Coordinate geometry
Gradients and straight lines
Two points fix a straight line. From them you can find how steep it is (gradient), how long the segment is (Pythagoras), its middle (average the coordinates), and its equation .
≈ 30 minParallel and perpendicular lines
Parallel lines have equal gradients. Perpendicular lines have gradients that multiply to : flip the fraction and change the sign. With these two facts, plus one point, you can write down any related line.
≈ 30 minTravel graphs and curves
On a distance–time graph the gradient is the speed. On a speed–time graph the gradient is the acceleration and the area underneath is the distance. Learn the shapes of quadratic, cubic, reciprocal and exponential graphs so you can recognise them at a glance.
≈ 35 minGradients of curves and graphical solutions
A curve's steepness changes, so its gradient at a point is the gradient of the tangent there: draw it with a ruler, pick two far-apart points on it, and find rise over run. Where two graphs cross, both equations are true at once, so the crossing points solve the equation formed by setting them equal.
≈ 30 min