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Complete Pure Mathematics 1 for Cambridge International AS & A Level

Develop advanced mathematical skills with a real-world focus

Author Jean Linsky, Author Brian Western, and Author James Nicholson

Suitable for:  Students of Cambridge International AS & A Level Mathematics (9709)

Price:  £29.99

ISBN: 978-0-19-842510-6
Publication date: 12/07/2018
Paperback: 256 pages
Dimensions: 246x189mm

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Providing complete syllabus support (9709), this stretching and practice-focused course builds the advanced skills needed for the latest Cambridge assessments and the transition to higher education. Engaging, real world examples make mathematics relevant to real life.


  • Be confident of full syllabus support with a comprehensive mapping grid drawn directly from the latest syllabus (9709) for examination from 2020
  • Help every student hone their skills with clear explanations and extensive graduated practice for every topic
  • Get students ready for higher education with a focus on real world application via up-to-date international examples
  • Give students realistic exam practice with exam style questions covering all topics
  • Eliminate confusion with worked examples that show important techniques so students can confidently tackle every question

This page was last updated on 28 September 2021 at 04:30 GMT

Table of Contents

Syllabus matching grid
1 Quadratics
1.1: Solve quadratic equations by factorising
1.2: Solving linear inequalities
1.3: Solving quadratic inequalities
1.4: The method of completing the square
1.5: Solving quadratic equations using the formula
1.6: Solve more complex quadratic equations
1.7: The discriminant of a quadratic equation
1.8: Solving simultaneous equations
1.9: Graphs of quadratic functions
2 Functions and transformations
2.1: Mappings
2.2: Composite Functions
2.3: Inverse Functions
3 Coordinate Geometry
3.1: Line segments
3.2: Parallel and perpendicular lines
3.3: Equation of a straight line
3.4: Points of intersection and graphs
Review exercise A
Maths in real-life: Parabolic reflectors
4 Circular measure
4.1: Radians
4.2: Arc length and sector area
4.3: Further problems involving arcs and sectors
5 Trigonometry
5.1: Exact values of trigonometric functions
5.2: Graphs of trigonometric functions
5.3: Inverse trigonometric functions
5.4: Composite graphs
5.5: Trigonometric equations
5.6: Trigonometric identities
6 Binomial expansion
6.1: Pascal's triangle
6.2: Binomial notation
6.3: Binomial expansion
6.4: More complex expansions

7 Series
7.1: Sequences
7.2: Finite and infinite series
7.3: Arithmetic progressions
7.4: Geometric progressions
7.5: Infinite geometric progressions
Review exercise B
Maths in real-life: Infinity
8 Differentiation
8.1: The gradient of the tangent
8.2: Gradient of a tangent as a limit
8.3: Differentiation of polynomials
8.4: Differentiation of more complex functions
8.5: The chain rule (differentiating function of a function)
8.6: Finding the gradient of the tangent using differentiation
8.7: The second derivative
8.8: Equation of the tangent and the normal
9 Further differentiation
9.1: Increasing and decreasing functions
9.2: Stationary points
9.3: Problems involving maximum and minimum values
9.4: Connected rates of change
10 Integration
10.1: Integration as the reverse process of differentiation
10.2: Finding the constant of integration
10.3: Integrating expression of the form (ax + b)n
10.4: The definite integral
10.5: Finding area using definite integration
10.6: Area bounded by two curves or a curve and a line
10.7: Improper integrals
10.8: Volumes of revolution
Review exercise C
Maths in real-life: Describing change mathematically
Exam-style paper A
Exam-style paper B
Glossary of terms