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

More graphs and coordinate geometry: 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: Shapes on coordinate axesAbout 20 min

Lessons

Practice and tests

Mixed practiceQuestions mixed across your lessons.

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)

Helps with: GCSE (AQA, Edexcel, OCR)

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