Formulas You Keep Forgetting: Practise Choosing, Not Just Recalling

This post is about training the decision. For the general card system and review dates, see the spaced repetition plan. For hour budgets and weekly sessions, see the timetable post. Here the subject is only the formulas.

Step 1: find out which formulas the paper gives you

Some papers print formulas. Some do not. You cannot know which until you read your syllabus.

As an example of how mixed this can be, take the Cambridge International AS and A Level Physics 9702 syllabus for 2025 to 2027. It states that a data and formulae page appears in the question papers. The page lists, among others, s = ut + ½at², v² = u² + 2as, p = ρgh, upthrust F = ρgV, and resistors in series and parallel. The learning outcomes in the same syllabus tell candidates to “recall” and use F = ma, E_K = ½mv², V = IR, P = VI and several others, and these are not on the sheet I opened. Source: Cambridge 9702 syllabus 2025 to 2027, opened 15 October 2026 (the sheet’s text extracted unevenly, so check the printed page rather than relying on my list).

The consequence is practical. A formula on the sheet needs recognition. A formula off the sheet needs recall and recognition. Spend your recall effort on the second list.

I did not verify what the Cameroon GCE Board prints for O Level and A Level papers. Until you have checked, assume nothing is supplied.

Step 2: build cards around the situation

A name-to-formula card (“kinetic energy” on the front) tests whether you can reproduce a string of symbols. A paper never asks that. It describes a situation and expects you to supply the relationship.

Turn the card round. Put the situation on the front, in the words a question would use. Put the formula, the reason it fits, and the clue on the back.

Here are six cards. They are illustrative, written by me for this post. The formulas are from the Cambridge syllabus above. The arithmetic is mine and you can check it.

Card 1 Front: A car starts from rest and accelerates uniformly at 2.0 m s⁻² for 5.0 s. How far does it travel? Back: s = ut + ½at². You are given time. Clue: “from rest” makes u = 0. Work: s = 0 + ½ × 2.0 × 5.0² = 25 m.

Card 2 Front: A car moving at 20 m s⁻¹ brakes uniformly and stops in 40 m. What is its deceleration? Back: v² = u² + 2as. You are not given time. Clue: distance and speeds, no time. Work: 0 = 20² + 2 × a × 40, so a = −400 ÷ 80 = −5.0 m s⁻². The car decelerates at 5.0 m s⁻².

Card 3 Front: A 1500 kg car has a resultant force of 3000 N on it. What is its acceleration? Back: F = ma. Clue: “resultant force” and “mass” together. Work: a = 3000 ÷ 1500 = 2.0 m s⁻².

Card 4 Front: A 2.0 kg trolley moves at 3.0 m s⁻¹. How much energy is stored in its motion? Back: E_K = ½mv². Clue: “energy” of a moving mass. Work: ½ × 2.0 × 3.0² = 9.0 J.

Card 5 Front: A 12 V supply is connected across a 4.0 Ω resistor. What current flows? Back: V = IR, rearranged. Clue: voltage and resistance given, current wanted. Work: I = 12 ÷ 4.0 = 3.0 A.

Card 6 Front: A 6.0 Ω and a 3.0 Ω resistor are connected in parallel. What is the combined resistance? Back: 1/R = 1/R₁ + 1/R₂. Clue: “in parallel”. Work: 1/R = 1/6 + 1/3 = 1/2, so R = 2.0 Ω. The result is smaller than either resistor, which is the check.

Cards 1 and 2 are the reason for the design. Both concern constant acceleration and both use the same symbols. Only one is correct for each problem, and the deciding fact is whether time is given. A name card never practises that distinction.

Now try one card from memory without looking back. Then try to say, for each card, what in the front told you which relationship to use. If you cannot, write that clue on the back before moving on. That written clue is the card’s real content.

Step 3: mix the practice

Mixing is the practice that matches the exam. Two studies and one trial give numbers.

Rohrer and Taylor (2007, Instructional Science) taught 18 university students to find the volume of four unfamiliar solids. Each solid’s volume depends only on a radius and a height. Both groups did the same practice problems over two sessions a week apart. One group did them blocked, four problems of one solid at a time. The other did them mixed. In practice, the blocked group scored higher (89% against 60%). One week after the last practice session, the test results reversed: the mixed group scored 63% and the blocked group 20%. The authors note the sample is small, though the effect was large. Source: Rohrer and Taylor 2007 (PDF), opened 15 October 2026.

Rohrer, Dedrick, Hartwig and Cheung (2020, Journal of Educational Psychology) ran a randomised trial in Grade 7 mathematics classes in Florida, with 787 students in the main sample. Over 103 days, one set of classes used worksheets that mixed four problem types. Comparison classes got the same problem types blocked by lesson. On a test the WWC lists at 43 days, the mixed group scored 62.17 and the blocked group 37.60 on a test written by the researchers. The US Department of Education’s What Works Clearinghouse rated the study as meeting its standards without reservations. Source: What Works Clearinghouse study page, opened 15 October 2026.

Dunlosky and colleagues (2013) rated interleaved practice as moderate utility, short of the top rating because the classroom evidence was still limited when they wrote. The trial above came afterwards. Source: Dunlosky et al. 2013 (PDF), opened 15 October 2026.

Expect mixing to feel worse. In the 2007 study, mixed practice scored 60% while blocked scored 89%. Low scores during mixed practice are normal and are not a reason to go back to blocks. Do not mix until you can solve each type on its own, since the unfamiliar first meeting with a method is better handled in a block.

A mixed set you can do tonight

Cut the six cards into slips and shuffle them. Without looking at the backs, write the formula you would choose for each slip before doing any arithmetic. Then calculate. Score the choice and the answer separately, in two columns. A wrong choice with correct arithmetic is a different problem from a right choice with an algebra slip.

Run the set again three days later with the order changed. Review dates for a longer programme come from the spaced repetition plan.

Step 4: collect the trigger phrases

Go through past papers for one topic. For each question, underline the words that told you which relationship applied. Write the phrase and the formula side by side. In the six cards above, the triggers were “from rest”, “stops in 40 m”, “resultant force”, “energy of a moving mass”, “across a resistor” and “in parallel”.

After a few papers you will find that the phrases repeat. That list is your own, specific to your syllabus, and it is more useful than a copied formula list because it connects the wording to the method.

Step 5: check units before you trust an answer

Run a units check on every answer. In card 5, volts divided by ohms gives amperes, and amperes are the unit of current. If your result came out in joules, the formula was wrong.

Units also let you rebuild a half-remembered relationship. If you remember that pressure is measured in newtons per square metre, you can reconstruct that pressure is force divided by area.

Mnemonics

A mnemonic helps when the thing to remember has an arbitrary order. It does not help you decide when to use a formula. The usual failure is remembering the mnemonic and forgetting what each letter stood for. Dunlosky and colleagues rated the keyword mnemonic as low utility in their review (same source as above). If you use one, add it on top of a card that already describes the situation.

When you are stuck in the exam

Write down every quantity the question gives you, with its unit. Beside each, write the quantity it asks for. Often the relationship is the only equation that links those quantities. If it is not, write what you do know and move on; a half-formed setup can earn method marks where a blank earns nothing. Return to the question later.

Quick plan

1. Check your syllabus for supplied formulas. List the ones you must recall.
2. Make one situation card per formula you keep losing: situation on the front, formula, clue and worked answer on the back.
3. Do not file the cards by chapter. Shuffle them for each session.
4. Score choice and arithmetic separately.
5. Review on the schedule in the spaced repetition plan.