Graphs and coordinates: shapes on axes, regions, areas and tangents

More graphs and coordinate geometry for the exam: shapes on coordinate axes, gradients and perpendicular lines in shapes, regions with strict and inclusive boundaries, the area under a curve from trapezia, and the gradient at a point from a tangent.

Start with Shapes on coordinate axes. In 30 minutes you will be able to find the length of a line segment from its end points with Pythagoras. 2 of the 5 lessons here are free.

Lessons

Based on your answers on this device and your account. It shows where practice will help most, not a grade.

Practise and test

By the end you can

Find lengths, midpoints, missing corners and areas of shapes whose corners are given as coordinates
Name a triangle or quadrilateral from squared lengths and gradients
Use parallel gradients and the equations of sides to solve problems about shapes
Use perpendicular gradients for right angles, heights of triangles, diagonals of a rhombus and the corners of a square (Higher)
Describe regions with strict and inclusive boundaries, count the whole-number points in them and find the greatest value of an expression there (Higher)
Estimate the area under a curve with trapezia, say whether it is an overestimate, and interpret it as a distance or a total (Higher)
Estimate a gradient at a point from a tangent and interpret it as a speed, an acceleration or a rate (Higher)
Use the kinematics formulae v = u + at, s = ut + ½at² and v² = u² + 2as (OCR J560)

Specifications

DfE content (all boards) G11, G20, A8, A9, A10, A15, A22
AQA 8300 Geometry and measures; Algebra
Pearson Edexcel 1MA1 Algebra; Geometry and measures
OCR J560 6.02e Kinematics formulae; 6.04b Inequalities in two variables; 7.02 Straight line graphs; 7.04b Gradients; 7.04c Areas; 8.01g x- and y-coordinates in plane geometry; 10.05a Pythagoras' theorem

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