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100+ Free CAPE Pure Maths Unit 1 Practice Questions

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Key Facts: CAPE Pure Maths Unit 1 Exam

45 questions

CAPE Pure Mathematics Unit 1 Paper 1 has 45 multiple-choice questions

CXC CAPE Pure Mathematics syllabus

3 Modules

Unit 1 covers Algebra & Functions, Trigonometry/Geometry/Vectors and Calculus I

CXC CAPE Pure Mathematics syllabus

15 per Module

Paper 1 draws 15 multiple-choice questions from each of the three Modules

CXC CAPE Pure Mathematics syllabus

90 minutes

Paper 1 is answered in 1 hour 30 minutes with no calculator

CXC CAPE Pure Mathematics syllabus

Grades I-VI

CAPE results use a six-grade scale, with Grades I-V certificated

CXC examination grading

USD $29.00

CAPE subject entry fee from the May-June 2026 sitting

CXC Scale of Examination Fees

USD $20.25

One-time CAPE candidate entry fee from the May-June 2026 sitting

CXC Scale of Examination Fees

100

Free original Paper 1-style practice questions in this bank

OpenExamPrep

CAPE Pure Mathematics Unit 1 is a Caribbean Examinations Council (CXC) Advanced Proficiency qualification built around three Modules: Basic Algebra and Functions, Trigonometry/Geometry/Vectors, and Calculus I. Paper 1 is 45 multiple-choice questions (15 per Module) answered in 90 minutes with no calculator; Paper 2 is a 2.5-hour extended-response paper; Paper 3 is the School-Based Assessment or a private-candidate written alternative. There is no fixed pass percentage: results are graded I-VI with Grades I-V certificated. From the May-June 2026 sitting the subject entry fee is USD $29.00 plus a one-time USD $20.25 candidate fee. This 100-question bank gives original Paper 1-style multiple-choice practice with worked explanations for every option.

Sample CAPE Pure Maths Unit 1 Practice Questions

Try these sample questions to test your CAPE Pure Maths Unit 1 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Simplify the surd expression sqrt(50) + sqrt(8).
A.7*sqrt(2)
B.sqrt(58)
C.5*sqrt(2)
D.12*sqrt(2)
Explanation: Write each surd in terms of sqrt(2): sqrt(50) = sqrt(25*2) = 5*sqrt(2) and sqrt(8) = sqrt(4*2) = 2*sqrt(2). Adding gives 5*sqrt(2) + 2*sqrt(2) = 7*sqrt(2).
2Rationalise the denominator of 3 / (sqrt(5) - 2).
A.3*sqrt(5) + 6
B.3*sqrt(5) - 6
C.(3*sqrt(5) + 6) / 9
D.sqrt(5) + 2
Explanation: Multiply numerator and denominator by the conjugate (sqrt(5)+2). The denominator becomes (sqrt(5))^2 - 2^2 = 5 - 4 = 1, so the result is 3*(sqrt(5)+2) = 3*sqrt(5) + 6.
3Evaluate log_2(32).
A.5
B.16
C.6
D.4
Explanation: log_2(32) asks for the power of 2 that gives 32. Since 2^5 = 32, log_2(32) = 5.
4If log(x) - log(3) = log(4), what is the value of x?
A.12
B.7
C.1
D.4/3
Explanation: Using the quotient law, log(x) - log(3) = log(x/3). Setting log(x/3) = log(4) gives x/3 = 4, so x = 12.
5Simplify (x^3 * x^(-5)) / x^(-2).
A.1
B.x^(-10)
C.x^4
D.x^(-4)
Explanation: Add and subtract indices: 3 + (-5) - (-2) = 3 - 5 + 2 = 0, so the expression is x^0 = 1.
6The quadratic equation 2x^2 - 4x + 5 = 0 has roots that are:
A.complex (non-real)
B.real and equal
C.real, rational and distinct
D.real, irrational and distinct
Explanation: The discriminant is b^2 - 4ac = (-4)^2 - 4(2)(5) = 16 - 40 = -24. A negative discriminant means the roots are complex (non-real).
7For what value of k does the equation x^2 + kx + 9 = 0 have equal roots (k > 0)?
A.6
B.3
C.9
D.18
Explanation: Equal roots require the discriminant to be zero: k^2 - 4(1)(9) = 0, so k^2 = 36 and k = 6 (taking the positive value).
8If a and b are the roots of 3x^2 - 5x + 2 = 0, what is the value of a + b?
A.5/3
B.-5/3
C.2/3
D.-2/3
Explanation: For a quadratic ax^2 + bx + c = 0, the sum of the roots is -b/a. Here that is -(-5)/3 = 5/3.
9If a and b are the roots of x^2 - 7x + 10 = 0, find the value of a^2 + b^2.
A.29
B.39
C.49
D.19
Explanation: Here a + b = 7 and ab = 10. Using a^2 + b^2 = (a + b)^2 - 2ab = 49 - 20 = 29.
10When the polynomial f(x) = x^3 - 2x^2 + 3x - 4 is divided by (x - 2), the remainder is:
A.2
B.0
C.-4
D.6
Explanation: By the remainder theorem the remainder is f(2) = 8 - 8 + 6 - 4 = 2.

About the CAPE Pure Maths Unit 1 Exam

CAPE Pure Mathematics Unit 1 is an Advanced Proficiency mathematics qualification from the Caribbean Examinations Council (CXC), taken mainly by sixth-form students across the Caribbean as preparation for university study in mathematics, science, engineering and economics. The Unit is organised into three Modules: Module 1, Basic Algebra and Functions; Module 2, Trigonometry, Geometry and Vectors; and Module 3, Calculus I. It is assessed by three papers. Paper 1 is a 45-question multiple-choice paper with 15 questions from each Module, answered without a calculator in 90 minutes. Paper 2 is a compulsory extended-response paper, and Paper 3 is either a School-Based Assessment project for school candidates or a written alternative paper for private candidates. This 100-question bank provides original Paper 1-style multiple-choice practice across all three Modules with full explanations.

Assessment

Three papers per Unit. Paper 1: 45 multiple-choice questions (15 per Module), no calculator. Paper 2: six compulsory extended-response questions in three sections (two per Module). Paper 3: School-Based Assessment for school candidates or the Paper 03/2 written alternative for private candidates.

Time Limit

Paper 1: 1 hour 30 minutes (90 minutes). Paper 2: 2 hours 30 minutes. Paper 03/2 (private-candidate alternative): 1 hour 30 minutes.

Passing Score

No fixed percentage pass mark. Results are reported on a six-grade scale (Grades I-VI), with Grades I-V certificated and Grade III usually regarded as a satisfactory standard. The Unit grade combines Paper 1, Paper 2 and Paper 3 across the three Modules.

Exam Fee

From the May-June 2026 sitting: USD $29.00 per subject entry plus a one-time USD $20.25 CAPE candidate entry fee. Local registrars may add territory-specific fees. (Caribbean Examinations Council (CXC))

CAPE Pure Maths Unit 1 Exam Content Outline

33%

Module 1: Basic Algebra and Functions

Paper 1 draws 15 questions from this Module. Topics include reasoning and logic, the real number system, indices, surds and logarithms, the modulus function and modulus inequalities, quadratic equations and the discriminant, the remainder and factor theorems, partial fractions, functions, composition and inverses, the principle of mathematical induction, and the sum and product of the roots of polynomial equations.

33%

Module 2: Trigonometry, Geometry and Vectors

Paper 1 draws 15 questions from this Module. Topics include radian measure with arc length and sector area, trigonometric ratios and exact values, identities and equations, compound, double and half-angle formulae, the R cos(x +/- a) / R sin(x +/- a) form, coordinate geometry of straight lines and circles, conics, and two- and three-dimensional vectors including magnitude, the scalar (dot) product and vector equations of lines.

33%

Module 3: Calculus I

Paper 1 draws 15 questions from this Module. Topics include limits, continuity and differentiation from first principles, the product, quotient and chain rules, gradients, tangents and normals, stationary points and curve sketching, rates of change, indefinite and definite integration including the area under a curve, and the volume of a solid of revolution.

How to Pass the CAPE Pure Maths Unit 1 Exam

What You Need to Know

  • Passing score: No fixed percentage pass mark. Results are reported on a six-grade scale (Grades I-VI), with Grades I-V certificated and Grade III usually regarded as a satisfactory standard. The Unit grade combines Paper 1, Paper 2 and Paper 3 across the three Modules.
  • Assessment: Three papers per Unit. Paper 1: 45 multiple-choice questions (15 per Module), no calculator. Paper 2: six compulsory extended-response questions in three sections (two per Module). Paper 3: School-Based Assessment for school candidates or the Paper 03/2 written alternative for private candidates.
  • Time limit: Paper 1: 1 hour 30 minutes (90 minutes). Paper 2: 2 hours 30 minutes. Paper 03/2 (private-candidate alternative): 1 hour 30 minutes.
  • Exam fee: From the May-June 2026 sitting: USD $29.00 per subject entry plus a one-time USD $20.25 CAPE candidate entry fee. Local registrars may add territory-specific fees.

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

CAPE Pure Maths Unit 1 Study Tips from Top Performers

1Master exact values and surd manipulation first; because Paper 1 has no calculator, most multiple-choice items are designed to be solved by exact algebra rather than decimals.
2Drill the trigonometric identities, including compound, double-angle and the R cos(x +/- a) form, until you can recognise which one a question is testing within seconds.
3Practise mathematical induction proofs and root relationships (sum and product of roots); these appear regularly and reward a fixed, memorised structure.
4For calculus, learn differentiation from first principles and the rules for tangents, normals and stationary points, then time yourself on integration and area/volume problems.
5Work past Paper 1 multiple-choice papers under the 90-minute / 45-question limit so you average about two minutes per question and learn to skip and return.
6Keep an error log of misread modulus, sign and index mistakes; these account for most avoidable Paper 1 losses in Module 1 and Module 3.

Frequently Asked Questions

How many questions are on CAPE Pure Mathematics Unit 1 Paper 1?

Paper 1 has 45 multiple-choice questions, with 15 questions drawn from each of the three Modules. It is answered in 90 minutes without a calculator.

What are the three Modules in Unit 1?

Module 1 is Basic Algebra and Functions, Module 2 is Trigonometry, Geometry and Vectors, and Module 3 is Calculus I. Each Module is weighted equally in the assessment.

Can I use a calculator in CAPE Pure Mathematics Unit 1?

No. Paper 1 (multiple choice) is taken without a calculator. Candidates rely on exact values, algebraic manipulation and standard results rather than numerical computation.

Is there a fixed pass mark for CAPE Pure Mathematics?

No. Results are reported on a six-grade scale (Grades I-VI). Grades I-V are certificated and Grade III is generally treated as a satisfactory standard. The Unit grade combines Papers 1, 2 and 3 across all three Modules.

How much does it cost to sit CAPE Pure Mathematics in 2026?

From the May-June 2026 sitting the CAPE subject entry fee is USD $29.00, plus a one-time CAPE candidate entry fee of USD $20.25. Local registrars in each territory may charge additional local fees.

What is the difference between Unit 1 and Unit 2?

Unit 1 covers Basic Algebra and Functions, Trigonometry/Geometry/Vectors, and Calculus I. Unit 2 covers Complex Numbers, Calculus II, and Counting, Matrices and Differential Equations. The two Units are examined and certificated separately.