Draw the line.
Three toys for GCSE Foundation maths: drag a straight line into place and read its gradient, build percentages as bars, and cut a corner off a rectangle.
Straight lines · y = mx + c
FIG. 01 · ALGEBRA A9 / A10How steep. Positive climbs left → right, negative falls. m is the rise for a run of 1.
Where the line crosses the y-axis. Change c and the whole line slides up or down.
Your line
y = x
Matched 0 so far.
Exam technique. Nearly every "find the equation of this line" question is two marks: count the rise over the run for m, then read where it cuts the y-axis for c. Do those two things and write y = mx + c — you are done. You do not need a formula.
Percentages · the multiplier
FIG. 02 · RATIO R9 / NUMBER N12What to do with it
One step, not two. 25% of 240 is 240 × 0.25. Finding the percentage and then adding it on is two chances to slip; the multiplier is one. To undo an increase you divide by the same multiplier — that is every "reverse percentage" question in one line.
Area & perimeter · cut the corner
FIG. 03 · GEOMETRY G16 / G17Watch the perimeter. Cut a corner out and the area drops — but the perimeter does not move at all. The two new edges you added are exactly as long as the two you removed, so it stays 2(w + h). Examiners love this one because most people assume both numbers must fall.