New KS3 Maths Workbook - Higher (includes answers): superb for Year 7, 8 and 9 (CGP KS3 Workbooks)

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Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

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 Define percentage as ‘number of parts per hundred’, interpret percentages and one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100% Our worksheet resources and activities can help to improve your child’s confidence when approaching Key Stage 3 maths problems and questions. Ideal for use at home or in a classroom environment, our online KS3 maths worksheets are accessible, engaging and designed to help make learning new concepts easy. Our year 7 maths worksheets, year 8 maths worksheets and year 9 maths worksheets are designed with student needs in mind - containing a mixture of educational resources and visual elements, making our KS3 maths activities perfectly balanced to maximise learning and fun! Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofsUse the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs. Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8) Solve problems involving direct and inverse proportion, including graphical and algebraic representations Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

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Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons Interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or zero Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) Draw and measure line segments and angles in geometric figures, including interpreting scale drawings Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities. Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a

Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions Use standard units of mass, length, time, money and other measures, including with decimal quantities Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids 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