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International GCSE in Further Pure Mathematics

Pearson Edexcel – Qualification Code: 4PM1

Who is This Course For?

The International GCSE in Further Pure Mathematics is designed for students who wish to extend their knowledge of mathematics beyond the standard International GCSE level. It is ideal for those who have a strong aptitude for mathematics and are looking to develop advanced problem-solving skills.

This qualification is perfect for students who:

  • Enjoy mathematical challenges and wish to deepen their understanding of key mathematical concepts.
  • Aspire to study mathematics at A-Level or pursue higher education in fields such as engineering, physics, economics, or computer science.
  • Want to develop analytical and logical reasoning skills, which are highly valued in academic and professional settings.
  • Seek to strengthen their foundation in algebra, calculus, geometry, and trigonometry

Who is This Course For?

This course is suitable for students who:

  • Have already mastered the content of the standard International GCSE in Mathematics (Specification A or B).
  • Are looking for a rigorous mathematical challenge to support further study in STEM (Science, Technology, Engineering, and Mathematics) fields.
  • Enjoy solving complex problems and applying mathematics in real-world situations.
  • Plan to study A-Level Mathematics or Further Mathematics.

1. Algebra and Functions

  • Polynomial functions and their graphs.
  • Rational functions and asymptotes.
  • Solving simultaneous equations.
  • Use of logarithms and exponentials.

2. Series and Sequences

  • Arithmetic and geometric sequences.
  • Binomial expansion for positive integer powers.
  • Sum of infinite geometric series.

3. Calculus

  • Differentiation techniques, including product, quotient, and chain rules.
  • Finding tangents and normals.
  • Integration methods, including definite and indefinite integrals.
  • Applications of calculus in kinematics.

4. Geometry and Trigonometry

  • Coordinate geometry, including equations of circles.
  • Trigonometric identities and equations.
  • Using radian measure in calculations.
  • Applications of trigonometry in three-dimensional problems.

5. Vectors and Matrices

  • Vector addition and subtraction.
  • Scalar and vector products.
  • Applications of vectors in geometry.
  • Introduction to matrices and their transformations.

The course assesses students based on the following objectives:

Objective Description Weighting
AO1 Demonstrate a confident knowledge of pure mathematics techniques 30%-40%
AO2 Apply mathematical knowledge to solve non-routine problems 20%-30%
AO3 Communicate clear and accurate mathematical solutions 35%-50%

Ideal for High-Achieving Students

The Further Pure Mathematics International GCSE is designed for students who have excelled in their mathematics studies and want to push themselves further.

Strong Preparation for A-Level and Beyond

This course provides a solid foundation for A-Level Mathematics, Further Mathematics, and other STEM-related qualifications.

Recognised by Top Universities

The Pearson Edexcel International GCSE in Further Pure Mathematics is widely recognised by universities and employers worldwide, demonstrating a student’s ability to handle complex mathematical concepts.

Develops Logical and Analytical Thinking

This qualification helps students develop logical reasoning, problem-solving abilities, and advanced mathematical skills, which are highly valued in academic and professional settings.

Course Structure

The qualification consists of two externally assessed papers:

Paper 1: Further Pure Mathematics (50%)

Exam Duration

2 hours

Assessment Format

External examination

Skills Assessed

  • Advanced Algebra – Manipulating expressions, solving complex equations.
  • Calculus – Differentiation and integration techniques.
  • Geometry and Trigonometry – Applications in coordinate geometry and transformations.
  • Vectors – Understanding and applying vector algebra.

Assessment Breakdown

  • Around 11 questions per paper, with varying mark allocations.
  • 40% of marks target grades 4 and 5, while 60% target grades 6, 7, 8, and 9.
  • A formulae sheet is provided.
  • Calculators are allowed in all examinations.

Paper 2: Further Pure Mathematics (50%)

Exam Duration

2 hours

Assessment Format

External examination

Skills Assessed

  • Functions and Graphs – Logarithms, exponential functions, transformations.
  • Series and Sequences – Arithmetic and geometric progressions.
  • Binomial Theorem – Expansion of expressions.
  • Differential Equations – Solving first-order differential equations.
  • Trigonometric Identities – Advanced applications in trigonometry.
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