Hardest A Level Maths Topics & How To Tackle Them

The leap from GCSE to A Level Maths can seem huge. Many students find themselves staring at a problem that seems insurmountable, wondering if they've bitten off more than they can chew.

It can be frustrating when you've understood algebra and geometry at GCSE, only to hit topics at A Level that feel like a completely different language. You might spend hours on a single question, watch your confidence dip, and worry whether you'll ever "get it" in time for your exams.

The good news is that every tricky topic in A Level Maths can be mastered with the right approach. This guide breaks down the hardest A Level Maths topics, explains exactly why they're challenging, and gives you practical strategies to tackle them head-on.

Key Takeaways

• The most difficult topics include:

  • Proof

  • Trigonometric identities

  • Differentiation and integration with trig and exponentials

  • Parametric equations

  • Vectors in 3D

  • Binomial expansion with non-integer powers

• These topics are challenging because they involve abstract thinking, multiple steps, and require solid understanding of earlier content.

• With focused practice, the right resources, and a willingness to ask for help, you can master the hardest A Level Maths topics and achieve your target grade.

What Makes a Topic in A Level Maths Difficult?

Some Maths concepts feel manageable, while others might leave you scratching your head. There’s no definitive list of the ‘hardest’ topics because it’s subjective. What you might find particularly challenging, someone else might find pretty straightforward, and vice versa. However, we’ve narrowed down a list of the hardest A Level Maths topics and what they have in common:

• Abstract concepts or tricky methods cause problems when you can't visualise what's happening or see why a method works. Unlike simpler algebra where you can "see" the answer taking shape, topics like proof require you to think in patterns and logic that feel unfamiliar.

• Multi-step problem-solving means you need to remember several techniques and apply them in the correct order. Miss one step or mix up the sequence, and your entire answer falls apart.

• Deep understanding of earlier topics is essential. If you struggled with basic differentiation, for example, tackling differential equations becomes nearly impossible. These harder topics build on foundations you should already have.

• Speed and accuracy under exam conditions add extra pressure. Even if you understand a topic, exam time limits force you to work quickly without making careless errors. This is particularly tough with topics that involve lengthy calculations.

Top 6 Hardest A Level Maths Topics

1. Proof

Proof can be a challenging topic to grasp. Unlike other areas where you calculate an answer, proof requires you to demonstrate that something is always true using logical steps. It's difficult because it demands a kind of abstract thinking that you don’t tend to use in other Maths topics. 

Common errors students make include:

• Missing steps in their logic, leading to a lack of proof

• Poor mathematical notation

• Unclear explanations

Tips for writing clear and correct proofs:

• State clearly what you're proving and what type of proof you'll use (direct proof, proof by contradiction, etc).

  • This is something you can keep referring back to throughout your step-by-step logical argument.

• Work with general algebraic expressions, not specific numbers. 

  • For example, represent an even number as 2n, where n is an integer.

• Write down every step, even if it feels obvious. Examiners need to see your logical flow.

• Practice reading worked solutions to learn how mathematicians structure their arguments. The more examples you study, the better you'll become at spotting patterns in proof techniques.

2. Trigonometric Identities and Equations

Remember when trigonometry was all about triangles? A Level is more advanced, as you work with complex identities and solve equations that require multiple transformations.

It's difficult because:

• You need to recognise which identity to use (there are many).

• You have to manipulate the equation correctly.

• The algebra can become messy quickly, especially when combining identities like double angle formulae or factor formulae.

• Working in radians rather than degrees can be confusing. 

• You need to understand how trig graphs transform and where solutions lie within specific intervals.

Revision strategies and example types:

Trigonometry at A Level can feel totally different from GCSE. It’s almost a new mathematical concept altogether. Here are some handy tips to help you get to grips with it quickly:

• Create a formula sheet with all the key identities (sin²θ + cos²θ = 1, double angle formulae, addition formulae). 

  • Memorise these until they're second nature.

• Practice questions that ask you to prove one identity equals another. 

  • These teach you manipulation skills.

• Work through problems that combine identities with equations.

  • For example, solve: 2sin²x - 3cosx = 0 for 0 ≤ x ≤ 2π.

• Always check your answers make sense by substituting back into the original equation.

3. Differentiation and Integration

You might not have heard of differentiation. That’s because it isn’t included in the standard Maths GCSE. Tackling a concept at A Level for the first time means there’s a lot to learn. At A Level, you're expected to differentiate and integrate functions involving: 

• Trigonometry

• Exponentials

• Logarithms

• Combinations of all three!

It's difficult because there are numerous rules to remember: 

• Product rule

• Quotient rule

• Chain rule

• Integration by substitution

• Integration by parts

Forgetting when to apply each rule or mixing them up leads to incorrect answers.

Common pitfalls include:

• Forgetting to use the chain rule when differentiating composite functions.

• Mixing up the product rule and quotient rule.

• Making sign errors, especially with integration by parts.

• Forgetting the constant of integration.

Revision strategies:

• Create a rules cheat sheet and test yourself regularly until the rules become automatic.

• Focus on recognising function types quickly. Ask yourself: "Is this a product? A quotient? A composite function?" before diving in.

• Practice mixed questions that combine different rules in one problem, as exams rarely test rules in isolation.

• When integrating, always differentiate your answer to check it's correct. This catches errors immediately.

4. Parametric Equations

Parametric equations represent curves using a parameter (usually t) rather than expressing y directly in terms of x. This concept feels alien at first.

It's difficult because you're thinking about x and y both depending on a third variable. Visualising what the curve actually looks like requires practice and patience.

Converting between parametric form and Cartesian form (eliminating the parameter) involves algebraic manipulation that can get messy. 

Techniques to convert into Cartesian form:

• Look for opportunities to use trig identities. If x = cosθ and y = sinθ, remember that cos²θ + sin²θ = 1.

• Sometimes you'll need to rearrange both equations and add or subtract them to eliminate the parameter.

• Practice sketching parametric curves by plotting points for different parameter values. This builds intuition about how the parameter affects the shape.

• Explore YouTube videos providing walk-throughs that answer parametric equation questions step-by-step.

5. Vectors in 3D

Vectors jump from 2D to 3D at A Level, adding an extra dimension that makes visualisation harder. You're working with three components (i, j, k) and solving problems in three-dimensional space.

It's difficult because spatial reasoning doesn't come naturally to everyone. Imagining lines, planes, and angles in 3D space is challenging without visual aids. YouTube can come in really handy, as walkthroughs often involve real-life examples to help cement understanding.

Problems often involve multiple steps. These include: 

1. Finding a vector

2. Finding the vector’s magnitude

3. Using this magnitude to find an angle or determine if lines intersect

Each step relies on the previous one being correct. Get a step wrong, and your final answer will be incorrect.

How to break down problems logically:

• Always start by drawing a diagram, even if it's rough. 

  • Label what you know and what you need to find.

• Break the problem into smaller questions. 

  • What information does the question give you? 

  • What do you need to find first before you can answer the main question?

• Write out vectors in component form clearly. 

  • This reduces errors when calculating dot products or vector equations of lines.

• Check your answer makes sense. 

  • If you've found an angle between two vectors and your answer is greater than 180°, something's gone wrong.

6. Binomial Expansion (With Non-Integer Powers)

Binomial expansion isn’t covered at GCSE, unless you opt to take GCSE Further Maths. At A Level, you’ll explore expanding expressions with two terms (like a + b) to the power of n. 

Remember: 

• When n is a positive whole number the expansion is finite. 

• When n is not, the expansion is infinite.

It's difficult because the formula looks intimidating: (1 + x)ⁿ = 1 + nx + [n(n-1)/2!]x² + ... and you need to understand when this expansion is valid (typically |x| < 1).

Finding a specific term in the expansion requires careful substitution into the general term formula. If you make one small arithmetic error at the start, these multiply throughout the calculation.

Tips for mastering binomial expansion:

• Memorise the general term formula and understand what each part represents.

• Practice identifying n and x correctly, especially when the bracket isn't in the form (1 + x). You may need to factorise first.

• Always state the validity condition in your answer.

• Work through several examples finding specific terms (e.g. the coefficient of x³) until the process becomes automatic. 

• On the Internet, you’ll also find some great binomial expansion tutorials that you can revisit as part of your revision schedule.

How to Tackle Difficult A Level Maths Topics

Focus on Understanding, Not Memorisation

Memorising methods without understanding why they work is a recipe for disaster. If you don’t understand the ‘how’ or ‘why’ behind an equation, rule, or quotient, you’ll struggle to apply these to unfamiliar situations.

Take time to understand the reasoning behind each step. Ask yourself "why does this work?" and "what would happen if I changed this part?" Exam questions don’t test your memory, they test your conceptual understanding.

Use visuals and alternative explanations when your textbook explanation doesn't click. Try:

• YouTube videos

• Different textbooks

• Joining online Reddit (opens in a new tab) or Facebook A Level Maths forums

Practice Regularly with Exam-Style Questions

There's no substitute for practice when it comes to mastering difficult maths topics. The more questions you attempt, the more patterns you'll recognise and the faster you'll work.

Don't just stick to easy questions. Challenge yourself with exam-style problems that combine multiple concepts.

Review mistakes effectively by:

• Checking the mark scheme to see where you went wrong

• Reworking the question without looking at the solution

• Writing notes on common errors you make

• Attempting similar questions to ensure you've fixed the problem

Save My Exams has a bank of A Level Maths past papers from Edexcel, AQA, OCR, WJEC, and CIE. Use them to familiarise yourself with how questions are worded and structured.

Use Online Resources and Revision Tools

Once you’ve had your fill of past papers, you’ll understand your weaker topics. Then it’s time to revise these topics to help strengthen your exam performance.

Save My Exams offers comprehensive revision notes created by expert teachers and examiners. Our resources are organised by exam board and topic, making it easy to target exactly what you need to improve.

And when you create your revision timetable, make sure you integrate different techniques to help those Maths concepts really stick. A mix of blocked practice, chunking, and elaboration should do the trick.

When to Ask for Help

Struggling with a topic doesn't mean you're not good at maths. Everyone hits roadblocks, and knowing when to ask for help is a sign of maturity and determination.

Signs you're stuck and need support:

• You've attempted multiple questions on a topic and still don't understand the basics.

• You're spending hours on homework without making progress.

• You feel anxious or overwhelmed when this topic appears.

• Your marks on this topic are consistently low.

Who to turn to:

Your teacher is your first port of call. They know you, they know the course, and they want you to succeed. Book a lunchtime appointment or ask for extra resources.

A maths tutor can provide personalised support focused on your weak areas. They can work at your pace and explain things in different ways.

Online forums like The Student Room (opens in a new tab) have active communities of A Level Maths students and teachers who answer questions. You can post specific problems you're stuck on.

Don't wait until exam season to seek help. The earlier you address difficulties, the more time you have to improve.

Frequently Asked Questions

Do I Need to Be Good at Every Topic to Get a Good Grade?

Not at all! A Level Maths papers cover a broad range of topics, and you don't need perfect marks on everything to achieve a high grade. That said, you can't afford to completely ignore major topics. Exam papers are designed to test across the specification, so weak areas will likely appear.

Focus on getting competent at difficult topics rather than achieving perfection. Being able to attempt questions and pick up method marks is often enough to secure the grade you need.

How Can I Improve A Level Maths Topics I Find Difficult?

Start by identifying exactly what you don't understand. Is it the concept itself, the method, or applying it to exam questions?

Work through worked examples slowly, covering up the solution and attempting each step yourself.

Complete lots of practice questions, starting with easier ones and gradually increasing difficulty.

Teach the topic to someone else (even if it's just explaining it out loud to yourself). Teaching forces you to organise your understanding clearly.

What Resources Are Best for the Hardest Topics?

Your textbook should be your foundation. Make sure you're completing all the exercises, not just the ones your teacher sets. But your textbook shouldn’t be your only resource. Explore YouTube, take Save My Exams A Level Maths mock exams, and find a friend to be a study buddy. Working through the hardest A Level Maths topics with someone else can really help solidify your understanding.

Final Thoughts

A Level Maths is undeniably challenging, but thousands of students succeed every year. The difference between those who struggle and those who thrive often comes down to practise, persistence, and asking for help when needed.

With consistent effort, even the hardest A Level Maths topics become manageable. Break them down into smaller pieces, focus on understanding rather than memorising, and practice regularly.

Remember that improvement takes time. You won't master proof or parametric equations overnight, and that's completely normal. What matters is that you keep working at it and don't give up.

References

Reddit - A Level Maths Forum (opens in a new tab)

The Student Room - Maths Study Help (opens in a new tab)