One-page revision sheet

• Coordinates are written (x, y) — always across first, then up or down.
• The origin is (0, 0), where the two axes cross.
• The axes divide the plane into four quadrants, numbered anticlockwise from the top right.
• Quadrant 1 (+, +), quadrant 2 (−, +), quadrant 3 (−, −), quadrant 4 (+, −).
• A point with x = 0 lies on the y-axis; a point with y = 0 lies on the x-axis.
• Points with the same y-coordinate lie on a horizontal line; same x-coordinate gives a vertical line.
• The distance between two points on the same horizontal line is the difference in their x-coordinates.
• The midpoint is found by averaging the x-coordinates and averaging the y-coordinates.

Key words: coordinates  ·  x-coordinate  ·  y-coordinate  ·  origin  ·  axis  ·  quadrant  ·  midpoint

• A straight line has the rule y = mx + c.
• m is the gradient: how much y changes for every 1 that x increases.
• c is the y-intercept: where the line crosses the y-axis, found by putting x = 0.
• To plot a line: make a small table of values, plot the points, then join them with a ruler.
• Two points fix a line, but always plot a third as a check.
• A negative gradient means the line goes down from left to right.
• y = 4 is horizontal; x = −2 is vertical. Neither is of the form y = mx + c.
• Lines with the same gradient are parallel and never meet.

Key words: gradient  ·  y-intercept  ·  straight-line graph  ·  table of values  ·  plot  ·  parallel

• Before reading anything, check what each axis shows and what one square is worth.
• A conversion graph goes through the origin, because 0 of one unit is 0 of the other.
• A graph with a fixed charge does not start at the origin — the intercept is that charge.
• On a distance–time graph, the gradient is the speed.
• A steeper line means faster; a flat section means stopped.
• A line going down means returning towards the start.
• Average speed = total distance ÷ total time.
• Read from the graph carefully: on a large scale, one square out is a big error.

Key words: conversion graph  ·  distance–time graph  ·  rate  ·  scale  ·  average speed