CAPE Pure Maths Unit 1 study guide
CAPE Pure Maths Unit 1 · Work through your exam, one topic at a time.
CAPE Pure Mathematics Unit 1 is the first of two units in the Caribbean Advanced Proficiency Examination suite, administered by the Caribbean Examinations Council (CXC). It is taken mainly by sixth-form and post-secondary students in the Caribbean who need a rigorous pre-university mathematics qualification for university entrance, for further study in engineering, physical sciences, economics or mathematics itself, or for professional routes that demand strong quantitative skills. The syllabus is built around four areas: algebra, functions and graphs; coordinate geometry and trigonometry; differentiation and integration; and applications of calculus such as rates of change, curve sketching, maxima and minima, areas and volumes. The exam rewards fluent manipulation and clear reasoning rather than memorised tricks: you are expected to prove results, justify steps and present solutions coherently. The CAPE Pure Maths Unit 1 study guide has 4 sections and about 2,335 words.
01Algebra
The Algebra domain of CAPE Pure Mathematics Unit 1 tests whether you can manipulate algebraic structure fluently: polynomials and their factors, surds and indices, logarithms, inequalities including modulus, and finite and infinite series. Questions are usually multi-step, so one sign slip early costs the whole item.
496 words, about 2 min02Functions and Graphs
This domain tests the function concept itself: domain and range, one-to-one behaviour, inverse and composite functions, transformations of graphs, and sketching modulus, exponential, logarithmic and rational curves. CAPE items often ask you to state a restriction or read a feature from a sketch, so precision in notation matters as much as the algebra.
506 words, about 3 min03Coordinate Geometry and Trigonometry
This domain combines straight-line and circle geometry with radian measure, trigonometric identities, trigonometric equations and triangle solution. CAPE rewards candidates who choose the most efficient identity and who track the required solution interval carefully.
507 words, about 3 min04Calculus I: Differentiation and Integration
This domain tests technique: differentiating from first principles and by rule, differentiating implicit and parametric forms, and integrating standard forms by substitution, identity or partial fractions. Marks are lost through missing chain-rule factors and constants far more often than through ignorance of the rule itself.
826 words, about 4 min