Super Simple Maths: The Ultimate Bitesize Study Guide

Description

All the core national curriculum maths topics in one book, an accessible, and indispensable guide for students, parents, and educators. Covering topics from probability to statistics, algebra to geometry, this study guide is what every young, budding mathematician needs to succeed in maths - both at home and in school. This maths book is the perfect support for coursework, homework, and exam revision. Inside students will find: - Key concepts are shown in visual form and summarised to just one page - Important aspects of each topic explained with step-by-step instructions and diagrams - Key fact boxes that break down core concepts and make the material easier to memorise - "How it works" and "Look closer" boxes explain essential ideas and work through problems with simple graphics - Practice questions to help students test their understanding of important topics Super Simple Maths is designed for learners between the ages of 11 - 16. Each maths topic in line with the national curriculum is simplified into manageable, bite-sized chunks explained using colourful, engaging diagrams and graphs. Perfect for visual learners, this guide brings maths clearly into focus, making mathematicians out of even the most reluctant of students. Instructive information panels use real-world examples to make maths relevant and less daunting for students, parents, and teachers alike. Fact boxes provide rapid-fire points for easy learning and are perfect for classroom quizzes. Studying for exams has never been easier using this exceptional educational tool. DK's Super Simple series of educational books cover a range of topics from Super Simple Physics, Super Simple Chemistry to Super Simple Biology. Each book contains colourful, engaging, diagrams, simple explanations and exam revision questions - perfect for students, teachers, and parents alike. Contents Number and arithmetic Introducing numbers Decimals Written addition and subtraction Adding and subtracting decimals Negative numbers Multiplying and dividing by 10, 100, and 1000 Methods of multiplication Methods of division Mental addition and subtraction Mental multiplication and division Powers of numbers Factors and multiples Prime numbers Prime factorization Common factors and multiples Order of operations Angles and shapes Angles Angle facts Angles and parallel lines Measuring and drawing angles Symmetry Properties of triangles Properties of quadrilaterals Properties of polygons Angles in a triangle Angles in a quadrilateral Exterior angles of a polygon Interior angles of a polygon Properties of a circle Practice question: Working with angles Fractions, decimals, and percentages Fractions Improper fractions and mixed numbers Comparing fractions Adding and subtracting fractions Fraction of an amount Multiplying fractions Dividing fractions Percentages Fractions, decimals, and percentages Percentage of an amount Mental percentage calculations Finding the percentage change Percentage increase and decrease Reverse percentages Growth and decay Compound interest Recurring decimals Recurring decimals and fractions Measure Metric units of measure and time Imperial units of measure Converting units of measure Converting units of area and volume Compound units of measure Practice questions: Working with compound units Perimeter and area Area formulas How area formulas work Circumference and area of a circle Length of an arc and area of a sector Practice questions: Compound 2-D shapes 3-D shapes 3-D sections Plans and elevations Volume of a cuboid Surface area of a cuboid Volume and surface area of a prism Volume and surface area of a cylinder Volume and surface area of a pyramid Volume and surface area of a cone Volume and surface area of a sphere Practice questions: Compound 3-D shapes Rounding and estimating Bounds of accuracy Introducing algebra Algebraic terms Expressions Substitution Indices in algebra Expanding brackets Expanding quadratics Factorizing Factorizing quadratics Factorizing harder quadratic expressions The difference of two squares Algebraic fractions Adding and subtracting algebraic fractions Multiplying and dividing algebraic fractions Formulas Rearranging formulas Functions Inverse functions Composite functions Powers and calculations Higher powers and estimating powers Roots Negative powers Multiplying and dividing with powers Raising a power to a power Fractional powers and roots Practice questions: Calculating with powers Surds and irrational numbers Simplifying surd expressions Surds in fractions Exact calculations Standard form Multiplying and dividing with standard form Adding and subtracting with standard form Equations and graphs Equations Solving simple equations Solving harder equations Equations with brackets Simultaneous equations Practice question: Real-world simultaneous equations Solving simple quadratic equations Solving harder quadratic equations Completing the square How to complete the square The quadratic formula Practice question: Choosing a method for quadratic problems Trial and improvement The coordinate grid Linear graphs Equation of a straight line Parallel and perpendicular lines Length and midpoint of a line segment Quadratic graphs Quadratics in the real world Solving simple equations using graphs Solving harder equations using graphs Inequalities Graphing linear inequalities Quadratic inequalities Ratio and proportion Ratios Dividing in a given ratio Direct proportion Inverse proportion Unitary method Scaling method Proportion Comparing proportions Proportion equations Practice questions: Ratio and proportion Geometry Vectors Working with vectors Adding and subtracting vectors Multiplying vectors Practice question: Vectors and geometry Translations Reflections Rotations Constructing rotations Enlargements Fractional and negative enlargements Scaling area and volume Practice questions: Combinations of transformations Scale drawings Bearings Constructing perpendicular lines Constructing angles Loci Practice questions: Using loci Congruent and similar shapes Congruent triangles Similar triangles Practice questions: Similarity and congruence Constructing triangles Circle theorems 1 Circle theorems 2 Trigonometry Pythagoras’s theorem Trigonometry Sine, cosine, and tangent Finding lengths and angles Special angles The sine rule The cosine rule Area of a triangle Practice question: Using trigonometry Angles of elevation and depression Pythagoras in 3-D Practice question: 3-D trigonometry Probability Probability scale Calculating probability Mutually exclusive events Counting outcomes Probability of two events Tree diagrams Conditional probability Conditional probability tables Venn diagrams Venn diagrams and probability Relative frequency Frequency trees Probability distributions Statistics Statistical inquiry Types of data Populations and samples Frequency tables Bar charts Pictograms Line graphs Pie charts Mean, median, mode, and range Frequency tables and averages Standard deviation Practice question: Using standard deviation Cumulative frequency Quartiles Histograms Drawing histograms Time series Box plots Practice questions: Comparing distributions Scatter graphs Lines of best fit Further graphs Distance-time graphs Speed-time graphs Area under a curve Gradient of a curve Linear real-life graphs Non-linear real-life graphs Domain and range of a function Cubic graphs Reciprocal graphs Exponential graphs Trigonometric graphs Transformations of graphs Equation of a circle Sequences Number sequences Term-to-term rule Position-to-term rule Finding the nth term The nth term formula Arithmetic pattern sequences Arithmetic series Square and cube number sequences The triangular number sequence Quadratic sequences Geometric sequences The Fibonacci sequence Glossary Index Acknowledgments