#### NUMBER

– Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), prime factorisation, including using product notation and the unique factorisation property

– Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

– Define percentage as ‘number of parts per hundred’,

– Interpret percentages and percentage changes as a fraction or a decimal,

– Interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

– Interpret fractions and percentages as operators

– Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b

#### ALGEBRA

– Simplify and manipulate algebraic expressions to maintain equivalence by taking out common factors (Factorisation)

– Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

– Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

– Reduce given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

– Recognise arithmetic sequences and find the nth term

– Interpret mathematical relationships both algebraically and graphically

#### Ratio, proportion and rates of change

– Use scale factors, scale diagrams and maps

– Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

#### Geometry and measures

– Derive and apply formulae to calculate and solve problems for volume of prisms (including cylinders)

– Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

– Derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

– Describe, sketch and draw using conventional terms and notations: regular polygons, and other polygons that are reflectively and rotationally symmetric

– Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

– Construct similar shapes by enlargement, with and without coordinate grids

– Understand and use the relationship between parallel lines and alternate and corresponding angles

– Interpret mathematical relationships both algebraically and geometrically.

#### PROBABILITY

– Enumerate sets and unions/ intersections of sets systematically, using tables, grids and Venn diagrams

#### STATISTICS

– Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

– Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs

## GCSE Maths Predicted Papers

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