Maths · AQA Paper 1
Vectors, Constructions and Loci
The vectors and construction skills tested on AQA Paper 1: column vectors and vector geometry, ruler-and-compass constructions, loci, bearings, scale drawings, and plans and elevations.
Lessons
Ticks are remembered on this device only.
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1
Column Vectors and Vector Arithmetic
Writing vectors as columns, adding, subtracting and multiplying them, and spotting parallel vectors.
9 terms -
2
Vector Geometry and Proof
Finding vectors by routes around a diagram, dividing lines in a ratio, and proving lines parallel or points collinear.
9 terms -
3
Ruler-and-Compass Constructions
Constructing perpendicular bisectors, angle bisectors, perpendiculars and triangles with ruler and compasses.
9 terms -
4
Loci
Drawing and shading regions defined by distances from points and lines, using bisectors and circles.
9 terms -
5
Bearings, Scale Drawings, Plans and Elevations
Three-figure bearings and back bearings, map scales, and the plan and elevations of simple solids.
9 terms
Key terms in this chapter
All 45, gathered from every lesson.
- Vector
- A quantity with a size and a direction.
- Column vector
- A vector written with the horizontal move above the vertical move.
- Scalar
- An ordinary number, such as 3, used to multiply a vector.
- Parallel
- Pointing in the same or opposite direction, with one vector a multiple of the other.
- Resultant
- The single vector that has the same effect as a combination of vectors.
- Magnitude
- The length of a vector.
- Displacement
- A change in position, with a direction.
- Opposite vector
- A vector of the same length in the opposite direction.
- Triangle rule
- Vectors added end to end give a resultant from the start to the finish.
- Vector proof
- A proof that uses vectors to show a geometric fact.
- Route
- A path from one point to another made from known vectors.
- Collinear
- Lying on the same straight line.
- Midpoint
- The point halfway along a line.
- Ratio
- A comparison of two parts of a line, such as \(2 : 3\).
- Position vector
- The vector from the origin to a point.
- Scalar multiple
- A vector multiplied by a number.
- Magnitude
- The length of a vector.
- Parallel
- Having the same direction, so one vector is a multiple of the other.
- Construction
- An accurate drawing made with a ruler and compasses.
- Bisect
- To cut into two equal parts.
- Perpendicular bisector
- A line that bisects another line at right angles.
- Angle bisector
- A line that divides an angle into two equal angles.
- Arc
- Part of a circle drawn with compasses.
- Compasses
- An instrument for drawing circles and arcs.
- Perpendicular
- At right angles.
- Equidistant
- The same distance from two or more things.
- Vertex
- The point where two lines meet to form an angle.
- Locus
- The set of all points that follow a given rule.
- Loci
- More than one locus.
- Equidistant
- The same distance from two or more things.
- Region
- An area of the drawing where the rules are true.
- Perpendicular bisector
- A line that cuts another line in half at right angles.
- Angle bisector
- A line that divides an angle into two equal parts.
- Radius
- The distance from the centre of a circle to its edge.
- Scale drawing
- A drawing in which all lengths are in proportion to the real ones.
- Arc
- Part of a circle drawn with compasses.
- Bearing
- A direction given as an angle measured clockwise from north.
- Three-figure bearing
- A bearing written with three figures, such as 045.
- North line
- A line pointing north, from which a bearing is measured.
- Back bearing
- The bearing of the start point from the end point.
- Scale
- The ratio between a length on a drawing and the real length.
- Plan
- A view of a solid from above.
- Elevation
- A view of a solid from the front or the side.
- Scale drawing
- A drawing in which lengths are in proportion to real lengths.
- Hidden edge
- An edge you cannot see, shown as a dashed line.