IGCSEMaths Sequences & Graphs.

Confusing position number with term value in sequences

n = position (1st, 2nd, 3rd), the nth term formula gives the value at that position. Always verify by substituting n = 1, 2, 3 back into your formula.

Getting composite function order wrong — fg(x) vs gf(x)

fg(x) means apply g first, then f. Read right to left: "f of g of x." These almost never give the same answer.

Not rearranging to y = mx + c before reading the gradient

If the equation is 2y + 4x = 10, the gradient is NOT 4. Rearrange first: y = −2x + 5, so m = −2.

Substituting back into the derivative instead of the original equation

When finding turning point coordinates, solve dy/dx = 0 for x, then substitute x into the ORIGINAL equation y = ... to find the y-coordinate.

Forgetting the "inside liar" rule for graph transformations

f(x + a) moves the graph LEFT by a (opposite to the sign). f(x) + a moves it UP by a (as expected). Outside = truthful, inside = reversed.