# Unit M1: Methods in Mathematics (Algebra and Probability)

```Methods in Mathematics (Unit M1) and Applications of Mathematics (Unit A1)
Higher Tier Revision List
Only in Methods in Mathematics (Unit M1)
NUMBER
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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
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
Carry out calculations relating to enterprise, saving and borrowing, appreciation and depreciation.
Understand AER.
Use mathematics in the context of personal and domestic finance
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.
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