Pure Mathematics is a foundational component that focuses on developing your abstract reasoning and problem-solving skills. It provides the essential tools for other areas of mathematics and science.
Key Topics:
Algebra: This includes solving quadratic equations and inequalities, working with functions, and understanding composite and inverse functions. You'll also learn to manipulate surds and indices.
Coordinate Geometry: You'll study the properties of lines and curves, including finding equations of lines, circles, and parabolas, and calculating slope and distances.
Trigonometry: You'll learn about trigonometric functions, identities, and equations, and apply them to various problems. This includes working with angles in both degrees and radians.
Calculus: This section covers differentiation and integration of power functions. You'll learn to find gradients of curves, rates of change, and areas under graphs.
Series: This topic covers arithmetic and geometric progressions, including finding the sum of a series and applying the binomial theorem.
This component teaches you how to collect, analyze, and interpret data, as well as model and predict chance events. It's a highly practical subject that prepares you for fields like data science, economics, and finance.
Key Topics:
Data Representation and Analysis: You'll learn to create and interpret various statistical diagrams like stem-and-leaf diagrams, box plots, histograms, and cumulative frequency graphs. The course also covers measures of central tendency (mean, median, mode) and dispersion (range, standard deviation).
Probability: You'll learn the fundamental concepts of probability, including calculating probabilities of simple events and using combinations and permutations. The course also introduces concepts like mutually exclusive and independent events, and conditional probability.
Probability Distributions: This section covers discrete random variables, including the binomial and geometric distributions. You'll also learn about the normal distribution, a crucial concept for modeling continuous data, and how to use it to approximate binomial probabilities.
Statistical Inference: You'll get an introduction to using sample data to make inferences about a larger population. This includes understanding sampling distributions and how to make informed decisions based on the data.
The AS Level qualification requires students to take two papers (exams) in the same examination series. Hopewell students will take the Pure Mathematics and Probability & Statistics route.
The exam is a written paper consisting of structured questions. All questions are compulsory.
Paper 1: Pure Mathematics 1 (P1)
Duration: 1 hour 50 minutes
Marks: 75 points
Weighting: 60% of the AS Level qualification
Format: This paper typically has 10 to 12 structured questions of varying lengths and difficulty.
Content: Topics include algebra, functions, coordinate geometry, circular measure, trigonometry, series, differentiation, and integration.
Paper 5: Probability and Statistics 1 (S1)
Duration: 1 hour 15 minutes
Marks: 50 marks
Weighting: 40% of the AS Level qualification
Format: This paper has 6 to 8 structured questions.
Content: Topics include data representation and summary, permutations and combinations, probability, discrete random variables, and the normal distribution.
Assessment: The questions are designed to test not only a student's knowledge of the content but also their ability to apply logical methodologies, problem-solving skills, and mathematical reasoning.
Formulae: While a list of formulae is provided in the exam, students are expected to know certain fundamental formulas and exact values (e.g., trigonometric values for standard angles) by heart.
Working: All working should be shown clearly and neatly in the provided spaces on the question paper.
Calculator: A scientific calculator is permitted, but students should be prepared for non-calculator questions as well.
Several U.S. states have adopted system-wide policies for awarding college credit for Cambridge International exams. This means that a student's qualifying exam grade will be accepted for credit at any public university or college within that state.
North Carolina: The University of North Carolina (UNC) System has a unified policy on awarding undergraduate credit for prior learning. This policy applies to all 16 public universities in the system.
Minimum Grade Requirement: Students who earn a score of E or higher on a Cambridge A-Level or AS-Level exam are eligible to receive college credit. This is a very student-friendly policy, as many institutions in other states require higher scores (e.g., A, B, or C). An AS level exam is typically awarded 3 credit hours.
Florida, Indiana, South Carolina, and others: These states also have similar policies that require public universities to grant credit for Cambridge exams, often with a minimum grade of E.