Full Description
Support achievement in the latest syllabus (9709), for examination from 2020, with a stretching, practice-driven approach that builds the advanced skills required for Cambridge exam success and progression to further study.
This new edition is fully aligned with the Pure Mathematics 1 part of the latest International AS & A Level syllabus, and contains a comprehensive mapping grid so you can be sure of complete support.
Get students ready for higher education with a focus on real world application. From parabolic reflectors to technology in sport, up-to-date, international examples show how mathematics is used in real life.
Students have plenty of opportunities to hone their skills with extensive graduated practice and thorough worked examples. Plus, give students realistic practice for their exams with exam-style questions covering every topic.
Answers are included in the back of the book with full step-by-step solutions for all exercises and exam-style questions available on the accompanying support site.
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
Answers
Glossary of terms
Index
