You want to know why most students get between 30% and 50% in Paper 1?
It is not because the paper is impossible. It is because they keep making the same 10 mistakes over and over again. Every year. Same mistakes. Same lost marks.
Mr Sawaya has been marking and teaching NSC Maths for 30 years. He sees these errors in almost every student's script. Fix these 10 things and your mark jumps immediately. Not gradually. Immediately.
Paper 1 is worth 150 marks. These mistakes alone can cost you 30 to 50 of them.
In This Post You Will Learn
✓ The 10 specific mistakes that cost the most marks in Paper 1
✓ Why each mistake happens and what triggers it during the exam
✓ The exact fix for each one so you stop repeating it
✓ Which topics each mistake typically shows up in
✓ A checklist you can use during the exam to catch errors before you hand in
Mistake 1: Not Showing Your Working
This is the biggest mark killer in Paper 1. Full stop.
Maths is not about the answer. It is about the method. The NSC awards marks for each correct step. If you jump from the question to the final answer, you get 1 mark instead of 4 or 5.
Where it hurts most: Calculus, sequences and series, functions.
The fix: Write every single step. Even if it feels obvious. One line per operation. If the question is worth 5 marks, your solution should have at least 4 to 5 lines of working.
Even if your final answer is wrong, correct intermediate steps still earn marks. A blank space earns zero. Always.
Mistake 2: Leaving Questions Blank
A blank answer is a guaranteed zero.
Students skip questions because they think they cannot do them. But partial attempts almost always pick up 1 to 3 marks. On a 6 mark question, writing down the formula and substituting the values can get you 2 marks even if you never reach the answer.
Where it hurts most: Probability, harder calculus, finance annuities.
The fix: Attempt every question. Write the relevant formula. Substitute what you know. Draw a diagram if it helps. Something is always better than nothing.
Mistake 3: Sign Errors in Algebra
This one is silent and deadly.
You work through an entire question correctly, but somewhere in line 3 you wrote +2 instead of -2. Now every line after that is wrong. And you have no idea because the method looked right.
Where it hurts most: Completing the square, solving quadratics, working with functions.
Common examples:
WRONG: (x - 3)² = x² - 6x - 9 (should be +9)
WRONG: -(2x + 1) = -2x + 1 (should be -2x - 1)
WRONG: -(-4) = -4 (should be +4)The fix: When you expand a bracket with a negative sign in front, change the sign of EVERY term inside. Not just the first one. Circle your negative signs as you work.
Mistake 4: Rushing Through Calculus
Calculus carries 35 marks. It is the biggest topic in Paper 1.
Students panic when they see calculus and try to rush through it. They skip steps in differentiation, forget to set the derivative equal to zero for turning points, or mix up the rules.
Where it hurts most: Finding turning points, sketching cubic graphs, optimisation.
The fix: Slow down. Calculus is systematic. Follow the same steps every time:
Step 1: Differentiate correctly (use the power rule)
Step 2: Set f'(x) = 0 to find turning points
Step 3: Substitute back to find y-values
Step 4: Check concavity with f''(x) if needed
Step 5: Sketch with all key points labelledFor full live lessons covering Paper 1 topics, see our Grade 12 Maths tuition page.
Mistake 5: Using the Wrong Sequences and Series Formula
There are multiple formulas for sequences and series. Students grab the wrong one.
| What You Need | Correct Formula |
|-------------------------|----------------------------------|
| nth term (arithmetic) | Tn = a + (n-1)d |
| nth term (geometric) | Tn = ar^(n-1) |
| Sum (arithmetic) | Sn = n/2[2a + (n-1)d] |
| Sum (geometric, r ≠ 1) | Sn = a(r^n - 1)/(r - 1) |
| Sum to infinity | S∞ = a/(1-r), only if |r| < 1 |The fix: Before you touch your calculator, ask two questions. Is it arithmetic or geometric? Am I looking for a term or a sum? Those two answers tell you exactly which formula to use.
We covered this in full in our guide on How to Answer Sequences and Series Questions in Grade 12 Maths.
Mistake 6: Ignoring Probability Completely
Most students skip probability entirely.
They see it at the end of the paper, decide it is too confusing, and move on. That is 15 marks gone. Fifteen marks that could be the difference between a 4 and a 5.
The fix: At minimum, know these three rules:
P(A or B) = P(A) + P(B) - P(A and B)
P(not A) = 1 - P(A)
Independent means P(A and B) = P(A) x P(B)
That is enough to answer most sub-questions and pick up 8 to 10 marks.
We broke this down step by step in Grade 12 Probability and Counting Principle Made Easy.
Mistake 7: Not Reading the Question Properly
Sounds basic. Costs more marks than almost anything else.
The question says "write down the range." The student writes down the domain.
The question says "for which values of x is f(x) > 0." The student solves f(x) = 0 and stops.
The question says "hence." The student ignores the previous answer and starts from scratch.
The fix: Underline the key instruction word before you start solving.
| Instruction Word | What It Means |
|-----------------|--------------------------------------------|
| Determine | Calculate it, show your method |
| Write down | No working needed, just the answer |
| Hence | You MUST use the previous answer |
| Show that | Prove it, the answer is already given |
| Sketch | Draw the graph with key points labelled |Mistake 8: Getting Domain and Range Wrong
Domain and range questions appear in every NSC Paper 1. Every year.
Students mix them up. Or they get the domain right but forget the restriction.
Common errors:
Writing x ∈ R for a hyperbola domain (should be x ∈ R, x ≠ p).
Writing y ≥ 0 for a parabola when the turning point is at y = 3 (should be y ≥ 3).
Giving the range when asked for the domain.
The fix: Domain = x-values (horizontal). Range = y-values (vertical). Check for asymptotes, turning points, and restrictions every time.
We covered every function type in Grade 12 Functions and Graphs - Everything You Need to Know.
Mistake 9: Calculator Errors in Finance
Finance carries about 15 marks. The formulas are on your formula sheet.
But students lose marks because they type the wrong thing into the calculator.
WRONG: Typing (1 + 0.08)^12 as 1 + 0.08^12
(you MUST bracket the base)
WRONG: Dividing 0.12 by 4 and getting 0.4
(should be 0.03)
WRONG: Using n = 5 years when interest is monthly
(should be n = 60 months)The fix: Always bracket (1 + i) or (1 - i) before raising to the power. Match your n to the compounding period. Monthly means n is in months. Quarterly means n is in quarters.
Mistake 10: Terrible Time Management
Paper 1 is 150 marks in 3 hours. That is 180 minutes.
The rule: roughly 1 minute per mark.
A 5 mark question should take about 5 minutes. If you have been on it for 15 minutes, move on.
Students spend 25 minutes on one hard question and then rush through 3 easy questions at the end. That is a terrible trade.
The fix: Wear a watch. Check after every question.
| Suggested Time Allocation |
|----------------------------------------------|
| Reading the paper: 5 min |
| Q1-3 (Algebra, Sequences): 30 min |
| Q4-5 (Functions): 30 min |
| Q6-7 (Finance, Calculus): 40 min |
| Q8-10 (Calculus, Probability): 50 min |
| Checking answers: 25 min |Your Pre-Submission Checklist
Before you hand in your paper, run through this:
✓ Did I attempt every question? No blanks?
✓ Did I show working for every question worth more than 2 marks?
✓ Did I check my signs in algebraic working?
✓ Did I answer what was actually asked (domain vs range, term vs sum)?
✓ Did I use the correct formula for each sequence type?
✓ Did I bracket my bases in finance calculations?
✓ Did I label all key points on graph sketches?
Takes 5 minutes. Catches 10 to 15 marks worth of silly errors.
How This Topic Appears in the NSC Exam
This post covers all of Paper 1.
Paper 1 is worth 150 marks and covers algebra, functions, sequences, finance, calculus, and probability.
Every examiner report published by the DBE highlights the same issues. Not showing working. Sign errors. Skipping probability. Rushing calculus.
The 2023 examiner report specifically noted that candidates lost significant marks in calculus due to incomplete working, in sequences due to incorrect formula selection, and in probability due to non-attempts.
These are not hard fixes. They are habits. Start building the right ones now.
Want live lessons covering every Paper 1 topic?
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