first of all i have never done tutoring let alone done a tutoring exam but just so yk, yr 10 math is piss easy (i didnt get below 90% till yearlies but even then i got a 87%) and it covers the following:
- statistics (its all calculator so doesnt even need thinking)
- algebra (rearranging stuff, subing in values, index laws, making a variable the subject)
- trig (exact values, cosine rule, sine rule, bearings, identifying sin/cos/tan graphs, ASTC - all of which are piss easy)
- surds
- probability (very basic like 'what is the probability a child is a girl?' umm 1/2 give harder bro)
- functions (this is absolutely new so if you dont know how to yet start preparing its so easy too! parabolas, exponentials, hyperbolas, cubics, linear, quadratics, circles, finding equations, vertex points, finding interception points)
- simultaneous equations (also used in functions in finding interception points)
- completing squares (just used when: asked to or when finding the equation for a circle)
- financial maths (simple interest, compound interest, earning money)
- bonus: towards the end of year 10 we took logarithms tho its only year 11 and is absolutely not significant in year 10
i listed all the year 10 5.3 topics (assuming u do 5.3) and these are from the top of my head
for early year 11 advanced math its just:
- functions (same as year 10 except you learn: absolute values (graphing and solving), piecewise functions, functions and relations, one-to-one, one-to-many, many-to-one and many-to-many)
- algebra (exactly the same)
- surds
- simultaneous equations (gets a bit complicated)
- discriminant (you wouldve touched upon this in year 10 but it becomes an 'actual' topic in year 11)
ig thats it but im like 97% sure (i feel that i missed something)
edit: i remember what i missed at my school we also did equating coefficients but im not sure if its in the syllabus
edit 2: also do graphing polynomials and even/odd functions
so there you go a list of everything in year 10 5.3 and early year 11 advanced
i cant speak for extension year 11 bc different schools start different topics, my school did combinatorics first but a lot of other schools do functions first idk