The Mistake That's Holding Back Your Revision & How to Fix It

Ever revised a topic, thought you nailed it, then bombed a question on it later?

It's not because you don't understand the topic - it's because you're revising the wrong thing.

Most students waste time revising the wrong topics.

They assume that if they get a sequences question wrong, sequences must be their weak area.

But often, the real issue is algebra, fractions, or some other hidden weakness inside the question.

This is why many students feel stuck. They revise for hours but don't improve.

When you get a question wrong, ask yourself this:

• What step did I get stuck on?
• Was it the topic itself, or the maths behind it?
• Could I do this if it was worded differently?

Let's take an example:

Question 1: Arithmetic Sequences (Easy)

Here are the first four terms of a sequence:

6, 10, 14, 18

(a) Write an expression, in terms of $n$, for the $n$th term.

The sequence increases by 4 each time, so the formula is:

$$\text{nth term} = 4n + 2$$

Question 2: Fibonacci-style Sequence (Harder)

Now let's try this:

The first three terms of a sequence are:

$a, b, a + b$

(a) Show that the 6th term of this sequence is $3a + 5b$.

Given that the 3rd term is 7 and the 6th term is 29,

(b) Find the value of $a$ and $b$.

Why Do Students Struggle?

The first question feels familiar. It has numbers.

The second question uses letters. Even though it's still sequences, students panic because it looks different.

The problem isn't sequences - it's algebra.

How to Actually Fix It

Step 1: Find the Real Weakness

• Review the question properly - Don't just say “I got this topic wrong.” Look at why you got it wrong.
• Write down the skill you actually struggled with - If the problem was algebra, not sequences, focus your revision on algebra.
• Go back to the fundamentals - If you struggle with algebra in sequences, go back and practice solving equations separately before trying sequences again.

Step 2: Break It Down

For the Fibonacci-style question, let's write out the terms:

$$\begin{aligned} 1^{st} &= a \\ 2^{nd} &= b \\ 3^{rd} &= a + b \\ 4^{th} &= (a + b) + b = a + 2b \\ 5^{th} &= (a + 2b) + (a + b) = 2a + 3b \\ 6^{th} &= (2a + 3b) + (a + 2b) = 3a + 5b \end{aligned}$$

Now, we're told:

$$a + b = 7, \quad 3a + 5b = 29$$

This gives us a simultaneous equations problem, not a sequences problem.

Solving:

1. $a + b = 7$
2. $3a + 5b = 29$

Multiply equation 1 by 3:

$$3a + 3b = 21$$

Now subtract:

$$(3a + 5b) - (3a + 3b) = 29 - 21$$

$$2b = 8 \Rightarrow b = 4$$

Substituting into $a + b = 7$:

$$a + 4 = 7 \Rightarrow a = 3$$

Final answer:

$$a = 3, \quad b = 4$$

Final Thoughts

Most students never do this.

They revise what they think is the problem, not what the problem actually is.

That's why they spend months revising but never feel more confident.

If you take just one thing from this: Before you revise, figure out exactly what you need to fix. It's the fastest way to improve.

Fix the hidden weakness first, and you'll improve much faster.

By Giuliano Grasso