Level 2 Certificate - Further Mathematics Paper 2 (Calculator) - Exam Instructions and Questions

Sep 5, 2026

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Level 2 Certificate Further Mathematics Paper 2 (Calculator) provides exam rules and candidate information, including required equipment such as a calculator and mathematical instruments, and an enclosed formula sheet. It specifies writing practices (black ink, pencil for diagrams), where answers must be recorded, and how to use extra lined pages and rough work within the book. The paper contains multiple worked-question tasks covering algebraic factorisation, matrices, linear algebra equations, inequalities, proof by parity, sequence formulae, curve gradients, and coordinate geometry, with a total mark of 80.

LanguageEnglish

CategoryExam

FormatPDF

Pages24

Reading Time1 h 0 min

AccessFree to download

Instructions

Candidate requirements

Answering guidance and marking

Questions

Algebra and factorisation

Matrices and equations

Inequalities and integers

Algebraic proof

Sequences and number construction

Graphs and trigonometry

Gradient and curve methods

| Please write clearly in block capitals. | | | | | --- | --- | --- | --- | | Centre number | | Candidate number | | | Surname
Forename(s)
Candidate signature
I declare this is my own work. | | | | Level 2 Certificate FURTHER MATHEMATICS Paper 2 Calculator Time allowed: 1 hour 45 minutes Materials For this paper you must have: • a calculator • mathematical instruments • the Formulae Sheet (enclosed) . Instructions • Use black ink or black ball-point pen. Draw diagrams in pencil. • Fill in the boxes at the top of this page. • Answer all questions. • You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages. • If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s) . • Do all rough work in this book. Cross through any work you do not want to be marked. • In all calculations, show clearly how you work out your answer. Information • The marks for questions are shown in brackets. • The maximum mark for this paper is 80. • You may ask for more graph paper and tracing paper. These must be tagged securely to this answer book. • The use of a calculator is expected but calculators with a facility for symbolic algebra must not be used. | For Examiner’s Use | | | --- | --- | | Pages | Mark | | 2–3 | | | 4–5 | | | 6–7 | | | 8–9 | | | 10–11 | | | 12–13 | | | 14–15 | | | 16–17 | | | 18–19 | | | 20 | | | TOTAL | | | Answer all questions in the spaces provided. | | --- | | 1 Factorise fully 12w + 18w2
[2 marks]

Answer
2 M is the midpoint of PQ.

Work out the value of a.
[2 marks]

Answer | outside the box 􀂧 4 2􀂷 􀂧 2 0 􀂷 3 (a) Work out 3 􀂩􀂨 1 0 􀂹􀂸 􀂨􀂩−1 5􀂹􀂸 Give your answer as a single matrix. [3 marks] Answer 3 (b) 􀂨􀂧􀂩7b 25􀂷􀂹􀂸 􀂧􀂩􀂨 2a􀂷􀂹􀂸 = 􀂨􀂧􀂩7182􀂷􀂹􀂸 Work out the values of a and b. [3 marks] a = b = outside the box | | | --- | | 10 | 4 Line A has equation y + 4x = 6 Line B is parallel to line A and passes through the point (2, 1) The point (d, 2d) lies on line B. Work out the value of d. [4 marks] Answer 5 Work out all the negative integer values of x for which 3x2 < 48 [3 marks] Answer box 6 Prove algebraically that when n is an integer (2n +1)2 − (2n −1)2 is always even. 4 [3 marks] 7 How many integers between 200 000 and 400 000 can be formed using only the digits 1 2 3 5 8 9 with no repetition of any digit? [2 marks] Answer box | | | --- | | 12 | 8 A curve has equation y = x3 – 5x2 At two points on the curve, the rate of change of y with respect to x is 4 8 (a) Work out an equation, in terms of x, to represent this information. Give your answer in the form ax2 + bx + c = 0 where a, b and c are integers. [2 marks] Answer 8 (b) Hence, work out the two possible values of x. Give your answers to 3 significant figures. [2 marks] Answer box 9 The first three terms of a linear sequence are 30 30 + 4k 30 + 8k where k is a constant. 9 (a) Work out an expression, in terms of k, for the 4th term. Give your answer in its simplest form. [1 mark] Answer 9 (b) The 100th term of the sequence is 525 Work out the value of k. [3 marks] Answer box | | | --- | | 8 | 10 Here are four sketch graphs. Circle the letter of the sketch graph that represents y = 3 × 2x [1 mark] box 11 Here is a right-angled triangle. You are given that a > 5 Use trigonometry to work out the range of values of x. [2 marks] Answer Turn over for the next question box | | | --- | | 3 | 12 Work out the gradient of the curve y = 12x3~~ ~~xx~~ ~~+~~ ~~3 at the point where x = –1 You must show your working. [5 marks] Answer outside the box

FAQs

What equipment is required for this paper?

A calculator, mathematical instruments, and the Formulae Sheet (enclosed) are required.

How must answers be presented?

Use black ink or black ball-point pen, draw diagrams in pencil, and write answers only in the spaces provided. Show calculations clearly and do rough work in the book.

What topics are covered in the questions?

The questions cover areas such as factorisation and algebra, matrices, solving equations and inequalities, algebraic proofs, sequences, number construction, graphs, trigonometry, and gradients of curves.

Sep 5, 2026

Upload by Miles