Add Maths 4037: Five Mistakes That Cost the Most Marks (and How to Fix Them)

 

By Zaheer | Updated 14 October 2026

Disclosure: I created the Add Maths Companion app mentioned at the end and sell it on Gumroad. Everything in this post is free to use without it. This is independent study material, not affiliated with Cambridge or any exam board.

Most marks lost in O Level Additional Mathematics (4037) are not lost on hard ideas. They are lost on small, repeatable slips, such as forgetting to reject an impossible answer or solving a trig equation in the wrong range. Here are five of the most common ones. For each, you will see the wrong working, the right working, and a quick way to avoid it.

Mistake 1: Keeping an answer the logarithm can't accept

Question: Solve log2 x + log2 (x − 2) = 3.

The slip: solving the quadratic correctly, then giving both roots as the answer.

Right working:

  • Combine the logs: log2 [x(x − 2)] = 3
  • Convert: x(x − 2) = 23 = 8
  • Rearrange: x2 − 2x − 8 = 0, so (x − 4)(x + 2) = 0, giving x = 4 or x = −2
  • Reject x = −2, because log2 of a negative number does not exist
  • Answer: x = 4

How to avoid it: after solving any log equation, substitute each answer back in. If a log would have a negative number or zero inside it, that answer is rejected. Also remember that log(a + b) is not log a + log b. Only multiplication turns into addition.

Mistake 2: Giving the wrong region for a quadratic inequality

Question: Solve x2 − 5x + 6 > 0.

The slip: writing 2 < x < 3, or writing "x > 2 and x > 3".

Right working:

  • Factorise: (x − 2)(x − 3) > 0, so the critical values are 2 and 3
  • The graph of y = x2 − 5x + 6 is a U-shape, which is above zero outside the roots
  • Answer: x < 2 or x > 3

How to avoid it: sketch the curve every time. For a U-shaped graph, "> 0" means outside the roots and "< 0" means between them. For example, x2 − 5x + 6 < 0 gives 2 < x < 3.

Mistake 3: Squaring a bracket with a surd

Question: Expand (3 + √2)2.

The slip: squaring each term separately and writing 9 + 2 = 11.

Right working:

  • (3 + √2)(3 + √2) = 9 + 3√2 + 3√2 + 2
  • Answer: 11 + 6√2

How to avoid it: always write the bracket out twice before expanding. The middle term (here 6√2) is exactly what the slip leaves out.

Mistake 4: Forgetting the chain rule

Question: Differentiate y = (3x + 2)4.

The slip: writing dy/dx = 4(3x + 2)3, which skips the derivative of the bracket.

Right working:

  • Bring down the power and reduce it by one: 4(3x + 2)3
  • Multiply by the derivative of the inside, which is 3
  • Answer: dy/dx = 12(3x + 2)3

How to avoid it: whenever the "inside" of a bracket or a function is more than just x, ask yourself: "What did I forget to multiply by?"

Mistake 5: Solving a trig equation in the wrong range

Question: Solve sin 2x = 0.5 for 0° ≤ x ≤ 360°.

The slip: solving for 2x as if the range were 0° to 360°, then giving only 15° and 75°.

Right working:

  • If 0° ≤ x ≤ 360°, then 0° ≤ 2x ≤ 720°, so the range for 2x is twice as long
  • sin 2x = 0.5 gives 2x = 30°, 150°, 390°, 510°
  • Divide each by 2
  • Answer: x = 15°, 75°, 195°, 255°

How to avoid it: before you solve, rewrite the range for the whole expression (here 2x). Doubling the angle doubles the range, and that gives you twice as many solutions.

Try these five questions

Write your working before you read the answers.

  1. Solve log3 x + log3 (x + 6) = 3.
  2. Solve x2 − 7x + 10 ≤ 0.
  3. Expand (2 + √5)2.
  4. Differentiate y = (5x − 1)3.
  5. Solve cos 2x = 0.5 for 0° ≤ x ≤ 180°.

Answers

  1. log3 [x(x + 6)] = 3, so x(x + 6) = 27, giving x2 + 6x − 27 = 0 and (x + 9)(x − 3) = 0. Reject x = −9 because it makes a logarithm negative. x = 3.
  2. (x − 2)(x − 5) ≤ 0, so the graph is on or below the axis between the roots. 2 ≤ x ≤ 5.
  3. 4 + 2√5 + 2√5 + 5 = 9 + 4√5.
  4. 3(5x − 1)2 × 5 = 15(5x − 1)2.
  5. The range for 2x is 0° to 360°. cos 2x = 0.5 gives 2x = 60° or 300°, so x = 30° or 150°.

Quick checklist

  • I substitute log solutions back in and reject impossible ones.
  • I sketch the curve for every inequality.
  • I write a bracket out twice before expanding it.
  • I multiply by the derivative of the inside when using the chain rule.
  • I rewrite the range before solving a trig equation with 2x, 3x or similar.

Practise more

My Add Maths Companion app covers all 15 topics in the 4037 syllabus, with a worked example for each, scored practice questions and instant feedback: Add Maths Companion, O Level Additional Mathematics (4037).

Always check the official syllabus and specimen papers for the latest requirements. No exam result is guaranteed.

Comments

Post a Comment

Popular posts from this blog

How to Write Reusable AI Image Prompts with Variables (5 Templates You Can Copy)

Image
  By Zaheer | Updated 10 October 2026 Disclosure: I sell image prompts on PromptBase, and some links in the last section are referral links. The techniques and templates before that section are free to use and don't need any purchase. The difference between a lucky AI image and a reliable one is usually the prompt. A one-off prompt gets you one picture. A reusable prompt, with a few clearly marked variables, lets you produce a whole series that looks consistent without rewriting anything. This guide explains how a good image prompt is built, how to turn it into a template, and gives you five templates you can copy and adapt for ChatGPT's image generation, Gemini or similar tools. The anatomy of a good image prompt Most weak prompts are short and vague: "a nice photo of a house". Stronger prompts answer the same handful of questions, in this order: Subject: what is the main thing in the picture? Setting: where is it, and what is around it? Style:...
Read more

Competitive Analysis Made Simple: What a Decision-Ready Competitor Report Includes

By Zaheer | Updated 11 October 2026 Disclosure: I created the Market Recon Engine skill mentioned in this post and sell it on Agensi. The guidance before that section works without it.   Every founder ends up doing the same late-night exercise: seven browser tabs, a half-finished spreadsheet, and a gut feeling about where the market has room. It is slow, easy to get wrong, and usually ends with a pile of facts instead of a decision. This post explains what a useful competitive analysis should actually contain, and shows a short sample from a real run of Market Recon Engine , a skill I just listed on Agensi that does this research in one pass. What a decision-ready competitive analysis includes A good analysis isn't a research summary you still have to interpret. It gives you something you can act on. These are the six parts I think matter most. 1. Feature comparison matrix The capabilities that actually move a purchase decision, rather than a padded checklist of every ...
Read more

Why You Can Rank #1 on Google and Still Be Invisible to ChatGPT (AEO Explained)

Image
  By Zaheer | Updated 9 October 2026 Disclosure: I created the AI Conversion Auditors Pack mentioned near the end of this post and sell it on Agensi. Everything before that section is useful without it. Your site can rank #1 on Google and still get zero mentions when someone asks ChatGPT or an AI Overview the exact same question. Traditional SEO gets you found by search engines. AI search visibility, often called AEO (Answer Engine Optimization), is about something different: whether an AI system can extract, trust and cite your content when it writes an answer. Many sites are tuned for one and blind to the other. SEO and AEO: what is actually different? Search engines return a list of links and let the reader choose. AI assistants and AI summaries return one composed answer and may name only a few sources, or none. That changes what your content needs to do: Traditional SEO AEO Goal Rank a page in a results list Be quoted or cited inside an answer ...
Read more