OpenRevise

Maths · Graphs

Knowledge organiser

The whole chapter on one page. Print it on A4 — it is already landscape — or cover a box and see how much of it you can say from memory.

Back to the chapter

Maths · OCR Paper 2

Graphs

Straight-Line Graphs

Plotting lines, finding gradients, and reading the gradient and intercept from y = mx + c.

  • Coordinates A pair of numbers (x, y) that give the position of a point on a grid.
  • Gradient A measure of how steep a line is, found by dividing the change in y by the change in x.
  • Intercept The point where a line crosses an axis.
A line on a grid with a gradient triangle drawn between two points, showing a rise of 4 and a run of 2, so a gradient of 2.

Equations of Straight Lines

Finding the equation of a line from two points, midpoints, and parallel and perpendicular lines.

  • Equation of a line A rule such as y = 2x + 1 that is true for every point on the line.
  • Midpoint The point halfway along a line segment.
  • Line segment The part of a line between two end points.
Two perpendicular lines on a grid with gradients 2 and minus a half, whose product is minus 1.

Quadratic Graphs

Plotting quadratics and using the roots, turning point and line of symmetry to read and solve.

  • Quadratic An expression or equation whose highest power of x is x^2.
  • Parabola The smooth U-shaped curve that is the graph of a quadratic.
  • Root A value of x where a graph crosses the x-axis, so y = 0.
A parabola with its roots, turning point, y-intercept and line of symmetry marked and labelled.

Cubic, Reciprocal and Other Graphs

Recognising and plotting cubic, reciprocal, exponential and circle graphs.

  • Cubic An equation whose highest power of x is x^3, with an S-shaped graph.
  • Reciprocal One divided by a number or expression, such as \dfrac{1}{x}.
  • Exponential A relationship where the unknown is in the power, such as y = 2^x.
Six graph shapes: a straight line, a parabola, a cubic curve, a reciprocal curve in two branches, an exponential curve and a circle.

Real-Life Graphs

Conversion graphs, filling containers and velocity-time graphs: gradient as rate and area as distance.

  • Conversion graph A graph for changing between two units, such as miles and kilometres.
  • Rate of change How quickly one quantity changes compared with another.
  • Acceleration The rate at which velocity changes, in metres per second per second.
A straight-line conversion graph from miles to kilometres, with 30 miles read across to 48 km.