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LearnEdexcel4MA12016 specificationPapers 1H, 2H · Higher tierSequences, functions and graphs

Papers 1H, 2H · Module

Sequences, functions and graphs

6 subtopics≈ 185 min in total

Start the module: Sequences Open graphing calculator

Sequences
A sequence follows a rule. Linear sequences go up by a constant difference, so their nth term is $dn+c$ . 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 min
Functions
A function $f(x)$ is a rule turning an input into an output. A composite $fg(x)$ means "do $g$ , then $f$ ". The inverse $f^{-1}$ undoes $f$ : swap $x$ and $y$ and rearrange. Some inputs can't be used, such as values that make you divide by zero.
≈ 30 min
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 $y=mx+c$ .
≈ 30 min
Parallel and perpendicular lines
Parallel lines have equal gradients. Perpendicular lines have gradients that multiply to $-1$ : flip the fraction and change the sign. With these two facts, plus one point, you can write down any related line.
≈ 30 min
Travel 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
Gradients 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