STUDY GUIDE TITLE

At a glance

Paper 1 is the basic skills paper. Three hours, 150 marks, five questions, and you answer every one of them. It draws on three application topics only:

Topic	Roughly	What it looks like in Paper 1
Finance	55%	Tariff tables, payslips and tax tables, banking fees, interest, break-even, exchange rates, budgets
Data handling	40%	Reading tables and graphs, mean, median, mode, range, quartiles, box-and-whisker
Probability	5%	Simple probability as a fraction, decimal or percentage; two-way tables

The cognitive-level split is fixed: 30% Level 1 (knowing), 30% Level 2 (applying routine procedures), 20% Level 3 (applying multi-step procedures) and 20% Level 4 (reasoning and reflecting). Question 1 is almost entirely Level 1. That is 30 marks of the cheapest marks in the paper, and the national data shows it is also the best-answered question every year. Do not rush it.

Measurement and Maps and plans belong to Paper 2, not Paper 1. They appear here only where a basic conversion or a plan-reading skill is folded into a finance or data context. This guide still carries a short section on each, because the trial papers do slip them in.

Reading the marks

Every marking guideline uses the same codes. Learning them tells you exactly what the marker is looking for, and therefore what you must put on the page.

Code	Means	What that tells you
RT	Reading from a table, graph, document or diagram	A mark just for lifting the right number off the source. Write the number down even if you then use it.
M	Method	The marker wants to see the operation, not only the answer.
MA	Method with accuracy	Right method and right numbers in it.
CA	Consistent accuracy	If you carried a wrong number forward, you still earn this mark for using it correctly. CA stops at the second calculation error.
MCA	Method with consistent accuracy	Same idea, applied to the method mark.
A	Accuracy	The final answer itself.
SF	Correct substitution in a formula	Write the formula, then write it again with the numbers in. That substitution is a mark on its own.
C	Conversion	A mark for the unit conversion. Show it as a separate line.
S	Simplification	The mark for reducing to the final simplest form.
R	Rounding	Rounding is an independent mark. You can lose it even with a correct calculation.
O	Opinion, explanation, reason, justification	A sentence is required. Numbers alone score nothing here.
P	Penalty	Deducted for no units, or wrong rounding.
NPR	No penalty for rounding	Applies if the first decimal is correct, except for money.
AO	Answer only	Full marks for a bare correct answer. Common in Question 1.

Four marking rules that decide borderline marks

1. Answer a question twice and only the first attempt is marked. If you cross out an attempt and do not redo it, the crossed-out version is marked. So never cross out unless you are replacing it.
2. Consistent accuracy stops at the second calculation error. One slip costs one mark and you keep going. Two slips and the rest of the question dies.
3. A conclusion mark needs the working to earn it. Most provinces require at least one third of the sub-question's marks before the "therefore the claim is VALID" mark is awarded. Writing only "VALID" scores nothing.
4. Extra readings are penalised. If a question asks you to read one value off a table or map and you hedge by writing two, you lose a mark for the extra item.

What the examiners actually saw

The 2025 NSC Diagnostic Report is blunt about where the marks go. 477 160 candidates wrote, 86,2% passed at 30% and 61,4% at 40%. Average performance on Paper 1 was 51%.

Paper 1 question	Topic	National average 2025
1	Finance and Data handling	69%
2	Finance and Probability	44%
3	Data handling and Probability	48%
4	Finance and Data handling	59%
5	Finance and Data handling	33%

Question 5 is where the paper is won or lost. In 2025 sub-question 5.2 averaged 21%. It is not harder mathematics. It is the same arithmetic buried in more reading, later in a three-hour paper.

The examiners' recurring complaints

• Candidates cannot reliably extract information from graphs, tables and maps. The report calls this "a significant barrier to success" and says the same thing every year.
• Basic arithmetic with large numbers and place value goes wrong. Candidates drop the hundred-thousand zero when writing numbers in words.
• Time calculations and unit conversions remain weak across the whole FET phase.
• Poor question interpretation: multiplying when the phrase "per kilogram" called for dividing; reading the Durban column when the question said Johannesburg.
• Confusing discrete and continuous data, and simple and compound interest.
• Forgetting to multiply by 100 when a percentage is asked for, or inverting the fraction.

Finance

Cost, income, profit and break-even

Three definitions carry most of the marks:

• Fixed costs stay the same no matter how much you make or sell: rent, salaries, insurance, licence fees.
• Variable costs change with the number of items: materials, ingredients, packaging.
• Total cost = fixed costs + (cost per item × number of items).

Then Income = selling price × number sold, and Profit = Income − Total cost. The break-even point is where income equals total cost: you have covered your costs and made nothing yet. Asked why a business owner needs to know it, any of these earns the mark: it gives the minimum number to sell to cover costs; it shows when the business starts making a profit; it helps set realistic sales targets; it informs pricing decisions.

A budget is a surplus when income exceeds expenditure, a deficit when expenditure exceeds income, and balanced when they are equal.

Percentages, VAT and mark-up

• VAT in South Africa is 15%. To add it, multiply by 1,15. To strip it out of a VAT-inclusive price, divide by 1,15 — never subtract 15%.
• To add a percentage increase of p%, multiply by (100 + p) ÷ 100.
• To work back to a price before an increase of p%, divide by (100 + p) ÷ 100.
• A 35% profit on cost means the selling price is 135% of the cost price.

Interest

	Simple interest	Compound interest
Interest earned on	the original amount only, every year	the original amount plus the interest already earned
Growth	the same rand amount each year	a growing rand amount each year
Manual method	Amount = P × (1 + n × i)	multiply by (1 + i) once per compounding period

Compounded half-yearly means the annual rate is halved and the number of periods is doubled. 7,12% per annum compounded half-yearly is 3,56% every six months. Get that one step wrong and the whole question goes.

Loans

• Total repaid = monthly repayment × number of months. A 20-year loan is 240 months, a 25-year loan is 300 months.
• Total interest = total repaid − amount borrowed. The amount borrowed is the price after the deposit has been taken off.
• The loan factor method: monthly repayment = loan amount × loan factor ÷ 1 000.
• Paying extra each month shortens the term and reduces total interest. Either statement earns the mark.

Income tax

The order never changes:

1. Find the annual taxable income (monthly × 12).
2. Find the bracket it falls in.
3. Tax = the fixed amount for that bracket + the percentage of the amount above the bracket's lower threshold.
4. Subtract the rebates you qualify for.
5. Subtract any medical tax credits (a monthly amount × 12).

Rebates are cumulative by age: everyone gets the primary rebate; from 65 you also get the secondary; from 75 you also get the tertiary. So a 72-year-old gets primary and secondary, not secondary alone.

Taxable income is the portion of income on which tax is calculated, after allowable deductions have been subtracted from gross income. Deductions that reduce it include pension fund, provident fund, retirement annuity, donations and travel expenses.

Exchange rates

Read the rate as a sentence and the direction takes care of itself. If 1 ZAR = 0,060 USD, then to turn rands into dollars you multiply by 0,060, and to turn dollars back into rands you divide by 0,060. Chain two rates carefully: MXN → USD → ZAR means divide by 17,47, then divide by 0,060.

Tariffs and stepped (block) rates

Water, electricity and bank fees are charged in blocks. Each block has its own rate and you pay the full block before moving to the next. Work block by block, keep a running total, and only then deal with the leftover.

"Per R100 or part thereof" means any fraction of R100 is charged as a full R100. R350 is four lots of R100, not three and a half. Always round up.

Data handling

The statistical cycle

Pose a question → collect data → classify (organise) data → summarise data → represent data → analyse and interpret. The stage where collected data is sorted into types is classifying data.

Types of data

Type	Definition	Example
Categorical (qualitative)	Data that can be put into groups; described in words	Province names, gender, brand of car
Numerical (quantitative)	Data recorded as numbers	Marks, prices, heights
Discrete	Counted. Whole values only, with gaps between them	Number of learners, number of cars
Continuous	Measured. Can take any value in a range	Height, mass, temperature, time

The examiners flag this confusion every single year. The test is simple: could you get a value halfway between two of them? If yes it is continuous, if no it is discrete.

Measures of centre and spread

• Mean = sum of all values ÷ number of values. If you are given the mean and asked for a missing value, multiply the mean by the count to get the total, then subtract everything you know.
• Median = the middle value once the data is in order. Ordering first is a mark. With an even count, average the middle two.
• Mode = the value that appears most often.
• Range = maximum − minimum.
• Q1 is the median of the lower half, Q3 the median of the upper half.
• Interquartile range (IQR) = Q3 − Q1.

The IQR is a more reliable measure of spread than the range because it describes the middle 50% of the data and is not affected by outliers, while the range uses only the two most extreme values.

Outliers

An outlier is a value abnormally large or small compared with the rest of the data set. Papers supply the rule they want you to use, usually:

Lower boundary = Q1 − 1,5 × (Q3 − Q1) and Upper boundary = Q3 + 1,5 × (Q3 − Q1)

Anything below the lower boundary or above the upper boundary is an outlier. Note that the lower boundary can come out negative, in which case nothing at the bottom end is an outlier.

Box-and-whisker

Five numbers: minimum, Q1, median, Q3, maximum. The box runs Q1 to Q3, the line inside is the median, the whiskers reach the extremes. Each quarter of the diagram holds 25% of the data, so "how many learners fall in the upper quartile" is 25% of the total, regardless of how wide that quarter looks.

To compare two box-and-whisker plots, compare a named statistic and then draw the conclusion: a higher median means better performance overall; a smaller IQR or range means more consistent performance. A conclusion without a supporting figure scores nothing.

Graph types

Graph	Best for
Bar graph	Comparing categories
Multiple or compound bar graph	Comparing categories across more than one group
Pie chart	Showing each part as a share of a whole
Histogram	Continuous data grouped into intervals
Line graph	Change over time
Broken-line graph	Discrete values tracked over time
Box-and-whisker	Spread and quartiles, comparing distributions
Scatter plot	Relationship between two variables

Probability

• Probability = number of favourable outcomes ÷ total number of outcomes.
• It runs from 0 (impossible) to 1 (certain), and can be written as a fraction, a decimal or a percentage. Give it in the form the question asks for.
• Read the instruction: "as a fraction in simplest form", "as a decimal", "as a percentage", "rounded to two decimal places". The rounding is a separate mark.
• A two-way table lists every combination. With 3 pizzas and 4 smoothies there are 3 × 4 = 12 outcomes.
• "and" narrows the outcomes, "or" widens them, and "except" means count the total and take away the excluded ones.
• Theoretical probability is what should happen; relative frequency is what did happen, out of the trials actually run.
• A prediction is a statement about a future event, often based on historical data.

Measurement and conversions in Paper 1

Measurement is a Paper 2 topic, but conversions appear in Paper 1 finance contexts constantly.

From	To	Do this
mm	cm	÷ 10
cm	m	÷ 100
m	km	÷ 1 000
g	kg	÷ 1 000
kg	ton	÷ 1 000
ml	litre	÷ 1 000
cm³	litre	÷ 1 000

Going the other way, multiply. The BMI formula BMI = mass in kg ÷ (height in m)² appears often; to find height from BMI, rearrange to height = √(mass ÷ BMI).

Maps, plans and representations in Paper 1

Also mainly Paper 2, but the vocabulary is examined in the Question 1 matching items:

• Floor plan: the top, aerial or bird's-eye view of the arrangement of the rooms.
• Elevation plan: the side view of the outside of a building.
• Number (ratio) scale, for example 1 : 158, means one unit on the plan represents 158 of the same units in reality.
• Bar scale: a small ruler printed on the map. Measure it, then convert.

Command words: what the question is actually asking

Word	What to write
Write down / State / Name / Identify	The answer alone. No working needed, and "answer only" usually earns full marks.
Determine / Calculate	Show the working. Method marks are available even if the answer is wrong.
Explain / Give ONE reason	A full sentence. This is an O mark and numbers will not earn it.
Verify / Show that	Do the calculation independently, get your own answer, compare it with the claim, then write the conclusion sentence: VALID or NOT VALID, CORRECT or INCORRECT.
Hence	Use the answer you just produced. Do not start again.
Compare	Two named figures, then a conclusion drawn from them.

Show me a "verify" answer that scores full marks

Question: Xolani claims the monthly repayment from the online calculator is R0,10 less than the repayment from a loan factor table. Loan amount R234 000, loan factor 9,65. Monthly repayment = loan amount × loan factor ÷ 1 000. (4)

Monthly repayment = R234 000 × 9,65 ÷ 1 000 (SF, the substitution)
= R2 258,10 (CA)
Difference = R2 258,10 − R2 258,00 = R0,10 (MCA)
Xolani's claim is VALID. (O, the conclusion)

Four separate marks, and the last one is a sentence. Candidates who stop at R0,10 throw it away.

The eight traps that cost the most marks

1. No conclusion sentence. Every "verify" and "is the claim valid" question ends with a written verdict. It is a mark on its own.
2. Rounding. It is an independent mark. Money is always two decimals. Round up for anything you have to buy or pay for a whole unit of, and follow the instruction when one is given.
3. Units left off. R, kl, km, %, mg/dL. A penalty applies.
4. Reading the wrong row or column. Put a finger or a ruler on the row. The diagnostic report names this every year.
5. Subtracting 15% to remove VAT. Divide by 1,15.
6. Forgetting × 100 for a percentage, or inverting the fraction.
7. Not ordering data before finding the median or quartiles. The ordering is a mark.
8. Halving the rate but not doubling the periods in half-yearly compounding.

The last thirty minutes

Question 5 is worth about 33 marks and averaged 33% nationally last year. It is not harder, it is later. Two practical moves:

• Bank Question 1 first and fast. Thirty Level 1 marks, mostly answer-only.
• Never leave an explanation blank. O marks need a sentence, not a calculation, so they are available even when the arithmetic has defeated you.

One-page summary

Thing	Rule
Total cost	fixed + (cost per item × number)
Profit	income − total cost
Break-even	income = total cost
Add VAT	× 1,15
Remove VAT	÷ 1,15
Selling price at 35% profit	cost × 1,35
Total repaid	monthly × number of months
Total interest	total repaid − amount borrowed
Half-yearly compounding	rate ÷ 2, periods × 2
Annual tax	bracket amount + % of income above threshold − rebates
Mean	total ÷ count
Median	middle value of ordered data
Range	max − min
IQR	Q3 − Q1
Lower boundary for outliers	Q1 − 1,5 × IQR
Probability	favourable ÷ total
Each quartile holds	25% of the data
BMI	kg ÷ (m)²
Per R100 or part thereof	round the number of hundreds up

Where these questions come from

The exam section below draws on the September and Preparatory 2026 Grade 12 Paper 1 papers from seven sources, each item badged with its province:

Badge	Paper	What is available
KZN	KwaZulu-Natal Preparatory Examination	Question paper and marking guideline
NW	North West September	Question paper, answer book and marking guideline
LP	Limpopo 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
NC	Northern Cape Provincial Preparatory	Question paper, answer book and marking guideline
EC	Eastern Cape September	Marking guideline only

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

Further reading

• 2025 NSC Diagnostic Report, Book 1, Chapter 9 — the examiners' own account of what candidates got wrong, question by question. Everything in "What the examiners actually saw" comes from it.
• Mathematical Literacy Examination Guidelines 2021 — the document the papers are set from, including the cognitive-level split.
• CAPS FET Mathematical Literacy Grades 10–12 — the full topic list and what each one requires.
• Your own provincial marking guideline. Marking a friend's script against the memo teaches the mark codes faster than reading about them.