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Methods in Mathematics (Unit M1) and Applications of Mathematics (Unit A1) Higher Tier Revision List Only in Methods in Mathematics (Unit M1) NUMBER ✔ x ✔ x Exact calculations with surds and π Numbers and their representations including powers, roots, indices (integers) Use the vocabulary of factor (divisor), multiple and prime numbers Understand and use the relationship between ratio, fractions and decimal representations Recurring and terminating decimals ALGEBRA Use letter symbols Distinguish in meaning between the words equation, inequality, formula and expression Set up and use equations that describe direct and inverse proportion Set up, and solve simultaneous equations in two unknowns where one of the equations might include squared terms in one or both unknowns Solve quadratic equations approximately using a graph Substitution into a formula Rearrange an equation (Changing the subject) Use algebra to construct simple proofs Write coordinates and plot points in all four quadrants 3D coordinates Plot straight-line graphs Use y = mx + c Draw, sketch, recognise graphs of linear, quadratic, simple cubic functions, the reciprocal function and trigonometric functions Understand and use the Cartesian equation of a circle centred at the origin and link to the trigonometric functions Construct the graphs of simple loci Sketch simple transformations of a given function PROBABILITY Use sample spaces Identify mutually exclusive and exhaustive outcomes Know the sum of all probabilities is 1 Use set notation Use Venn diagrams Use tree diagrams Use the ‘and’ and ‘or’ rules Compare experimental data with theoretical probabilities In both Methods in Mathematics and Applications of Maths Unit 1s NUMBER Understand and use number operations, including inverse operations and hierarchy of operations. BODMAS/BIDMAS Numbers and their representations including powers, roots, indices (integers) Using fractional and negative indices Standard form Approximating to appropriate degrees of accuracy (eg 3sf) Understand that 'percentage' means 'number of parts per 100' Use multipliers for percentage change. Compound interest Reverse percentages Finding fractional and percentages of amounts Direct proportion and inverse proportion Sharing in a ratio Efficient use of a calculator ALGEBRA Simplifying by collecting like terms Expanding brackets Factorising including quadratics Form and solve equations Form and solve inequalities PROBABILITY Use the vocabulary of probability Calculate expected probabilities Relative frequency Know that repeating experiments can give different results Only in Applications of Mathematics Unit 1 Finance and Business Applications Carry out calculations relating to enterprise, saving and borrowing, appreciation and depreciation. Understand AER. Use mathematics in the context of personal and domestic finance Use spreadsheets Construct and use flow charts ALGEBRA Linear programming STATISTICS AND PROBABILITY Data Handling Cycle Design experiments or surveys Design data collection sheets Design and interpret two-way tables Analyse data Compare distributions and make inferences Produce and interpret charts and diagrams for categorical data including bar charts, multiple bar charts, pie charts and pictograms Produce and interpret diagrams for grouped and ungrouped numerical data, including tally charts, vertical line graphs, stem-and-leaf diagrams, frequency polygons and histograms Produce and use cumulative frequency graphs and box-and whisker plots. Work with time series including their graphical representation Work with moving averages including their graphical representation Calculate, median, mean, range, mode and modal class For grouped data, estimate quartiles and inter-quartile range. Recognise correlation and draw and/or use lines of best fit by eye Discuss and start to estimate risk. ✔ x