 Year 8 Maths • Use index notation for simple positive integer powers; substitute positive and negative numbers into expressions such as 4x – 2, 3x² + 4 and 2x^3.
• Plot graphs of linear functions in which y is given explicitly or implicitly in terms of x.
• Draw and interpret graphs modelling real situations.
• Use parallel lines, alternate angles and corresponding angles; calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; calculate and use the angles of regular polygons; understand simple proofs involving triangles and quadrilaterals.
• Recall the meaning of circle, chord, tangent, arc, sector, segment; find circumferences and areas enclosed by circles, recalling relevant formulae.
• Construct triangles and other 2-D shapes using a ruler and a protractor, given information about their sides and angles; construct inscribed regular polygons; construct nets of cubes, regular tetrahedra, square-based pyramids and other 3-D shapes.
• Recall and use the formula for the area of a parallelogram and a triangle; use the formula for the area of a trapezium; calculate perimeters and areas of shapes made from triangles and rectangles; find the surface area of simple shapes using the area formulae for triangles and rectangles.
• Calculate volumes of shapes made from cubes and cuboids.
• Analyse 3-D shapes through 2-D projections and cross-sections, including plans and elevations.
• Recognise, visualise and construct enlargements of objects using positive integer and fractional scale factors; identify the centre and the scale factor of enlargement; understand the implications of enlargement for perimeter.
• Transform triangles and other 2-D shapes by rotation or reflection or translation using vectors; recognise and visualise rotations, reflections and translations including reflection symmetry of 3-D shapes; understand the properties preserved by these transformations; understand congruence in the context of transformations.
• Identify different mutually-exclusive outcomes and know that the sum of the probabilities of all these outcomes is one.
• Draw and interpret scatter graphs including using lines of best fit; have a basic understanding of correlation, identifying ‘correlation’ or ‘no correlation’.
• Use and interpret diagrams for discrete and continuous data, including frequency polygons and stem and leaf diagrams; identify the modal class; calculate the mean of grouped discrete data compare distributions and make inferences, using the shapes of the distributions and measures of average and range.
• Use and understand terminating and recurring decimals including exact fraction equivalents; solve problems involving multiplication and division by decimals with up to two decimal places
• Use the terms cube root, negative square root; recall the squares to 15²and the corresponding square roots; recall the cubes of 2, 3, 4, 5, and 10; use index laws with numerical and algebraic expressions involving multiplication and division of positive integer powers.
• Use and generate formulae in context; substitute positive and negative numbers into a formula.
• Form and solve equations.
• Change the subject of a formula in cases where the subject only appears once.
• Know that measurements using real numbers depend on the choice of unit; recognise that a measurement given to the nearest whole unit may be inaccurate by up to one half in either direction.
• Solve angle problems involving intersecting and parallel lines, and polygons; understand that the tangent at any point on a circle is perpendicular to the radius at that point.
• Understand, recall and use Pythagoras’ theorem.
• Solve problems involving area and circumference of circles; use pi in exact calculations.
• Understand and use rates and compound measures, including speed and density.
• Solve probability problems involving theoretical models or relative frequency.
• Calculate the mean from grouped continuous data.