Sequences, functions and graphs
Sequences
A sequence follows a rule. Linear sequences go up by a constant difference, so their nth term is . Quadratic sequences have a constant second difference; geometric sequences multiply by the same number each time; Fibonacci-type sequences add the previous two terms.
≈ 30 minGradients 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 min