where it usually goes wrong
the six that cost
the most marks
the equals sign means balance
most errors are doing something to one side and forgetting the other. it is not carelessness, it is a habit that has to be built deliberately.
negatives and distribution
a minus sign in front of a bracket changes every term inside it. this single thing accounts for a startling share of lost marks.
fractions inside equations
multiply through by the denominator early. people who fight fractions all the way down the page usually arrive somewhere wrong.
word problems are a translation task
the maths is easy once it is written as an equation. the hard part is turning a sentence into one, and that is a separate skill worth practising alone.
a function is a machine
input goes in, output comes out. treating f(x) as a formula to memorise rather than a process is why function notation feels alien.
factoring patterns repeat
difference of squares, perfect square trinomials, and grouping. there are not many, and recognising them on sight is most of the work.
what to post
a photo of the problem, or a sentence about where you got stuck. set the deadline and attach anything that matters.
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