STUDY GUIDE TITLE

At a glance

Paper 2 is the application paper. Three hours, 150 marks, five questions, all compulsory. It draws on three application topics:

Topic	What it looks like in Paper 2
Measurement	Conversions, perimeter, area, volume, surface area, time, speed, distance, cooking and medicine quantities, paint and material coverage
Maps, plans and other representations	Strip charts, national and street maps, seating plans, floor plans, elevation plans, cross-sections, assembly diagrams, scale
Probability	Probability from a plan or map, two-way tables, tree diagrams, combinations

The cognitive-level split is the same as Paper 1: 30% Level 1, 30% Level 2, 20% Level 3 and 20% Level 4. But Paper 2 is where the multi-step questions live. A single sub-question can be worth nine marks and need six separate operations in the right order.

Finance is mostly a Paper 1 topic. It appears in Paper 2 only where money attaches to a measurement, such as the cost of the paint needed to cover a calculated area.

Reading the marks

The same codes run through every marking guideline. In Paper 2 three of them matter more than the rest:

Code	Means	Why it matters most in Paper 2
SF	Correct substitution in a formula	Papers hand you the formula. Writing it out with the numbers in is a mark before you calculate anything.
C	Conversion	Almost every measurement question needs one. Show it on its own line and it is a mark.
CA / MCA	Consistent accuracy	Multi-step questions carry errors forward. One slip costs one mark; the chain keeps earning until the second error.
RT	Reading from a table, map, plan or diagram	Every map question starts with a reading mark.
R	Rounding	An independent mark, and Paper 2 often tells you which way to round.
O	Opinion, explanation, reason	Every "verify" ends with a sentence.

Rules that decide borderline marks

1. Only the first attempt is marked. Cross something out without redoing it and the crossed-out version is what gets marked.
2. Consistent accuracy stops at the second calculation error.
3. A conclusion mark needs working behind it, usually at least a third of the sub-question's marks.
4. Extra readings are penalised. Asked for one town off a map, name one.
5. Use the formula you are given. The examiners note that it tells you which values belong in the calculation.

What the examiners actually saw

Average performance on Paper 2 in 2025 was 52%, almost identical to Paper 1. The shape of it is what matters:

Question	Topic	Average
1	Maps, plans and Measurement	62%
2	Maps and plans	54%
3	Measurement and Probability	57%
4	Measurement, Maps and Probability	50%
5	Measurement, Maps and plans and Probability	36%

Sub-question 5.3 averaged 21% and 5.2 averaged 39%. The paper does not get mathematically harder at the end; it gets longer, and candidates run out of time and patience.

The examiners' recurring complaints

• Confusing floor plan, elevation plan and layout plan. The report recommends teaching all three together so the differences stick.
• Confusing area and perimeter: "the region covered by the shape" against "the distance around the shape".
• Radius and diameter. Candidates halve when they should not, or forget to.
• Unit conversions, especially not knowing whether to multiply or divide, and two-dimensional conversions such as mm² to cm².
• Time against duration. Candidates put a clock time into a speed formula instead of the length of the journey.
• Bar scale measuring. Most could not measure the bar scale and instead worked backwards from a distance they were given.
• Clockwise and anticlockwise, and compass directions on a map.
• Key words missed: "pairs", "both sides", "each". Candidates calculated one side of 48 pairs of earrings instead of both sides of 96 earrings.
• Impossible events. Asked for the probability of something that cannot happen, candidates wrote "no probability" instead of 0.
• Rounding up for capacity. 62,999... passengers is 63, not 62.

Measurement

Conversions

Quantity	Conversion
Length	10 mm = 1 cm, 100 cm = 1 m, 1 000 m = 1 km
Mass	1 000 mg = 1 g, 1 000 g = 1 kg, 1 000 kg = 1 ton
Volume and capacity	1 000 ml = 1 litre, 1 000 cm³ = 1 litre, 1 000 litres = 1 m³
Area	1 m² = 10 000 cm², 1 cm² = 100 mm², 1 km² = 1 000 000 m²
Imperial length	1 inch = 2,54 cm, 1 foot = 12 inches = 0,3048 m, 1 mile = 1,609 km
Cooking	1 teaspoon = 5 ml, 1 tablespoon = 15 ml, 1 cup = 250 ml
Temperature	°C = 5/9 × (°F − 32)

Area conversions are not the same as length conversions. Because area is two dimensional, the factor is squared: 1 m = 100 cm, but 1 m² = 100² = 10 000 cm². The diagnostic report singles this out.

Direction rule: going to a smaller unit, multiply. Going to a bigger unit, divide.

Perimeter, area, volume and surface area

Shape	Formula
Perimeter of a rectangle	2 × (length + width)
Circumference of a circle	2 × π × radius, or π × diameter
Area of a rectangle	length × width
Area of a triangle	½ × base × height
Area of a circle	π × radius²
Volume of a rectangular prism	length × width × height
Volume of a cylinder	π × radius² × height
Surface area of a closed cylinder	2 × π × radius² + 2 × π × radius × height
Surface area of an open cylinder (no lid)	π × radius² + 2 × π × radius × height

The papers use π = 3,142 unless they say otherwise. Watch the difference between a closed and an open container: a tin-can lantern with the top cut off has one circle, not two.

Radius = diameter ÷ 2. Formulas are almost always written with the radius, and questions almost always give you the diameter.

Coverage and how much to buy

The standard chain is: area → divide by the spread rate → multiply by the number of coats → divide by the tin size → round up → multiply by the price.

The rounding up is the step that is missed. You cannot buy 3,2 tins of paint, so you buy 4.

Time, distance and speed

• Speed = distance ÷ time, Distance = speed × time, Time = distance ÷ speed.
• The time in the formula is a duration, not a clock time. From 09:15 to 11:45 is 2,5 hours, not 11,45.
• Convert minutes to hours by dividing by 60. 34 minutes is 34 ÷ 60 = 0,5667 hours, not 0,34.
• 36 hours and 6 minutes is 36,1 hours, because 6 ÷ 60 = 0,1.
• Adding time: 12:36 + 34 minutes = 13:10. Carry at 60, not at 100.

Maps, plans and other representations

Know the seven representations

Type	Shows
Floor plan	The top, aerial or bird's-eye view of how the rooms are arranged
Elevation plan	The outside of the building seen from one side
Cross-section	A cut through the building showing what is inside, such as the staircase between floors
Layout plan	How the furniture and fittings inside a space are arranged
Seating plan	How seats are arranged, in a cinema, bus or exam room
Strip chart or strip map	A route drawn as though it were straight, with the distance between the places on it
Street, national or regional map	Roads, towns and routes, with a scale and a compass

Scale

• A number scale or ratio scale is written 1 : 115. One unit on the plan represents 115 of the same units in reality.
• A bar scale, also called a line scale or graphical scale, is a small ruler printed on the map. It is the one that stays correct when the map is resized, which is exactly what the Mpumalanga paper asks.
• To find a scale: measure the map distance, convert both to the same unit, then simplify to 1 : something. 210 mm on a map representing 580 km becomes 210 mm : 580 000 000 mm, which is 1 : 2 761 904, or 1 : 2 800 000 to the nearest hundred thousand.
• To find a real distance: measure in mm, then multiply by the scale number, then convert.

Direction and route

• Compass: north at the top unless the map says otherwise. North-west is up and to the left.
• Describing a route earns a mark per instruction, so give turns and landmarks, not just "go to the room".
• Clockwise follows the hands of a clock. Trace it with a finger before answering.

Probability

• Probability = favourable outcomes ÷ total outcomes. Give it in the form asked for: fraction, decimal, percentage, or in words.
• In words: impossible (0), unlikely, even chance, likely, certain (1).
• If the event cannot happen, the answer is 0 or 0% or "impossible". Writing "no probability" scores nothing.
• A tree diagram and a two-way table both list every outcome. With 2 popcorn sizes, 3 drinks and 2 sweets there are 2 × 3 × 2 = 12 combinations.
• "and" narrows, "or" widens, "except" means count the whole set and take the excluded ones away.
• Probability questions in Paper 2 often sit on top of a map or a plan: the probability that a randomly chosen room is a theatre, or that a spectator can watch at a water point.

Command words: what the question is actually asking

Word	What to write
Write down / Name / Identify / State	The answer alone. Answer only usually earns full marks.
Measure	Use a ruler on the printed page. The memo accepts a small range, for example 92 to 94 mm.
Determine / Calculate	Show the working, starting with the formula and the substitution.
Describe the route	One instruction per mark, naming turns and landmarks.
Define / Explain	A sentence. This is an O mark.
Verify / Show that	Calculate independently, compare against the claim, then write VALID or NOT VALID, CORRECT or INCORRECT.
Hence	Carry your previous answer forward rather than starting again.

Show me a multi-step measurement answer that scores full marks

Question: The area to be painted is 60,45 m². The spread rate is 1 m² per 0,1 litre. Two coats will be applied. Paint is sold in 5 litre tins at R500 each. Calculate the cost of the paint needed. (9)

Paint for one coat = 60,45 × 0,1 = 6,045 litres (MA, A)
Paint for two coats = 6,045 × 2 = 12,09 litres (MCA, CA)
Number of tins = 12,09 ÷ 5 = 2,418 (MCA, CA)
Tins to buy = 3 (R, the rounding up)
Cost = 3 × R500 = R1 500 (MCA, CA)

Nine marks, and two of them are just for rounding up and multiplying by the price. Candidates who buy 2,418 tins lose the last three.

The nine traps that cost the most marks

1. Diameter used where the formula wants radius. Halve it first.
2. Area conversions done as length conversions. 1 m² is 10 000 cm², not 100.
3. Not rounding up when buying tins, packets, taxis or seats.
4. Clock time put into a speed formula instead of the duration.
5. Minutes treated as decimals. 6 minutes is 0,1 hours, not 0,06.
6. Closed and open containers confused in surface area.
7. "Pairs" and "both sides" ignored. Read the question twice for quantity words.
8. No conclusion sentence on a verify question.
9. Units left off the final answer, or the wrong unit given. A penalty applies.

The last thirty minutes

Question 5 averaged 36% and its last sub-question averaged 21%. Two practical moves:

• Bank Question 1 fast. It is the short-context, Level 1 question and averaged 62%. Terminology, a measurement or two, and a plan reading.
• Write the formula and the substitution even when you cannot finish. SF is a mark on its own, and so is the conversion line above it.

One-page summary

Thing	Rule
Radius	diameter ÷ 2
Circumference	π × diameter, with π = 3,142
Area of a circle	π × radius²
Volume of a cylinder	π × radius² × height
Surface area, closed cylinder	2πr² + 2πrh
1 m²	10 000 cm²
1 000 cm³	1 litre
1 inch / 1 foot / 1 mile	2,54 cm / 0,3048 m / 1,609 km
Speed	distance ÷ duration
Minutes to hours	÷ 60
Paint or material	area → spread rate → coats → tin size → round up → price
Number scale 1 : 115	one unit on the plan is 115 units in reality
Bar scale	the one that stays correct when the map is resized
Floor plan	top view of the room arrangement
Elevation plan	side view of the outside
Cross-section	a cut through, showing the inside
Impossible event	probability 0
Certain event	probability 1
Combinations	multiply the number of options in each set

Where these questions come from

The exam section below draws on the September and Preparatory 2026 Grade 12 Paper 2 papers:

Badge	Paper	What is available
NW	North West September	Question paper, answer book and marking guideline
MP	Mpumalanga September	Question paper, answer book and marking guideline
WC	Western Cape September	Question paper, answer book and marking guideline
LP	Limpopo September	Question paper, answer book and marking guideline
KZN	KwaZulu-Natal Preparatory	Question paper and answer book. No marking guideline was issued with this paper, so KZN items below carry a worked solution instead of the memo, and say so.

Each exam item shows the resource it is read from, exactly as it was printed. Click any table, map or plan to enlarge it.

Further reading

• 2025 NSC Diagnostic Report, Book 1, Chapter 9 — the examiners' own account, question by question. Everything under "What the examiners actually saw" comes from it.
• Mathematical Literacy Examination Guidelines 2021 — the document the papers are set from, including the formula sheet you are entitled to.
• CAPS FET Mathematical Literacy Grades 10–12 — the full topic list.
• A ruler. Paper 2 asks you to measure, and a question that says "measure in mm" cannot be answered without one.