Hodder Education
Common Entrance 13+ Additional Mathematics for ISEB CE and KS3
Serena Alexander
Science & Math
Common Entrance 13+ Additional Mathematics for ISEB CE and KS3
US$ 45.59
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Exam board: ISEB
Level: 13+ CE and KS3
Subject: Mathematics
First teaching: September 2021
First exams: November 2022


Serena Alexander brings her renowned passion and love of Mathematics to help you stretch and challenge pupils aiming for the Additional Mathematics paper or the Common Academic Scholarship Exam (CASE). The resource is packed with activities, examples and exercises to help pupils develop a comprehensive knowledge of Mathematics.

· Push your pupils to achieve high scores: Covers all content for the Core Mathematics paper, with new material for the Additional Mathematics paper and the Common Academic Scholarship Exam (CASE).
· Ensure an in-depth knowledge of Mathematics: Chapters include Fractions and Decimals, Geometry (with more of a focus on angle calculations using algebra), and Trigonometry.
· Develop a wider understanding with projects: End-of-chapter projects and investigations cover current affairs, mathematical proof and mathematical paradox, and using probability to model real-life scenarios.
· Support your pupils in developing their analytical and research skills: Investigations include Mersenne primes, perfect numbers and Goldbach's conjecture.
· Encourage your pupils to think beyond Mathematics: Cross-curricular boxes inform pupils where mathematical skills may be required in other subjects (including other examination subjects, PSHEE and ICT) with suggestions of cross-curricular activities.
· Guide your pupils to develop an understanding of the role of Mathematics in the world: SCEE (Social, Cultural, Empathy and Environmental) boxes encourage pupils to learn the mathematical relevance in society, links to different cultures including their role in the history of Mathematics, and the use of Mathematics in exploring environmental issues.

Accompanying answers available in a paid-for PDF download at galorepark.co.uk (ISBN: 9781398321403).

Language
English
ISBN
9781398321328
Cover
Title Page
Copyright
Contents
Introduction
1 Working with numbers
Number terminology
Place value
Rounding
Ordering numbers
Factors and multiples
Highest common factors and lowest common multiples
Calculation strategies
Problem solving
Calculating with negative numbers
Activity: More about prime numbers
2 Fractions and decimals
Calculating with fractions
Mixed addition and subtraction
Multiplying fractions
Dividing with fractions
Problem solving
Fractions on the calculator
Decimals
Multiplying decimals
Dividing with decimals
Working with other metric units
Units of area – metric measure
Extension: The Eye of Horus
Activity: The National Elf problem
3 Indices
Indices and products of primes
Multiplying and dividing numbers with indices
Squares and square roots
More about roots
Negative indices
Large and small numbers
Standard index form
More calculations with a calculator
Calculator problems
Extension: Calculating with roots
Project: Current affairs – environment
4 Percentages
Fractions, decimals and percentages
Rules of conversion
Finding a percentage
Percentages as decimals
Percentage increase and decrease
Percentage change
Finding the original amount
Simple interest
Extension: Compound interest
Project: Percentages in the news
5 Equations and inequalities
Using algebra to solve problems
Problem solving
Equations with fractions
Multiple terms
Equations with more than one denominator
Inexact answers
Solving inequalities
Using inequalities to describe error intervals
Extension: Alien algebra
Project: The life and times of al-Khwarazmi
6 Indices in algebra
Multiplication
Division
The power 0
Negative index numbers
Fractions and powers
Powers of powers
Simplifying expressions with indices
Indices and brackets
Factorising
Extension: Fractional indices
Investigation: Great Uncle Ben’s bequest
7 Sequences
Working with sequences
Sequences and patterns
Working to a rule
Problem solving
Harder sequences
Extension: An introduction to fractals
Investigation: Polygonal numbers and Fermat’s theory
8 Using formulae
Writing a formula
Substituting into formulae
Area, perimeter and volume formulae
Calculating an unknown quantity
Distance, speed and time formulae
Average speed
Rearranging formulae
Extension: Units of formulae
Project: Fastest, longest, highest
9 Geometry
Angles
2D shapes
Quadrilaterals
Polygons
Constructions
Geometric proof
Project: Platonic solids
10 Pythagoras’ theorem
Right-angled triangles
Perigals’s dissection
Calculating the hypotenuse
Using Pythagoras’ theorem to solve problems
Special triangles
Isosceles triangles
Problem solving
Extension: Mixed problems
Investigation: Pythagorean triplets
11 Area and volume
Circles
Fractions of circles
Calculating the radius and diameter
More circle problems
3D shapes
Extension: More volume problems
Activity: Packaging the litre
12 More algebra
Brackets
Factorising expression
Quadratic equations
Two sets of brackets
Algebraic proof
More about brackets
Squares and differences
Factorising a squared expression
The difference between two squares
Factorising the difference between two squares
More quadratic equations
Solving problems by factorising and brackets
Extension: More proof
Investigation: Proof or paradox?
13 Simultaneous equations
What is an equation?
Problems in two variables
Solving simultaneous equations
The graphical method
The elimination method
The scale factor method
The re-arrangement and substitution methods
Solving problems with simultaneous equations
Extension: Equations with more than one unknown
Project: More about fractals
14 Graphs
Travel graphs
Everyday graphs
From functions to graphs
Graphs of quadratic or non-linear functions
Points of intersection
Project: Graphs in the news
15 Probability
Calculating probability
Using theoretical probability
Probability with two events
Possibility space diagrams for combined events
Extension: Tables and Venn diagrams
Project: Practical probability
16 Transformations
Reflections
Rotations
Line symmetry
Rotational symmetry
Translations
Enlargements
Mixed transformations
Extension: Finding a general rule for a transformation
Project: The Alhambra Palace
17 Ratio and proportion
Ratio
Working with ratio
Proportion
Inverse proportion
Area in enlargements
Volume in enlargements
Scale drawing
Activity: The golden ratio
18 Trigonometry
Terminology
The tangent
Calculating the tangent
Working with triangles
Problem solving
Sine and cosine
Calculating the sine and cosine
Calculating opposite and adjacent sides
Calculating the hypotenuse
Calculating the angle
Solving problems using trigonometry
Investigation: Dragon patrol
19 Handling data
Investigating a set of data
Finding the total
Frequency tables and diagrams
Grouped data
More about averages
Pie charts
Scatter graphs
Project: How to model the spread of a virus
Glossary
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