NSC Mathematics Paper 1: Where the Marks Actually Go

by Braintiq Academic Team

Most matric maths advice is about working harder. Very little of it is about where the marks are, which is strange, because the NSC publishes the weighting and it does not change much year to year.

Paper 1 is 150 marks, written in three hours. That is 1.2 minutes per mark. If you are spending eight minutes on a four mark question, you are not bad at maths, you are budgeting badly, and those are different problems with different fixes.

This is what the paper is made of and where the marks are actually lost.

The weighting, in plain numbers

Paper 1 covers algebra, sequences and series, functions and graphs, finance, calculus, and probability. The rough mark allocation, based on the CAPS subject statement and the pattern of recent papers:

Two things follow immediately. Functions and calculus together are nearly half the paper, so they deserve nearly half your preparation. And finance, which many students quietly skip because it feels like a different subject, is 15 marks of some of the most formulaic work on the paper. Fifteen marks is the difference between 60 percent and 70 percent.

Method marks are the whole game

The single most valuable thing to understand about NSC marking is that the memo awards marks for steps, not for answers. A question worth 4 marks has roughly 4 identifiable things the marker is looking for, and a correct final answer with no working can score less than a wrong final answer with correct working.

This has three practical consequences.

Never leave a question blank. Write the formula. Write the substitution. If a question asks you to find the equation of a tangent and you can only remember that you need a gradient from the derivative, write the derivative. That is a mark.

Do not erase working that looks wrong. Cross it out with one line if you must, but crossed-out work is still marked if nothing else is offered. Erased work cannot be.

Carry the error forward. If you make an arithmetic slip in part (a) and use that wrong number correctly in part (b), you get the marks for part (b). This is a real rule and it is applied. It only works if your method is visible.

Algebra: the quadratic formula question is not testing algebra

There is almost always a question that asks you to solve a quadratic where the roots are not rational, so factorising fails and you must use the formula.

$$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$

What that question is really testing is whether you can write down $a$, $b$ and $c$ correctly from an equation that has not been arranged for you. If the equation arrives as $3x^{2} = 5x - 1$, the first mark is for rearranging to $3x^{2} - 5x + 1 = 0$, and the students who lose marks here lose them by reading $b$ as $5$ instead of $-5$.

Write $a =$, $b =$ and $c =$ on their own line, every time, before touching the formula. It looks slow. It is faster than the alternative.

The other algebra mark that goes begging is the nature of roots question. If you are asked to show that the roots are real and unequal, the whole answer is the discriminant.

$$\Delta = b^{2} - 4ac$$

If $\Delta > 0$ the roots are real and unequal. If $\Delta = 0$, real and equal. If $\Delta < 0$, non-real. You do not need to solve anything. Students routinely solve the full quadratic to answer a question that wanted one calculation.

Sequences: identify the type before anything else

Every sequences question begins with the same decision. Is it arithmetic, geometric, or quadratic?

Write down which one it is before you write anything else. Most of the marks lost in this section come from applying the arithmetic formula to a geometric sequence, which is a decision error made in the first ten seconds and then never revisited.

For the sum of an infinite geometric series, the condition matters as much as the formula:

$$S_{\infty} = \frac{a}{1 - r}, \quad \text{valid only when } -1 < r < 1$$

If a question asks for what values of $x$ a series converges, it is asking you to solve $-1 < r < 1$ where $r$ is written in terms of $x$. That is the entire question, and it is usually 3 marks.

Functions and graphs: the sketch is worth more than you think

Thirty five marks live here and they are unusually recoverable, because a graph sketch is marked on features, not artistry. For a parabola the marker is looking for the shape, the intercepts, the turning point and the axis of symmetry. Each is a mark. Draw a rough shape and label those four things and you have most of the question even if the curve itself is untidy.

For the hyperbola $y = \frac{a}{x + p} + q$, the asymptotes are $x = -p$ and $y = q$. Write them down first. They are marks, they are quick, and they also tell you where the curve goes.

The question that separates the 70s from the 80s is usually the one that asks for the values of $x$ for which one graph is above another, or for which a function is increasing. These are read off the sketch, not calculated. If you did the sketch properly, they take fifteen seconds. If you skipped the sketch, they are nearly impossible.

Calculus: first principles is free marks

There is almost always a question asking you to determine the derivative from first principles. The definition never changes:

$$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$

It is the same four steps every time. Write $f(x + h)$. Subtract $f(x)$. Divide by $h$ and simplify until the $h$ in the denominator cancels. Take the limit.

This is the most predictable question on the paper. It is worth about 5 marks and requires no insight whatsoever, only care with the algebra. Practise it until it is automatic, because it is the closest thing to a guaranteed block of marks in Paper 1.

The other calculus marks people leave behind are in the applications. When a question describes a rate of change in words, the sentence that matters is the one that tells you what to differentiate with respect to what. Underline it. "The rate at which the volume changes with respect to time" is $\frac{dV}{dt}$, and once you have written that symbol the rest is mechanical.

For optimisation, the method is always: write the quantity to be maximised or minimised as a function of one variable, differentiate, set the derivative to zero, solve. If you have two variables, you have missed a constraint somewhere in the question and you need to go back and find it.

Probability: draw the diagram

Fifteen marks, and the students who do well here are the ones who draw something. A Venn diagram or a tree diagram converts a wordy question into a picture where the answer is visible.

The two rules that are examined most:

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

and, for independent events,

$$P(A \text{ and } B) = P(A) \times P(B)$$

The trap is being asked whether events are independent and answering by intuition. It is a calculation. Work out $P(A) \times P(B)$ and compare it to $P(A \text{ and } B)$. If they are equal, the events are independent. If not, they are not. Your sense of whether two things "feel related" is not evidence.

A three hour plan

Read the whole paper for four minutes before writing anything. Mark the questions you know you can do. Do those first, in any order. The paper is not designed to be answered from front to back, and question 1 being first does not make it easiest.

Budget roughly 1.2 minutes per mark and check yourself at the halfway point. At 90 minutes you should be at about 75 marks. If you are at 50, you are going too slowly on something, and the fix is to move on and come back, not to push harder on the question you are stuck on.

Leave ten minutes at the end. Not to check everything, which is impossible, but to fill in the questions you left blank with whatever formula or first step you can remember. That ten minutes is usually worth five to eight marks, which is most of a grade boundary.

Practising against real papers

Textbook exercises teach one technique at a time, with the chapter heading telling you which one to use. Exam questions do not tell you. The skill of recognising which method applies is separate from the skill of executing it, and only the first one is really being tested by the time you get to matric.

So work from past papers, and mark yourself against the official memo rather than against your own sense of whether you got it right. The memo is where you find out that you have been losing a mark per question by not writing the formula down.

Braintiq was built around that idea. You upload your own past papers and memos into a subject space, and what it builds comes from those documents rather than from a general model of what matric maths is.

Braintiq on a phone, showing a module workspace with a bottom bar for Sources, Ask and Tools

You can ask it about a specific past paper question and it will work through it against your own memo. There is a free version you can use without signing up at braintiq.app/try.

The short version