Due to the potential to fail here I am assuming the Foundation paper
Non calc (almost) guaranteed
Factors and multiples
Calculations with fractions and mixed numbers (+ - x / ) including fractions of amounts
Finding percentages of amounts, including increase and decreasing by a percentage
Using money (e.g. Bob goes to the cafe and buys two teas and a bun with a £20 note, how much change should he get?)
A long multiplication or division, possibly with decimals (this could be worth 3 marks and they get method marks even if they make a mistake so worth a try)
BIDMAS (e.g. what is 4 + 6 x 2)
Basic powers and square roots (e.g. what is the square root of 64 or what is 2^3)
Arithmetic with negative numbers
'Estimate...' where you have to round all the values to an easier calculation
You could get more difficult powers like 3-2 or 250.5 as well, but only look at those if you've nailed the rest.
Exact trig values - guess the answer is 1/2. Put no more effort into it than that!
Calc paper only
Using your calculator to e.g. put in a complicated fraction with roots. Make sure they can use the fraction and power buttons and know how to 'finish' a square root sign. This will often be followed by a 'round your answer to 2d.p.
Compound interest (there is a formula for this in the formula booklet that might be worth explaining)
Don't bother with trig, it ain't worth it
Everything else is pretty much fair game for both papers.
Major topics that always come up in some form:
Simplifying algebra - collecting like terms when adding or subtracting, sorting out indices when multiplying or dividing or raising to a power
Solving equations
Subbing into formulae
Mean, median, mode, range (use the song to remember which is which )
Angle rules (basic ones like straight lines, triangles, around a point) and something involving parallel lines.
Basic probability
Ratio, including simplifying and sharing in a ratio
Converting between fractions, decimals and percentages
Calculations with time
Circles - circumference and area - the formulae ARE ON THE FORMULA SHEET (on the non-calc paper this will probably ask for answers in terms of pi)
Other topics also come up most of the time but you wanted some focus...
Things that need to be memorised
Times tables (or a times tables grid)
Prime numbers up to 50 is best (not the whole song!) up to 30 is most useful. 1 is NOT A PRIME
Names of shapes - do they know their trapezium from a parallelogram? Hexagon from an octagon? Cuboid from a cone? Flash cards and self-testing help here
The difference between a factor and a multiple
Metric conversions - how many cm in a m etc.
The most important thing about getting a 4 is remembering each mark is equally valuable. There is no point in spending weeks learning trig which will be worth a couple of marks and then losing a couple of marks on the first page because you can't remember the name of a pentagon.
The first double page is key, those are the easiest marks to get, and yet most students won't get them all meaning they have to pick up harder marks later on to make up for it.
So go to mathsgenie and do all the pages 1-2. If anything is wrong there, fix it first!
https://www.mathsgenie.co.uk/papers.php
And use https://www.mathsgenie.co.uk/gcse.php for topic focused revision. Watch the video, do some questions, mark your answers. Only look at grade 1-4 topics, leave the grade 5.