Learning overview for: Mathematics Term Key topics What most pupils will learn (prior assessment may alter starting point & content) Number Factors, multiples and primes HCF and LCM Calculate with negative numbers Efficient use of a calculator Standard form Year group: Higher GCSE Indices Surds How might this learning be extended? How will this learning be assessed? Angles Construction Angles in polygons Angles in parallel lines Bearings Collecting and interpreting data Questionnaires Sampling Averages from: (i) Discrete data (ii) Frequency tables (iii) Grouped frequency tables Moving averages Fractions and Decimals Add, subtract, multiply and divide fractions Calculate fraction of an amount Add, subtract, multiply and divide decimals Convert recurring decimals to fractions
Expressions and sequences Rounding (decimal places and significant figures) Estimation Simplifying Expanding Factorising Nth term Factorising quadratic expressions Factorising expressions involving the difference of 2 squares Measures Displaying data Speed, distance and time Travel graphs Density Length, area, volume formulae Convert measurements Stem and leaf diagrams Scatter graphs Frequency polygons Box plots Cumulative frequency Upper and lower bounds Histograms Area Area of 2D shapes (triangles and quadrilaterals) Area of compound shapes Area and circumference of a circle Sector area and arc length Equations Solve linear equations with: (i) Unknown on one/both sides (ii) Brackets Solve linear equations with Fractions Solve equations using trial and improvement
Percentage Straight Line Graphs Solve simultaneous equations by adding/subtracting Calculate % of an amount Increase/decrease by a % Increase/decrease using a multiplier Calculate % change Simple and compound interest Draw horizontal/vertical line (given equation) Complete table and plot graph Calculate gradient Solve simultaneous equations by multiplying one/both equation Reverse % Apply y = mx+c Parallel and perpendicular lines Solve simultaneous equations graphically Transformations Reflect shapes Rotate shapes Translate shapes Enlarge shapes with positive scale factors Describe transformations Enlarge shapes with negative and fractional scale factors Inequalities Show inequalities on a number line Describe an inequality Write down integer values Solve inequalities Show regions on a graph Change subject of a formula (subject appears twice) Formulae Substitute values into an expression Construct a formula Change subject of a formula (subject appears once)
Pythagoras and Trigonometry Ratio and Proportion Pythagoras and Trigonometry Simplify ratios Share a quantity in a ratio Apply direct proportion to calculate missing quantities Apply Pythagoras/Trigonometry to 3D problems Direct proportion Inverse proportion 3D Shape & Plans & Elevations Identify planes of symmetry on 3D shapes Sketch plan, front and side view of 3D shapes Calculate volume of straight edged prisms Calculate surface area of straight edged prisms Calculate volume of cylinder Calculate surface area of cylinder Calculate volume of a sphere/hemisphere, cone and pyramid Calculate surface area of a sphere/hemisphere, cone and pyramid Curved Graphs and Intersections Plot graphs of quadratic functions and estimate minimum and maximum values Use graphs of quadratic functions to estimate solutions Plot graphs of quadratic and linear functions to solve simultaneous quadratic/linear equations Probability Calculate the probability of a single event Construct/apply a tree diagram (independent and conditional events) Calculate the probability of mutually exclusive events (1 p) Construct/apply sample space
diagrams Estimate probability from relative frequency Construction, Loci and Congruence Construct a triangle, bisect a line/angle Construct a right angle at a point on a line Prove that two triangles are congruent Construct angles of 90o, 60o, 45o, and 30o Circle Theorems Construct the loci of points that are a given distance from a point/line Label the parts of a circle Identify and apply a circle theorem to calculate a missing angle Label the parts of a circle Identify and apply a circle theorem to calculate a missing angle Quadratics Factorise quadratics Factorise quadratics Solve quadratic equations by factorising Solve quadratic equations by factorising
Sine and Cosine Rule Similar Shapes Use the Sine Rule to calculate the area of a triangle Identify when two shapes are similar Calculate the scale of enlargement Calculate the missing lengths of similar shapes Use the Sine Rule to calculate the area of a triangle Calculate the area/volume of similar shapes Vectors Use vector notation Calculate the magnitude of a vector Add vectors Understand the properties of parallel vectors Solve geometric problems involving vectors Transforming Functions Use function notation Apply vertical and horizontal translations to functions Apply reflections to functions Apply stretches to functions Apply transformations to the graphs of sin x and cos x