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Maths · AQA Paper 1

Graphs

The graph skills tested on AQA Paper 1: straight lines and their equations, quadratic, cubic and reciprocal graphs, and real-life graphs including velocity-time graphs.

  • 5 lessons
  • AQA
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Lessons

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Key terms in this chapter

All 45, gathered from every lesson.

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.
Table of values
A table of \(x\)-values and the matching \(y\)-values, used to plot a graph.
Linear
A graph or equation that gives a straight line.
Parallel lines
Lines with the same gradient, which never meet.
Rise
The vertical distance between two points on a line.
Run
The horizontal distance between two points on a line.
Origin
The point \((0, 0)\), where the axes cross.
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.
Perpendicular
At a right angle to each other.
Negative reciprocal
A number turned upside down with its sign changed, such as \(-\dfrac{1}{2}\) for 2.
Substitute
Replace letters in an equation with numbers.
Gradient-intercept form
The form \(y = mx + c\).
Parallel
Lines with the same gradient.
Reciprocal
One divided by a number, such as \(\dfrac{1}{4}\) for 4.
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 \(y = 0\).
Turning point
The point where a curve changes direction, such as the lowest point of a U.
Line of symmetry
A line that divides a shape into two mirror-image halves.
Maximum
The highest value, found at the turning point of an upside-down U.
Minimum
The lowest value, found at the turning point of a U.
y-intercept
The point where a graph crosses the \(y\)-axis.
Completing the square
Rewriting a quadratic as \((x - a)^2 + b\) to find its turning point.
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 \(y = 2^x\).
Asymptote
A line that a curve gets closer and closer to without ever touching.
Branch
One of the separate pieces of a graph such as \(y = \dfrac{1}{x}\).
Function
A rule that gives one output for each input.
Circle equation
\(x^2 + y^2 = r^2\) for a circle with centre the origin and radius \(r\).
Power
The small number showing how many times to multiply, such as 3 in \(x^3\).
Smooth curve
A curve drawn freehand with no corners or breaks.
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.
Deceleration
A negative acceleration, when something is slowing down.
Velocity
Speed in a given direction.
Velocity-time graph
A graph of velocity against time, where the gradient is acceleration.
Fixed charge
An amount paid whatever the quantity used.
Tangent
A straight line that touches a curve at one point.
Trapezium
A shape with a pair of parallel sides, used to estimate areas under curves.