1 400 mm ÷ 2 = 700 mm, then 700 ÷ 10 = 70 cm

Height: 1 800 mm ÷ 10 = 180 cm

V = πr²h = 3,142 × 70² × 180

V = 3,142 × 4 900 × 180

V = 2 771 244 cm³

6.3.2 Determine the weight, in kilograms, of the water that fills the tank. (3)

This is the volume to mass chain, and two of its three steps involve no arithmetic at all.

Step 1. 1 cm³ = 1 ml, so 2 771 244 cm³ = 2 771 244 ml. The number does not change.

Step 2. For water 1 ml = 1 g, so that is 2 771 244 g. Again the number does not change.

Step 3. Grams to kilograms: divide by 1 000.

2 771,244 kg

Only the last step is a calculation. Learners lose marks here by trying to convert at each stage as though every step needed a factor.

The terminology baseline

The lesson opened with a matching exercise on definitions, the kind that opens a real paper. These are the pairings as worked in the broadcast:

Term	Definition
Street map	A map of a small area such as a town or city
Metric system	A system of measurement that uses metres, litres and kilograms
Surface area	The area of all the faces of an object added together
Growth chart	A graph consisting of a series of percentile curves

The method the presenter modelled matters as much as the answers: read every option before committing, even when you are confident, and even for the last item where only one option remains.

One pairing to check with your teacher. The broadcast matched "an event" to "the likelihood of something happening or not happening", having read past the option "something that may or may not occur when an action is performed". In standard Mathematical Literacy usage those are the wrong way round: an event is something that may or may not occur, while probability is the likelihood of it happening. The original table is not visible in the transcript, so this may be an artefact of how the options were listed. Learn the standard distinction, and query it if a memo says otherwise.

Marks learners lose most, and what to do instead

What goes wrong	Where it bites	Do this instead
Substituting values that are in different units	Every area, surface area and volume question	Let the unit of the required answer decide, and convert everything to it before substituting
Rounding a given conversion factor before calculating	Metric to imperial	Use every decimal place given. Round once, at the end
Rounding a purchase quantity down	Paint, tiles, tins, bags	Round up. 1,267 litres of paint means buying 2 litres
Confusing radius and diameter, in either direction	Circles and cylinders	Diameter divided by 2 gives radius. Radius times 2 gives the diameter
Doing a verify calculation but not stating the conclusion	Any "verify the claim" question	Write "the claim is correct" or "not correct". There is a mark for it
Answering a define-in-context question generically	Scale, circumference, any definition	Give the general definition, then name the object from the question
Giving a unit ratio when simplified form was asked, or the reverse	Ratios in question 1	Simplified means divide by the common factor. Unit means make one side equal 1
Measuring from the end of the ruler	Measuring on maps and plans	Start at the zero mark, which is often set in from the edge
Assuming a given formula points the way the question asks	Temperature, speed and distance	Read the question first, then rearrange the given formula if needed
Converting at every step of the volume to mass chain	Tanks and containers	1 cm³ = 1 ml = 1 g for water. Only grams to kilograms is a calculation
Dropping marks in question 1	The first 30 marks	These are the cheapest marks in the paper. Slow down and bank all of them

What the lesson did not get to

The presenter ran out of time and said so plainly, along with a warning worth repeating: do not try to spot the examiner. Prepare everything.

• Worked examples on bar scales and calculating actual distance from a measured map distance.
• Elevation plans and floor plans as exam questions, rather than as definitions.
• Packaging calculations, which were listed as required but not demonstrated.
• Speed, distance and time worked through, beyond the rearranging warning.
• Growth charts, which can appear in either paper.
• Finance in Paper 2, and imperial to metric conversion questions.

One-page summary

• The split. Maps and plans about 60 marks, measurement about 82, probability 7 to 8. Almost the entire paper is the first two.
• The shape. Four or five questions. Question 1 is about 30 easy marks and you should take at least 90% of it. Question 2 maps and plans, question 3 measurement, questions 4 and 5 a mixture.
• Map types. National, provincial or regional, strip chart, street, elevation, seating plan, layout plan.
• Roads. N is national, R is regional, M is municipal.
• Scale. Number scale or bar scale. Explain it as "one unit on the drawing represents n units in reality", and name the object when asked in context.
• Memorise the metric conversions. Length, mass and capacity. Imperial and cooking factors are always given.
• The water chain. 1 cm³ = 1 ml, 1 ml = 1 g, 1 000 g = 1 kg.
• Radius and diameter. Divide by 2 one way, multiply by 2 the other.
• The unit rule. The unit of the required answer decides what unit everything gets converted to before substitution.
• Rounding. 5 or more rounds up. Never round a given factor early. Purchases always round up.
• Verify questions need a stated conclusion, and it carries its own mark.
• Define in context means the general definition with the object of the question named in it.
• Take the calculator you practised on, the same model.

Source: Grade 12 Mathematical Literacy Paper 2 preparation broadcast, 4 September 2026, Gauteng Department of Education with the Sci-Bono Discovery Centre. Solutions transcribed and worked as presented. Not an official DBE memorandum. Diagrams are reconstructions built to the figures quoted in the lesson.