OpenRevise GCSE

Maths · Topic 1: Year 10

Graphs

Straight-line graphs and their equations, parallel and perpendicular lines, distance-time and velocity-time graphs, real-life graphs, midpoints and line segments, and the shapes of quadratic, cubic, reciprocal, exponential, circle and trigonometric graphs.

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Key terms in this chapter

All 37, gathered from every lesson.

Linear
Making a straight line when plotted.
Gradient
The steepness of a line: change in \(y\) divided by change in \(x\).
\(y\)-intercept
Where a line crosses the \(y\)-axis.
Coordinates
A pair \((x, y)\) giving a point's position.
Origin
The point \((0, 0)\) where the axes cross.
Parallel
Lines with the same gradient that never meet.
Perpendicular
Lines that meet at a right angle.
Negative reciprocal
\(-\dfrac{1}{m}\): the gradient of a line perpendicular to one with gradient \(m\).
Intercept
Where a line crosses an axis.
Speed
Distance travelled per unit of time.
Average speed
Total distance divided by total time, including stops.
Rate of change
How fast one quantity changes compared with another; the gradient.
Velocity
Speed in a given direction.
Acceleration
Rate of change of velocity, in m/s².
Deceleration
Slowing down; a negative acceleration.
Conversion graph
A graph for changing between two units.
Fixed charge
A cost that is paid whatever the amount used; the \(y\)-intercept.
Direct proportion
Two quantities whose graph is a straight line through the origin.
Break-even point
Where two cost lines cross, so both options cost the same.
Line segment
The part of a line between two end points.
Midpoint
The point exactly halfway along a line segment.
Bisect
Cut into two equal parts.
Perpendicular bisector
A line that cuts a segment in half at right angles.
Quadratic
An expression whose highest power of \(x\) is \(x^2\).
Parabola
The U-shaped (or ∩-shaped) curve of a quadratic graph.
Roots
The \(x\)-values where a graph crosses the \(x\)-axis.
Turning point
The point where the curve changes direction: a minimum or maximum.
Line of symmetry
The vertical line through the turning point.
Cubic
An expression whose highest power of \(x\) is \(x^3\).
Reciprocal graph
A graph of the form \(y = \frac{k}{x}\).
Asymptote
A line that a curve gets closer and closer to but never touches.
Root
An \(x\)-value where a graph crosses the \(x\)-axis.
Exponential
A function where the variable is the power, such as \(y = 2^x\).
Growth and decay
An exponential that increases (\(b > 1\)) or decreases (\(0 < b < 1\)).
Asymptote
A line a graph approaches but never touches.
Circle equation
\(x^2 + y^2 = r^2\): centre the origin, radius \(r\).
Period
The interval after which a graph repeats.