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100+ Free CCEA GCSE Further Maths Practice Questions

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Key Facts: CCEA GCSE Further Maths Exam

A* to G

CCEA GCSE Further Mathematics is graded A* to G from aggregated unit uniform marks

CCEA GCSE Further Mathematics (2017) specification

Unit 1 = 50%

Mandatory Pure Mathematics is a 2-hour written paper worth half the qualification

CCEA GCSE Further Mathematics (2017) specification

2 of 3 options

Students also take two of Mechanics, Statistics, and Discrete and Decision Mathematics

CCEA GCSE Further Mathematics (2017) specification

25% each

Each optional unit is a 1-hour external written examination

CCEA GCSE Further Mathematics (2017) specification

40% terminal

At least 40% of assessment weightings must be taken at the final cash-in series

CCEA GCSE Further Mathematics (2017) specification

Subject code 2260

Qualification number QAN 603/1054/6; classification code 2330

CCEA GCSE Further Mathematics (2017) specification

Written not MCQ

Official papers are structured written booklets; this bank is an MCQ study adaptation

CCEA specification / OpenExamPrep

100

Free original practice questions with numeric calculations here

OpenExamPrep

CCEA GCSE Further Mathematics is Northern Ireland's unitised further-maths GCSE: mandatory Unit 1 Pure Mathematics (2 hours, 50%) plus two optional units from Mechanics, Statistics and Discrete (1 hour, 25% each). Official assessment is structured written papers, not MCQ. Content goes beyond Higher Tier GCSE Mathematics into calculus, matrices, applied mechanics, distributions and decision maths. Grades are A* to G. This 100-question bank is an original free single-best-answer adaptation with numeric working, not past papers.

Sample CCEA GCSE Further Maths Practice Questions

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

1Simplify (x^2 - 9)/(x + 3) for x != -3.
A.x - 3
B.x + 3
C.x - 9
D.x^2 - 3
Explanation: Factorise: x^2 - 9 = (x - 3)(x + 3). Cancel (x + 3) to leave x - 3 (x != -3).
2Express as a single fraction: 2/x + 3/(x + 1) (x != 0, -1).
A.(5x + 2)/(x(x + 1))
B.(5x + 3)/(x(x + 1))
C.(2x + 3)/(x(x + 1))
D.(5x + 2)/(2x + 1)
Explanation: Common denominator x(x + 1): 2(x + 1)/(x(x + 1)) + 3x/(x(x + 1)) = (2x + 2 + 3x)/(x(x + 1)) = (5x + 2)/(x(x + 1)).
3Expand and simplify (x + 1)(x + 2)(x + 3).
A.x^3 + 6x^2 + 11x + 6
B.x^3 + 5x^2 + 6x + 6
C.x^3 + 6x^2 + 6x + 6
D.x^3 + 6x^2 + 11x + 5
Explanation: (x + 1)(x + 2) = x^2 + 3x + 2; then (x^2 + 3x + 2)(x + 3) = x^3 + 6x^2 + 11x + 6.
4Complete the square for x^2 - 6x + 5.
A.(x - 3)^2 - 4
B.(x - 3)^2 + 4
C.(x - 6)^2 - 31
D.(x - 3)^2 - 5
Explanation: (x - 3)^2 = x^2 - 6x + 9, so x^2 - 6x + 5 = (x - 3)^2 - 9 + 5 = (x - 3)^2 - 4.
5By completing the square, find the minimum value of y = x^2 + 4x + 7.
A.3
B.7
C.-1
D.11
Explanation: x^2 + 4x + 7 = (x + 2)^2 - 4 + 7 = (x + 2)^2 + 3. Minimum is 3 at x = -2.
6For x + y + z = 6, 2x - y + z = 3, x + 2y - z = 2, what is x?
A.1
B.2
C.3
D.0
Explanation: Elimination gives x = 1, y = 2, z = 3. Check: 1+2+3=6; 2-2+3=3; 1+4-3=2.
7Solve x^2 - 5x + 6 < 0.
A.1 < x < 6
B.2 < x < 3
C.x < 2 or x > 3
D.x <= 2 or x >= 3
Explanation: (x - 2)(x - 3) < 0 between the roots: 2 < x < 3.
8Solve x^2 + x - 12 >= 0.
A.-4 <= x <= 3
B.x <= -4 or x >= 3
C.x <= -3 or x >= 4
D.-3 <= x <= 4
Explanation: (x + 4)(x - 3) >= 0 outside and at the roots: x <= -4 or x >= 3.
9Solve 2 sin x° = 1 for 0 <= x <= 180.
A.x = 30 only
B.x = 30 and x = 150
C.x = 60 and x = 120
D.x = 45 and x = 135
Explanation: sin x° = 1/2 => x = 30° and x = 150° in [0, 180].
10Solve cos x° = -1/2 for 0 <= x <= 360. Sum of solutions?
A.240
B.360
C.300
D.480
Explanation: x = 120° and 240°. Sum = 360.

About the CCEA GCSE Further Maths Exam

CCEA GCSE Further Mathematics (2017 specification) is the Northern Ireland GCSE for students who need mathematics beyond Higher Tier GCSE Mathematics. It is unitised: Unit 1 Pure Mathematics is mandatory (algebraic fractions, completing the square, three-variable simultaneous equations, quadratic inequalities, trigonometric equations, differentiation, integration, logarithms and 2×2 matrices) and is assessed by a 2-hour written paper worth 50%. Students also take two of three optional 1-hour units — Mechanics (kinematics, vectors, forces, Newton's laws, moments), Statistics (mean and standard deviation, probability, binomial and normal distributions, bivariate analysis), and Discrete and Decision Mathematics (counting, logic, linear programming, time series, critical path analysis) — each worth 25%. Official papers are structured written question-and-answer booklets with a formula sheet; calculators with trigonometric, logarithmic and statistical functions are required and full working is expected. Grades run A* to G. This OpenExamPrep bank adapts the same content areas into original single-best-answer practice with real numeric calculations; it is not an official paper and does not replace written multi-step exam practice.

Assessment

Unitised qualification (subject code 2260, QAN 603/1054/6). Students must complete Unit 1: Pure Mathematics and two of Units 2, 3 and 4. Unit 1 is worth 50%; each optional unit is worth 25%. At least 40% of the assessment (by unit weightings) must be taken as terminal assessment. Individual units may be resat once before cash-in, subject to the terminal rule.

Time Limit

Unit 1 Pure Mathematics: 2 hours. Unit 2 Mechanics, Unit 3 Statistics, and Unit 4 Discrete and Decision Mathematics: 1 hour each. Typical total for three units entered: 4 hours of external written examination.

Passing Score

No single pass mark. Grades A* to G are awarded by aggregating uniform marks from the three units taken. Raw mark boundaries are set independently each series. Unclassified (U) is reported below grade G.

Exam Fee

No fee is paid directly by students. Entry fees for CCEA GCSE Further Mathematics units are paid by schools and registered centres; private candidates are charged by the centre that enters them. (CCEA (Council for the Curriculum, Examinations and Assessment), Northern Ireland)

CCEA GCSE Further Maths Exam Content Outline

50%

Unit 1: Pure Mathematics

Algebraic fractions with linear and quadratic terms; expanding three linear brackets; completing the square (a = 1) for solving and turning points; three equations in three unknowns; factorisable quadratic inequalities; trig graphs and equations in a given range; differentiation and integration of integer powers of x (x ≠ −1 for integration); tangents, normals, optimisation and area under a curve; laws of logarithms and indicial equations; 2×2 matrix arithmetic, inverses and simultaneous equations.

25%

Unit 2: Mechanics

Displacement–time and velocity–time graphs; constant acceleration (suvat) formulae; vector magnitude and direction; i and j components; resolving forces and resultants; equilibrium; F = ma for horizontal/vertical motion, inclined planes and connected bodies (friction given when needed); principle of moments for a horizontal uniform rod with one or two supports.

25%

Unit 3: Statistics

Mean and standard deviation from raw or grouped data; combined data sets; linear transformation effects; addition rule and conditional probability; tree and Venn diagrams; binomial expansion and binomial probabilities (n ≤ 8); normal distribution probabilities via z = (x − μ)/σ; Spearman's rank correlation coefficient; line of best fit through (x̄, ȳ).

25%

Unit 4: Discrete and Decision Mathematics

Addition and multiplication counting principles; permutations and combinations; Boolean AND/OR/NOT and truth tables (up to three variables); linear programming with up to five inequalities and graphical maximisation/minimisation; three-, four- and five-point moving averages and trend-line predictions; activity networks, earliest/latest times, critical path, float and basic Gantt scheduling.

How to Pass the CCEA GCSE Further Maths Exam

What You Need to Know

  • Passing score: No single pass mark. Grades A* to G are awarded by aggregating uniform marks from the three units taken. Raw mark boundaries are set independently each series. Unclassified (U) is reported below grade G.
  • Assessment: Unitised qualification (subject code 2260, QAN 603/1054/6). Students must complete Unit 1: Pure Mathematics and two of Units 2, 3 and 4. Unit 1 is worth 50%; each optional unit is worth 25%. At least 40% of the assessment (by unit weightings) must be taken as terminal assessment. Individual units may be resat once before cash-in, subject to the terminal rule.
  • Time limit: Unit 1 Pure Mathematics: 2 hours. Unit 2 Mechanics, Unit 3 Statistics, and Unit 4 Discrete and Decision Mathematics: 1 hour each. Typical total for three units entered: 4 hours of external written examination.
  • Exam fee: No fee is paid directly by students. Entry fees for CCEA GCSE Further Mathematics units are paid by schools and registered centres; private candidates are charged by the centre that enters them.

Keys to Passing

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

CCEA GCSE Further Maths Study Tips from Top Performers

1Confirm which two optional units you are entered for and download matching CCEA past papers and mark schemes for Unit 1 plus those options only.
2Show full algebraic working on every multi-step pure question; CCEA awards method marks even when the final answer is wrong.
3Drill differentiation and integration of integer powers until tangent, normal, optimisation and area-under-curve questions are routine.
4For Mechanics, always draw a force diagram and resolve parallel/perpendicular to the plane before applying F = ma.
5For Statistics, practise mean and SD by hand and know when to use tree diagrams, Venn diagrams or the binomial expansion.
6For Discrete, memorise P(n,r) and C(n,r), complete truth tables carefully, and label earliest/latest event times on activity networks before finding float.

Frequently Asked Questions

What is the structure of CCEA GCSE Further Mathematics?

It is unitised. Students must take mandatory Unit 1: Pure Mathematics (2 hours, 50%) and two of the three optional units — Unit 2 Mechanics, Unit 3 Statistics, or Unit 4 Discrete and Decision Mathematics (each 1 hour, 25%). At least 40% of the assessment must be terminal.

How is CCEA GCSE Further Maths graded?

Grades run A* to G. Uniform marks from the three units taken are aggregated to give the subject grade. Raw mark boundaries are set each series. Results below grade G are unclassified (U).

Is the official exam multiple choice?

No. Official CCEA papers are structured written question-and-answer booklets with a formula sheet. Full working is required. This practice bank adapts the same topics into four-option MCQs for extra drill — it does not copy or replace past papers.

What pure mathematics topics are on Unit 1?

Algebraic fractions and manipulation, completing the square, three-variable simultaneous equations, quadratic inequalities, trigonometric equations, differentiation and integration of integer powers, logarithms, and 2×2 matrices including inverses.

Which optional units should I choose?

Your school decides with you based on teaching and progression plans. Many STEM-leaning routes pick Mechanics and Statistics; Discrete suits decision-maths and computing pathways. You only need two of the three options.

Are these official CCEA questions?

No. These are original OpenExamPrep single-best-answer practice questions modelled on the CCEA 2017 Further Mathematics content. Download official past papers and mark schemes from the CCEA subject page for authentic written-paper practice.