When you review a math question, ask two things: do I recognise an approach, and can I complete it? Those checks give you four types of questions and a clearer idea of what to practise next.
I describe them as the questions you “know you know”, “don’t know you know”, “know you don’t know” and “don’t know you don’t know”. The names sound like a tongue-twister, but the distinction is practical: familiarity and the ability to solve a question are separate things.
For H2 Math students, my main advice is to clear the familiar questions you still get stuck on before the exam, while building the understanding needed for unfamiliar problems. This is my teaching framework, rather than an official SEAB classification or a way to predict your grade.
Type 1: You recognise the question and can solve it. Maintain accuracy and check your reasoning.
Type 2: The question looks new, but you can solve it. Notice which clue connected it to a familiar idea.
Type 3: You have seen the question before but get stuck. Clear the doubt, then practise similar questions independently.
Type 4: You cannot yet identify an approach or finish. Prepare through deeper understanding and give yourself thinking time in the exam.
The Four Types at a Glance
The diagram uses two checks:
- Familiarity: Do you recognise the question or a possible method?
- Independent completion: Can you explain the steps and finish without copying a solution?
Classify a question after a genuine attempt. A question that is Type 3 for you may be Type 1 for your friend. It can also change category as you learn. Use the classification to choose your next action.
Type 1: You Know You Know
You recognise the question and can complete it independently. You have seen the underlying idea before and know how to apply it.
For example, if you can differentiate $y=3x^2+5x-7$ to obtain $\frac{dy}{dx}=6x+5$ and explain the working, that question is Type 1 for you.
Keep these skills dependable through regular practice. Check conditions, algebra and calculator inputs, and show the reasoning clearly. Recognising a familiar question is a useful start; the independent attempt confirms that you can actually do it.
Type 2: You Don’t Know You Know
The question looks unfamiliar, but you can connect it to something you already understand and solve it. You may not have seen that wording, diagram or context before.
For example, a new context about a changing quantity might lead you to a familiar differentiation method. Once you identify the relationship, you can carry out the working without a solution beside you.
Afterwards, record the clue that helped: what did the wording tell you, and why did you choose that method? This gives you something useful to look for when the same idea appears in another form.
Type 3: You Know You Don’t Know
You have seen the question or recognised the method, but you still get stuck. You may have a school tutorial question that looks familiar every time you open it, yet you cannot complete the working.
Clear that doubt before the exam. Identify the first step you cannot justify, then use your notes, a reliable explanation or a teacher’s feedback to resolve it. Bring your attempt and ask a specific question about that step.
Once you understand the explanation, close it and try again. Then attempt a similar question with different values or wording. The aim is to turn that Type 3 question into Type 1: something you recognise and can do independently.
In the TGM Question Bank, the Similar Questions feature can help you find related practice. Use the written or video explanations available to you to resolve the gap, then return to your own working. Your school worksheets and topical practice sets can serve the same purpose.
If the same error returns, trace whether it comes from the concept, the interpretation of the question or an execution habit such as copying a sign. Our self-monitoring guide gives you questions to use in that review.
Type 4: You Don’t Know You Don’t Know
You cannot yet identify an approach or complete the question. It may combine familiar ideas in a way you have not encountered, or reveal a gap you did not know you had.
You cannot rehearse every possible question in advance. My approach is to prepare students by strengthening their understanding of the mathematics underneath the methods. Ask why a formula works, what its conditions are and how you could derive it.
For AP and GP, try explaining where the sum formulas come from. For an AP, consider pairing the first and last terms. For a GP, compare the sum with the same sum multiplied by the common ratio, and consider the case where the ratio is 1 separately.
These are ways to explore the ideas, not a guarantee that any unfamiliar question will become easy. The purpose is to have mathematical relationships you can reason from when a familiar template is missing.
A Worked Example: Why the Variance Formula Works
One example I use is the variance formula. Why do we subtract the square of the mean from the mean of the squares?
For a random variable $X$ with finite $E(X^2)$, write $\mu=E(X)$. Variance is the expected squared distance from the mean:
$$\operatorname{Var}(X)=E\left[(X-\mu)^2\right].$$
Expand the square and use the fact that $\mu$ is a constant:
$$\begin{aligned}\operatorname{Var}(X)&=E(X^2)-2\mu E(X)+\mu^2\\&=E(X^2)-2\mu^2+\mu^2\\&=E(X^2)-[E(X)]^2.\end{aligned}$$
The distinction matters: $E(X^2)$ means square each value first, then take the expectation. $[E(X)]^2$ means find the mean first, then square it.
As a check, suppose $X$ takes values 1 and 3 with equal probability. Then $E(X)=2$ and $E(X^2)=5$, so the variance is $5-2^2=1$. Both values are one unit from the mean, so their squared distances are both 1. The definition and the formula agree.
This is an illustrative reasoning exercise: explain the formula, test a simple case and connect the result back to its meaning.
Give Unfamiliar Questions Thinking Time in the Exam
When a Type 4 question appears, try to keep engaging with it. Read the conditions, write down what you know and consider a diagram or a simpler related case. An unfamiliar opening does not tell you how much of the question you can eventually do.
My advice is to complete the questions you can tackle and check your Type 1 and Type 2 working carefully, while leaving time to return to the unfamiliar parts. Avoid letting one question take all the time needed for the rest of the paper.
On your return, ask: which relationship connects the given information to what I need to find? Write down valid steps and see where they lead. Practise this process in timed sets so you have experience deciding when to continue and when to move on.
There is no fixed number of Type 4 questions in this framework. The category describes your experience of a question, rather than an official allocation of marks or grades.
Use Types 3 and 4 to Assess a Tutor’s Fit
A distinction I make is that a good tutor helps you work through Type 3 questions, while a great tutor also prepares you to face Type 4 questions. I use this as a practical check of the teaching, rather than a label based on how quickly a teacher can produce an answer.
During a trial lesson or consultation, look for two things:
- Can the teacher resolve your familiar doubt? Bring a Type 3 attempt. Look for an explanation of the first gap, then check whether you can apply it yourself.
- Can the teacher help you reason through a new problem? Ask why the method works, what happens if a condition changes and how the same idea could appear differently.
For example, after explaining the variance formula, a teacher could ask you to interpret it or test it on a simple distribution. You should have an opportunity to think and explain, as well as listen.
As a tutor at Tim Gan Math, I recommend applying these checks to our lessons too. Use what you can demonstrate afterwards to judge whether the approach fits your needs. You can ask the same questions in school consultations or a study group; the framework does not mean every student needs tuition.
For more criteria to use at a trial, see our guide to choosing an H2 Math tutor.
Turn the Framework Into Your Next Revision Session
Choose a small mixed set and make a genuine attempt before classifying it. Then select the follow-up that matches the gap:
- Type 1: Check accuracy and maintain the skill through mixed practice.
- Type 2: Record the connection that made the new-looking question solvable.
- Type 3: Clear the first doubt, then attempt related questions with the explanation closed.
- Type 4: Review the underlying ideas, discuss the choice of approach and try a related variation later.
If you are aiming for a stronger result, do not let all your revision stay within the comfortable Type 1 and Type 2 questions. Make time for the Type 3 doubts you can identify and the deeper reasoning that helps you prepare for Type 4. This is a way to organise your work, not a grade guarantee.
Use our H2 Math study-system guide to build this practice and feedback into a routine. The revision-order guide can help you decide which topics to revisit.
Conclusion
After your next practice set, choose one familiar doubt to resolve and one underlying idea to explain more deeply. Check the change through a later independent attempt.
Action Steps:
Bring one unfinished tutorial question to your next consultation.
After the explanation, attempt a similar question without the solution.
Choose a formula and explain where it comes from and when it applies.
The useful outcome is a clearer next step and evidence that you can do more on your own.