Six graded worksheets on surds for GCSE Higher, with full mark schemes. Builds from simplifying and rationalising the denominator through to surd problems and equations. How the series builds: Simplifying, multiplying and dividing — √n to a√b, products, quotients and powers Adding and subtracting — simplifying surds and collecting like terms Expanding brackets — single and double brackets, squares and conjugates Rationalising the denominator I — single-surd denominators Rationalising the denominator II — conjugate (two-term) denominators Surd problems and equations — solving, finding unknowns and writing in the form a + b√n Board-agnostic (AQA, Edexcel, OCR) and supplied as print-ready PDFs — 6 worksheets and 6 mark schemes, with answers in exact, simplified form throughout. Ideal for KS4 higher-tier lessons, homework, starters, revision and exam practice.

Five graded worksheets on polynomial division and the factor and remainder theorems for A-Level, with full mark schemes. Builds from the factor theorem through to factorising and solving cubics and quartics. How the series builds: The factor theorem — showing a bracket is a factor, finding an unknown, non-unit factors The remainder theorem — remainders by substitution, finding an unknown from a given remainder Polynomial division — dividing exactly by linear and quadratic divisors, dividends with missing terms Division with a remainder — quotient and remainder, and writing the answer as a quotient plus a proper fraction Factorising and solving — using a given factor to factorise and solve cubics and quartics Board-agnostic (AQA, Edexcel, OCR). Answers given in factorised and quotient form, with full mark schemes throughout. Print-and-go PDFs for lessons, homework, starters and revision.

Seven graded worksheets that take A-Level students from their first partial fractions all the way to improper and awkward denominators — dense, exam-style practice with full mark schemes throughout. Each worksheet is a focused, one-topic drill (two full pages) with a matching answer key, building in difficulty across the series. How the series builds: Level 1 — Two distinct linear factors Level 2 — Three distinct linear factors Level 3 — Repeated linear factors Level 4 — Factorise the denominator first Level 5 — Improper fractions: divide first Level 6 — Denominators with an x factor (including fractional constants) Level 7 — Improper and awkward denominators, including reversed and negative-leading forms Board-agnostic and suitable for all A-Level specifications. Full mark schemes included for every worksheet.

Five graded worksheets on algebraic fractions for GCSE Higher, with full mark schemes. Builds from simplifying through to solving fractional equations. How the series builds: Simplifying — cancelling common factors, factorising, difference of two squares Multiplying and dividing — factorise and cancel, dividing by the reciprocal Adding and subtracting — common denominators, combining into a single fraction Compound (stacked) fractions and rearranging formulae Solving fractional equations — clearing denominators, linear and quadratic Board-agnostic (AQA, Edexcel, OCR). Answers given in factorised form, with full mark schemes throughout. Print-and-go for lessons, homework, starters and revision.

Five graded Simultaneous Equations worksheets for GCSE Higher, with full mark schemes. Dense practice from linear elimination up to line-meets-circle and tangency. How the series builds: Linear systems by elimination Linear systems by substitution and rearrangement Line meets curve: parabolas Line meets curve: circles and implicit curves Non-linear systems: reciprocal equations, tangency, and points of intersection Board-agnostic (AQA, Edexcel, OCR). Full mark schemes throughout. Print-and-go for lessons, homework, starters and revision.

Five graded worksheets on solving quadratic equations by factorising, for GCSE Higher, with full mark schemes. Builds from standard equations to applied reasoning. How the series builds: Factorising, a = 1 Factorising, a > 1 Rearrange, then factorise Expand, then factorise (brackets, disguised quadratics, higher-power equations) Reasoning & applications (roots from sum/product, unknown coefficients, worded and consecutive-integer problems) Board-agnostic (AQA, Edexcel, OCR). Every question has a worked answer. Print-and-go for lessons, homework, starters and revision.

Five graded worksheets on completing the square for GCSE Higher, with full mark schemes. From the basic form through to solving, turning points and reasoning. How the series builds: Expressing in the form (x + a)² + b The form a(x + p)² + q (non-monic, negative leading coefficient, fractional a) Solving quadratics by completing the square (exact/surd roots) Turning points, lines of symmetry, least/greatest values, and meeting the x-axis Reasoning & proof (identities, always-positive arguments, discriminant reasoning) Board-agnostic (AQA, Edexcel, OCR). Every question worked in the mark scheme. Print-and-go for lessons, homework, starters and revision.

Five graded worksheets on the quadratic formula for GCSE Higher, with full mark schemes. From substitution and surd-form answers through to the discriminant. How the series builds: The formula: substitute and evaluate Surd-form (exact) answers Decimal answers (2 d.p. / 3 s.f.), including rearrangement The discriminant: number and nature of roots Conditions on k: equal roots, no real roots, distinct roots, tangency to the x-axis Board-agnostic (AQA, Edexcel, OCR). Every question worked in the mark scheme. Print-and-go for lessons, homework, starters and revision.

Five graded worksheets on quadratic inequalities for GCSE Higher, with full mark schemes. From standard factorisable inequalities to exact surd critical values. How the series builds: Standard-form, monic, factorisable Non-monic, negative-leading, and rearrange-first Surd critical values in exact form Integer solution sets, simultaneous systems, and curve contexts Reasoning, proof, and applications Board-agnostic (AQA, Edexcel, OCR). Every question worked in the mark scheme. Print-and-go for lessons, homework, starters and revision.

Five graded Factorising Quadratics worksheets for GCSE Higher, with full mark schemes. Dense practice that builds from first principles to exam standard. How the series builds: Common factors (single and double brackets, negatives, common-bracket grouping) Quadratics with a = 1 Quadratics with a > 1 Factorise fully (common factor first, then the quadratic; higher powers) Reasoning & applications (spot-the-error, missing coefficients, algebraic fractions, area problems) Board-agnostic (AQA, Edexcel, OCR). Every question has a worked answer. Print-and-go for lessons, homework, starters and revision.

A topic-locked practice paper for Edexcel GCSE Foundation Paper 1 (1MA1), focusing entirely on Number and Arithmetic — the topic area that anchors the first half of the real paper. What’s inside 17 original questions (45 marks, 50 minutes) Full step-by-step mark scheme with examiner notes Both Word (.docx) and PDF formats — edit the Word file to fit your scheme of work, or print the PDF straight off Topics covered Ordering decimals · FDP conversion · BIDMAS · negative numbers · powers and roots · fractions of amounts · rounding · percentages of amounts · HCF and prime factorisation · long multiplication · decimal arithmetic · mixed number arithmetic · fraction multiplication and division · multi-step money problems · multi-step percentages · estimation · reverse percentages How to use it As a topic-locked diagnostic before the May exam As a homework or in-class assessment As a low-stakes mock to identify which Number topics need re-teaching As intervention material for grade-3/4 borderline students Pitched at Foundation tier candidates working towards grades 3–5. Question difficulty gradient mirrors the structure of recent Edexcel Foundation Paper 1 papers.

A 50-minute non-calculator practice paper focused on the algebra and sequences questions that appear on GCSE Foundation Paper 1 (Edexcel 1MA1). 17 questions, 45 marks, pitched at Foundation grade 2-5. Topic mix audited against three recent Edexcel 1MA1 Foundation Paper 1 papers (June 2023, November 2023, May 2024) so the question types and difficulty profile match what students will actually face in the exam. All numbers and contexts are original — not lifted from any past paper. WHAT’S INCLUDED Worksheet (Word .docx and PDF) — 17 questions, 45 marks, 50 minutes Mark scheme (Word .docx and PDF) — full method credit, examiner notes, common-error commentary TOPICS COVERED Simplifying expressions, solving one-step and two-step linear equations, coordinates and plotting points, substitution into formulae (positive and negative values), continuing arithmetic sequences and finding the term-to-term rule, collecting like terms, factorising, finding the nth term of a linear sequence, forming a formula from a worded context, function machines (forwards, reverse, and “input equals output”), expanding single brackets, solving linear equations with brackets, plotting straight-line graphs from y = mx + c, finding the equation of a straight line from a graph, solving linear inequalities. PERFECT FOR Year 11 Foundation revision in the run-up to Paper 1 In-class timed practice (50 minutes) Foundation tier mock or assessment Setting alongside Practice 1 (Number & Arithmetic) to build a complete Foundation Paper 1 revision pack The Word .docx files are fully editable so you can adjust questions or rebrand for your school. Part of the Foundation Paper 1 Practice series. Practice 1 (Number & Arithmetic) also available; Practice 3 to follow.

A 50-minute non-calculator practice paper covering the Ratio, Geometry and Statistics questions that appear on GCSE Foundation Paper 1 (Edexcel 1MA1). 17 questions, 45 marks, pitched at Foundation grade 2-5. This is the third paper in the Foundation Paper 1 Practice series. Together with Practice 1 (Number & Arithmetic) and Practice 2 (Algebra & Sequences), it completes a full topic sweep of Foundation Paper 1 — buy all three for a complete revision pack in the run-up to the exam. Topic mix audited against three recent Edexcel 1MA1 Foundation Paper 1 papers (June 2023, November 2023, May 2024) so the question types and difficulty profile match what students will actually face in the exam. All numbers and contexts are original — not lifted from any past paper. WHAT’S INCLUDED Worksheet (Word .docx and PDF) — 17 questions, 45 marks, 50 minutes Mark scheme (Word .docx and PDF) — full method credit, examiner notes, common-error commentary TOPICS COVERED Simplifying ratios, writing a ratio in the form 1 : n, sharing in a ratio, working with ratios from a difference, recipe scaling, best value for money, finding the mean, mode, range and median, frequency tables, two-way tables and probability, basic probability with a fair dice, angles on a straight line, angles in parallel lines, area of a triangle, perimeter and area of a compound shape, reflection in a horizontal line on a coordinate grid, interior and exterior angles of a regular polygon, unit conversion. PERFECT FOR Year 11 Foundation revision in the run-up to Paper 1 In-class timed practice (50 minutes) Foundation tier mock or assessment Completing the Foundation Paper 1 Practice series alongside Practice 1 and Practice 2 The Word .docx files are fully editable so you can adjust questions or rebrand for your school. Part of the Foundation Paper 1 Practice series. Practice 1 (Number & Arithmetic) and Practice 2 (Algebra & Sequences) also available — buy all three for full Foundation Paper 1 topic coverage.

A 50-minute non-calculator practice paper focused on the algebra and number questions that appear on GCSE Higher Paper 1 (Edexcel 1MA1, AQA 8300, OCR J560). 16 questions, 47 marks, ramping from grade 6 to grade 9. Perfect for last-minute Paper 1 revision, in-class timed practice, or homework before the exam. Excludes shape, geometry and statistics — designed as a focused stretch pack alongside other revision resources. WHAT’S INCLUDED Worksheet (Word .docx and PDF) — 16 questions, 47 marks, 50 minutes Mark scheme (Word .docx and PDF) — full method credit, examiner notes, common-error commentary TOPICS COVERED Expanding and simplifying brackets, factorising quadratics, linear equations, indices laws, surds, evaluating fractional and negative powers, simultaneous equations, quadratic sequences, simplifying algebraic fractions, factorising-led quadratics, adding algebraic fractions, linear-quadratic simultaneous equations, completing the square, algebraic proof, composite functions, inverse functions. PERFECT FOR Year 11 Higher revision in the run-up to Paper 1 In-class timed practice (50 minutes) Setting as homework before mock or live exams Identifying gaps in algebra and number ahead of the exam The Word .docx files are fully editable so you can adjust questions or rebrand for your school. Part of the Higher Paper 1 Practice series — Practice 2 (grade 7-9) and Practice 3 (grade 8-9 stretch) also available.

A 50-minute non-calculator practice paper focused on the algebra and number questions that appear on GCSE Higher Paper 1 (Edexcel 1MA1, AQA 8300, OCR J560). 16 questions, 50 marks, pitched at pure grade 8-9 stretch — every question is a stretch problem. The most challenging in the Higher Paper 1 Practice series, designed for students targeting grade 8 or 9. There is no warm-up section. WHAT’S INCLUDED Worksheet (Word .docx and PDF) — 16 questions, 50 marks, 50 minutes Mark scheme (Word .docx and PDF) — full method credit, examiner notes, alternative methods, common-error commentary TOPICS COVERED Triple-bracket expansion, quadratic inequalities (factorise then solve), full factorisation of x⁴-style differences, harder fractional linear equations, harder index laws, rationalising surds with conjugates, fractional powers of compound expressions, simultaneous equations with fractional answers, finding the nth term of a quadratic sequence from terms, simplifying algebraic fractions with non-monic numerators, completing the square with surd solutions, harder algebraic fractions, non-linear simultaneous equations (x²+y²=25 type), algebraic proof, composite functions and solving, recurring decimals to fractions. PERFECT FOR Year 11 grade 8/9 stretch revision In-class timed practice (50 minutes) Top-set assessment Stretching students who completed Practice 1 and Practice 2 The Word .docx files are fully editable so you can adjust questions or rebrand for your school. Part of the Higher Paper 1 Practice series. Practice 1 (grade 6-9) and Practice 2 (grade 7-9) also available.

A 50-minute non-calculator practice paper focused on the algebra and number questions that appear on GCSE Higher Paper 1 (Edexcel 1MA1, AQA 8300, OCR J560). 16 questions, 47 marks, pitched at grade 7-9. Harder than Practice 1 in the same series, with stretch problems towards the end. Perfect for top-set Year 11 revision and grade 7-9 students aiming to consolidate exam technique. WHAT’S INCLUDED Worksheet (Word .docx and PDF) — 16 questions, 47 marks, 50 minutes Mark scheme (Word .docx and PDF) — full method credit, examiner notes, common-error commentary TOPICS COVERED Harder bracket expansion, two-variable factorising, harder trinomial factorising, fractional linear equations, index laws on algebraic fractions, rationalising surds, evaluating fractional and negative powers, simultaneous equations with fractional answers, quadratic sequences, simplifying algebraic fractions with difference of squares, completing the square with surd solutions, harder algebraic fractions, linear-quadratic simultaneous equations, completing the square with non-unit leading coefficient, algebraic proof, recurring decimals to fractions. PERFECT FOR Top-set Year 11 revision targeting grade 7-9 In-class timed practice (50 minutes) Setting as homework or assessment Stretching students who completed Practice 1 The Word .docx files are fully editable so you can adjust questions or rebrand for your school. Part of the Higher Paper 1 Practice series. Practice 1 (grade 6-9) and Practice 3 (grade 8-9 stretch) also available.

Worksheet 3 of the Vectors series — 15 questions on vector geometry and proof for GCSE Higher (Edexcel 1MA1, AQA 8300, OCR J560). 47 marks, 50 minutes. Builds on Vectors 1 and Vectors 2, applying vector skills to triangles and parallelograms with full proof and collinearity questions. Perfect for top-set Year 11 revision and grade 8/9 stretch. WHAT’S INCLUDED Worksheet (Word .docx and PDF) — 15 questions, 47 marks, ~50 minutes Mark scheme (Word .docx and PDF) — full method credit, examiner notes, common-error commentary WORKSHEET STRUCTURE Section A — Fluency (Q1–Q7, 15 marks): expressing vectors in terms of given vectors a and b on triangles and parallelograms, midpoints, and points dividing line segments in given fractions Section B — Exam-Style (Q8–Q11, 14 marks): mid-segment theorem of triangles, parallelogram diagonals bisecting each other, parallel-line proofs Section C — Problem-Solving (Q12–Q15, 18 marks): combined ratio and midpoint problems, “show MN = pa + qb” stretch questions, and a full collinearity proof TOPICS COVERED Vector addition along chained paths, expressing vectors via two given vectors, midpoints of triangle sides, ratio division of a line segment, parallelogram diagonal properties, mid-segment theorem, parallel lines (vectors as scalar multiples), collinearity proofs (parallel + shared point). PERFECT FOR Year 11 Higher revision targeting grade 8/9 Top-set Year 10 stretch and challenge Setting as a timed assessment for high-attaining students Teacher-led model answer practice for vector proof technique The Word .docx files are fully editable so you can adjust questions, swap names, or rebra

Worksheet 2 of the Vectors series — 15 questions on position vectors and geometry for GCSE Higher (Edexcel 1MA1, AQA 8300, OCR J560). 47 marks, 50 minutes. Builds directly on Vectors 1 (Column Vectors and Arithmetic) and prepares students for vector geometry and proof in Worksheet 3. Perfect for Year 10 progression or Year 11 revision. WHAT’S INCLUDED Worksheet (Word .docx and PDF) — 15 questions, 47 marks, ~50 minutes Mark scheme (Word .docx and PDF) — full method credit, examiner notes, common-error commentary WORKSHEET STRUCTURE Section A — Fluency (Q1–Q7, 15 marks): finding vectors between points, midpoints, and magnitudes from position vectors Section B — Exam-Style (Q8–Q11, 14 marks): point dividing a line in a given fraction, distance problems with surd answers, algebraic position vectors, collinearity Section C — Problem-Solving (Q12–Q15, 18 marks): ratio AP:PB along a line segment, two-unknown algebraic midpoints, parallelogram fourth-vertex problems, magnitude with surds TOPICS COVERED Position vectors, finding the vector AB as b − a, midpoints, magnitude (Pythagoras), distance between points, ratio division of a line segment, parallelograms in vector form, collinearity proofs, algebraic position vectors with unknowns, surd simplification. PERFECT FOR Year 10 Higher students moving beyond column vector arithmetic Year 11 Higher revision and intervention Setting as homework, in-class practice, or end-of-topic assessment Stretching top-set students with Section C ratio and parallelogram problems The Word .docx files are fully editable so you can adjust questions, swap names, or rebrand for your school. Pairs with Vectors 1: Column Vectors and Arithmetic. Worksheet 3 (vector geometry and proof) will follow shortly.