Year 10 – Solving Quadratics by Completing the Square (IGCSE Edexcel Maths) This worksheet develops students’ ability to complete the square and use it to analyse and solve quadratic equations. Students write quadratics in completed square form and use it to find turning points. They work backwards from a sketch to find the equation of a quadratic, and solve quadratics exactly, giving answers in simplified surd form. In the final sections, they use completing the square to prove results, find unknown constants, describe graph transformations and solve real-life maximum and minimum problems. The work is split into five colour-coded sections from Grade 5 to Grade 9, so students can start at the right level and move on. Green – Practice (Grade 5) Students write expressions such as x² + 6x + 5 in the form (x + p)² + q. From the completed form they state the turning point, decide whether it is a minimum or maximum, and find the y-intercept. Amber – Further Practice (Grade 6) Students complete the square when the x coefficient is odd, giving fractional answers. Using sketches with a turning point given, they find the equation of the quadratic and where the graph crosses the axes, including one curve with a maximum point. They also spot and correct a common sign error when reading a turning point. Red – Developing Understanding (Grades 6–7) Students solve quadratics by completing the square, giving answers in surd form. They simplify surds such as √12 = 2√3 and give answers in the form (a ± √b)/2, including where a ≠ 1. They also give answers to 2 decimal places. TIF – Problem Solving (Grades 7–8) Students complete the square when a ≠ 1 and write expressions in the form q − (x − p)² to find maximum points. They find unknown constants in identities and prove that an expression is always positive. They also find the values of k for which an equation has no real roots, describe a translation of y = x² as a vector, and solve an area problem with an exact surd answer. TIEF – Challenging Real-Life Problems (Grades 8–9) Students apply completing the square to real contexts: finding the maximum height of a ball and when it lands the selling price that gives a café the greatest profit the largest area of a fenced pen whether a boat can pass under a bridge arch the width of a phone screen in exact surd form using Pythagoras the turning point of a family of curves

Sequences and Series – Extension Work (IGCSE Further Maths, Chapter 5) This extension work gives you more practice with real exam questions on arithmetic and geometric series. It is worth 154 marks and is split into colour-coded sections that get harder as you go. Each question shows its grade, its marks and the exam paper it came from. Starter diagnostic (teal): four quick questions on sums of arithmetic series, sigma notation, sum to infinity and finding the common ratio. Use your score and the table under the starter to decide which section to start at. Section 1 (red), Grade 5–6: finding the first term, common difference and common ratio, using sigma notation, and using the Sₙ formulas. Section 2 (blue), Grade 7: forming and solving equations from two conditions, including quadratics in n, and comparing an arithmetic series with a geometric one. TIF (green), Grade 8: problem solving with logarithms, sums to infinity, convergence, and finding the least value of n. TIEF (purple), Grade 9: the hardest “show that” questions, using logs and powers of e.

These booklets give you past exam questions sorted by topic. They come from Pearson Edexcel International GCSE Further Pure Mathematics papers from 2019 to 2026. There is one booklet for each topic from Chapter 1 (Surds, Logarithms and Indices) to Chapter 11 (Trigonometry). Each booklet has a matching Worked Solutions PDF so you can check and mark your own work. How each booklet works The questions are sorted into five levels, so you can start where you feel confident and work up: Green – Practice: check you can use the key methods. Amber – Further Practice: use those methods in slightly longer questions. Red – Developing Understanding: multi-step exam questions that combine ideas. TIF (Take It Further) – Problem Solving: harder questions where you decide the method. TIEF (Take It Even Further) – Further Developing Problem Solving Skills: the most challenging exam questions.

This is the first lesson in the Year 8 unit “Atoms, Elements and Mixtures of the Periodic Table”. Students learn that everything is made of tiny particles called atoms, and that an element is a substance made of only one type of atom. There are about 118 elements. The lesson covers: Chemical symbols: every element has a one‑ or two‑letter symbol. The first letter is always a capital and the second is lower case, which is why Co (cobalt) and CO (carbon monoxide) are different. Some symbols come from Latin names, such as Na for sodium (natrium) and Fe for iron (ferrum). The structure of the atom: a central nucleus contains protons (positive) and neutrons (no charge). Electrons (negative) move around the nucleus in shells. Atoms are neutral because they have the same number of protons and electrons. Drawing atoms: electrons fill the shells from the inside. The first shell holds 2, then up to 8 in each of the next shells. For example, carbon is 2, 4. Atomic number and mass number: the atomic number is the number of protons, and it decides which element an atom is. The mass number is protons plus neutrons. Students calculate protons, neutrons and electrons, for example sodium‑23 has 11 protons, 12 neutrons and 11 electrons. Chemical formulae: a formula shows which atoms are in a substance and how many of each. For example, H₂O has 2 hydrogen atoms and 1 oxygen atom. By the end of the lesson, students should be able to: identify the symbols of common elements describe and draw the structure of an atom use atomic number and mass number to work out the numbers of protons, neutrons and electrons The lesson ends with an application task about labelling a museum exhibit on carbon‑12 and carbon‑14. This shows that atoms of the same element can have different numbers of neutrons. The KS4 extension goes further into GCSE ideas: isotopes, relative atomic mass, ions, electron configuration, the history of the atomic model and relative formula mass.

Binomial Expansion – Extension Homework (IGCSE Further Maths, Chapter 6) This homework stretches your understanding of binomial expansion beyond the core questions. It is worth 83 marks and is split into colour-coded sections that get harder as you go: Questions 1–3 (red): past exam questions. Expanding expressions with fractional and negative powers, finding unknown constants, and using an expansion to estimate a square root. Questions 4–6 (blue): exam-style questions. Rewriting an expression in the form (1 + bx)ⁿ before expanding, finding unknown powers and constants from given coefficients, stating when an expansion is valid, and using a suitable value of x to estimate a value. Questions 7–8 (green, TIF): problem solving. Finding unknown constants by comparing coefficients, and multiplying two expansions together to estimate √51. Question 9 (purple, TIEF): the hardest question. Expanding an expression in x² and using it to estimate √101.

Sets and Venn Diagrams: Exam Practice (Year 10, IGCSE Edexcel Maths) This booklet contains 28 Pearson Edexcel IGCSE past-paper questions on sets and Venn diagrams, sorted from easiest to hardest. There are 114 marks in total. Each question shows its marks, its grade and the exam paper it came from, and has a square grid for your working. Start with the three-question starter on the front page. Your score tells you which section to begin with. Green – Practice (Grade 4–5, questions G1 to G6, 20 marks): listing the members of sets and reading a Venn diagram. Amber – Further Practice (Grade 5–6, questions A1 to A8, 30 marks): completing two-set Venn diagrams from set notation and working with described sets. Red – Further Developing Understanding (Grade 6–7, questions R1 to R7, 25 marks): three sets, including n( ) notation, shading regions and building a diagram from information. TIF – Problem Solving (Grade 7–8, questions T1 to T4, 24 marks): longer three-set problems with probability and algebra. TIEF – Hard Challenge (Grade 8–9, questions E1 to E3, 15 marks): the three hardest questions.

Year 10 Maths Homework: Index Notation (Negative and Fractional Powers) This homework practises the index work we have been doing in class: evaluating numbers with zero, negative and fractional powers, and simplifying algebraic expressions that have negative and fractional powers. It follows the Edexcel IGCSE style, and it should be done without a calculator. Start with the four starter questions on page 1. Your score tells you which level to begin at: Green (Grade 5–6): practice with negative and fractional powers and simple algebra. Amber (Grade 6–7): further practice with fractions to negative powers and brackets with fractional powers. Red (Grade 7–8): harder algebraic fractions, expanding brackets and solving a power equation. TIF (Grade 8–9): problem-solving questions. TIEF (Grade 9): three hard challenge questions.

Year 8 Science revision assessment on Fungi, Bacteria and Protists, written in the style of ExamPro exam questions. It’s worth 57 marks and comes as two separate PDFs: an 8-page question paper and a 4-page mark scheme. It’s based on your Fungi, Bacteria and Yeast lesson slides, the budding and binary fission support slides, and the ordering worksheet. It checks whether students can explain how the structures of bacteria, fungi and protists help them survive, and how yeast and bacteria reproduce. It covers the lesson’s success criteria: recalling examples, identifying cell parts, describing budding and binary fission, explaining what key structures do, everyday uses of microbes, and calculating population growth from a graph. How it’s organised The paper is split into four colour-coded sections that match the lesson’s grade bands. Students start at Green and work up as far as they can. Green, Section A (Foundation, Grade 4), 15 marks. Recall and identification: sorting mushroom, Salmonella, Amoeba, yeast, E. coli, algae and mould into bacteria, fungi or protists, which microbe makes bread rise, a food made using bacteria, labelling a bacterial cell, naming binary fission, and completing sentences about binary fission. Amber, Section B (Core, Grade 5–6), 15 marks. Describing structures and reproduction: labelling a yeast cell, giving the functions of the flagellum, mitochondrion and contractile vacuole, and putting the stages of budding and binary fission in order (from your worksheet). It also asks for one similarity and one difference between the two processes, and why asexual reproduction produces identical cells. Red, Section C (TIF, Grade 7–9), 17 marks. Explaining and calculating: a population growth graph where students describe the pattern, calculate the increase, calculate the rate of growth, predict the population and link the curve to binary fission. It also includes calculating how many bacteria grow on rice left out for 4 hours, why this is dangerous, and which microbe is best adapted to rotting fruit. Purple, Section D (TIEF, Grade 9+ extension), 10 marks. Applying knowledge to new situations: a 6-mark question on whether a lab should grow bacteria or yeast to get microorganisms as quickly as possible, and a 4-mark question on harmful algal blooms (red tides) in UAE waters, covering why they spread so fast and how to reduce them.

Year 8 Science revision assessment on Unicellular and Multicellular Organisms, written in the style of ExamPro exam questions. It’s worth 57 marks over 12 pages, with 8 pages of questions and 4 pages of mark scheme. It’s based on your lesson slides and the Amoeba and Euglena information sheet. It checks whether students can compare unicellular and multicellular organisms and explain how unicellular organisms like Amoeba and Euglena survive. It covers the lesson’s success criteria: naming examples, identifying structures, comparing the two groups, linking structure to survival, and explaining how diffusion limits cell size. How it’s organised The paper is split into four colour-coded sections that match the lesson’s grade bands. Students start at Green and work up as far as they can. Green, Section A (Foundation, Grade 4), 17 marks. Recall and identification: matching cell parts to their functions, the meaning of “unicellular”, sorting organisms into unicellular and multicellular, completing sentences about multicellular organisms, labelling an Amoeba diagram, where Euglena live, and naming binary fission. Amber, Section B (Core, Grade 5–6), 17 marks. Describing and comparing: labelling a Euglena diagram, completing a comparison table, and describing how an Amoeba feeds, how a Euglena moves towards light, what the contractile vacuole does, the stages of binary fission, and two differences between Amoeba and Euglena. Red, Section C (TIF, Grade 7–9), 14 marks. Explaining and calculating: why Euglena need chloroplasts, and why multicellular organisms survive losing some cells but unicellular organisms don’t. It also includes a surface area to volume calculation with cubes and a 4-mark explanation of why Amoebas can’t grow to the size of whales, using the words diffusion, surface area, volume and distance. Purple, Section D (TIEF, Grade 9+ extension), 9 marks. Applying knowledge to new situations: predicting and explaining how Euglena respond in a half-covered test tube, and a 6-mark “Lost in the Pond” question on whether an Amoeba or a Euglena is more likely to survive a week in a dark pond.

Changing the Subject of a Formula (Year 10, IGCSE Edexcel Higher) This worksheet builds your skills in rearranging formulas where the subject appears more than once, including formulas with squares, cubes, square roots and cube roots. It is split into five colour-coded levels, so you can start where you feel confident and work your way up. Green (Grade 6): The subject appears twice. Collect the terms with the subject on one side, then factorise. Amber (Grade 7): The subject is squared or cubed. Factorise out x² or x³, then take the square root (±) or cube root. Red (Grade 8): Formulas with square roots and cube roots. Square or cube both sides first, then collect terms and factorise. TIF (Grade 8–9): Exam-style problem-solving questions, including intersecting chords, spotting a mistake in someone’s working and a “show that” proof. TIEF (Grade 9): Three challenging real-life problems: a pendulum clock, a spherical water tower and a wind turbine. Show every step of your working in the grid below each question, one step per line. When you have finished a level, check your answers using the worked solutions.

Surds – Differentiated Worksheet with Worked Solutions (Pearson Edexcel IGCSE 9–1, Higher Tier) This worksheet develops the surds content of the Pearson Edexcel International GCSE (4MA1) Higher Tier specification. Students start with simplifying surds and build up to exam-style problems in shape and real-life contexts. The pack has two PDFs: the student worksheet and a separate set of full worked solutions. It works well for classwork, homework, independent revision and exam preparation. The worksheet has five colour-coded levels, each on its own page with a matching border and a clear grade label, so students know how hard the work is before they begin. Every question has a square grid for working out and an answer line, and all the questions are designed to be answered without a calculator. Green – Practice (Grade 5): six questions on simplifying surds such as √50 and √48, multiplying surds, and adding and subtracting surds after simplifying them. Amber – Further practice (Grade 6): six questions on expanding single and double brackets containing surds, including a difference of two squares and squaring a bracket, with answers in the form a + b√n. Red – Developing understanding (Grade 7): six questions on rationalising the denominator. They move from simple denominators such as 6/√3 to denominators of the form 3 − √5 and √7 + 2, which need the conjugate. TIF – Problem solving (Grade 8): six exam-style shape problems where students find an exact height, width, radius or length: the width of a rectangle and the height of a triangle, both needing rationalising the radius of a circle the radius and curved surface area of a cylinder the hypotenuse of a triangle with surd sides the height and area of an equilateral triangle TIEF – Real-life challenge (Grade 9): four illustrated problems that show where surds appear in everyday life: the √2 ratio behind A4 and A5 paper the gradient and exact length of a wheelchair ramp the dimensions of a solar panel the radius of a pizza with double the area The worked solutions show one step per line going down the page, and give each part of an answer on its own line so students can follow every stage of the method. They highlight key techniques such as finding the largest square factor, using the conjugate to rationalise, recognising the difference of two squares, and giving exact answers in simplest surd form.

Intersecting Chords – Differentiated Worksheet with Worked Solutions (Pearson Edexcel IGCSE 9–1, Higher Tier) This worksheet develops the internal and external intersecting chord theorems from the Pearson Edexcel International GCSE (4MA1) Higher Tier specification. Students start with simple chords crossing inside a circle and work up to multi-mark exam-style questions involving quadratics and surds. The full worked solutions come as a separate PDF, which makes the pack useful for classwork, homework, independent revision and exam preparation. The worksheet has five colour-coded levels, each on its own page with a matching border and a clear grade label, so students know how hard the work is before they begin. Every question has an exam-style diagram marked “Diagram NOT accurately drawn”, a square grid for working out and an answer line. Green – Practice (Grade 5–6): four questions on chords intersecting inside a circle, using AP × PB = CP × PD with whole-number lengths. Amber – Further practice (Grade 6–7): three questions on chords that meet outside the circle, where students must add the outside part and the chord to get the whole line, plus one inside-circle question with decimals. Red – Developing understanding (Grade 7): four questions where students form and solve equations in x. Two lead to linear equations and two to quadratics, where students must reject the negative root. TIF – Problem solving (Grade 8): four exam-style questions with marks shown: finding the radius from a diameter and a crossing chord a “show that” quadratic answered to 3 significant figures a six-mark question combining the internal and external theorems with a circle centre O a question where the chord segments are given as a ratio TIEF – Challenge (Grade 9): four exam-style questions with surds. Students rationalise denominators, use the difference of two squares, solve a quadratic by completing the square, and give exact answers in the form a + b√3. The worked solutions set out every step for all 20 questions. They show how to set up each equation from the correct theorem, handle quadratics and surds, and give answers to the required accuracy. They also highlight common mistakes, such as using only the outside part of the line instead of the whole line in external chord questions, and not rejecting negative lengths.

The Disease paper is a Year 8 Science revision assessment on Disease and Pathogens, written in the style of ExamPro exam questions. It’s worth 54 marks and comes as two separate PDFs: an 8-page question paper and a 3-page mark scheme. It’s based on your Disease lesson slides. It checks whether students can explain what pathogens are, how they cause disease and how communicable diseases spread. It covers the lesson’s success criteria: defining a pathogen, naming the four types of pathogen and their diseases, communicable and non-communicable diseases, how diseases are transmitted, and applying this to real examples such as COVID-19. How it’s organised The paper is split into four colour-coded sections that match the lesson’s grade bands. Students start at Green and work up as far as they can. Green, Section A (Foundation, Grade 4), 13 marks. Recall and identification: defining a pathogen, naming bacteria, virus, fungus and protist from pictures, choosing true statements about microorganisms, which pathogen causes influenza, HIV, cholera, rose black spot and malaria, sorting seven diseases into communicable and non-communicable, and two ways pathogens spread. Amber, Section B (Core, Grade 5–6), 15 marks. Describing how pathogens cause and spread disease: putting the stages of infection in order, how each type of pathogen causes disease, the difference between communicable and non-communicable diseases, how each of the five diseases is spread, and what a vector is (the mosquito for malaria). Red, Section C (TIF, Grade 7–9), 16 marks. Explaining and applying: correcting the “all bacteria are pathogens” and “malaria must be bacteria” misconceptions, why you don’t feel ill straight away with flu, identifying a mystery disease from clues (cholera), and the “How did COVID-19 reach Dubai?” plenary turned into exam questions. Purple, Section D (TIEF, Grade 9+ extension), 10 marks. Applying knowledge to new situations: the Dubai Health Emergency question on why knowing both the pathogen and how it spreads matters for controlling an outbreak, and a 6-mark question on which method of transmission is hardest to control.

Surface Area of a Cylinder – Differentiated Worksheet with Worked Solutions (KS3 and GCSE) This worksheet takes students from finding surface area using a net through to working backwards from a given surface area and solving multi-step real-life problems. It suits KS3 and GCSE Foundation and Higher students. The worked solutions come as a separate document, which makes the pack useful for classwork, homework, intervention and revision. The worksheet has five colour-coded levels, so students can start where they need to and move up as their confidence grows. Each level is on its own page with a matching coloured border, which makes it easy to print only the levels a class or student needs. Every question has a square grid for working out and a clear answer line, and the cylinders are coloured to help students tell the circular faces from the curved surface. Green (Practice): four cylinder nets with no scaffolding. Students find the area of the two circles and the rectangle, and two of the nets give the diameter rather than the radius. Amber (Further practice): four cylinders with whole-number measurements, some giving the radius and some the diameter. The cylinders are drawn upright, lying down and tilted, so students learn to spot the radius and height whatever the orientation. Red (Further developing understanding): four cylinders in different positions with decimal radii and diameters, some in centimetres and some in metres. This builds accuracy and careful rounding. TIF (Problem solving): six questions where students work backwards to find a missing height, length or radius. They cover: working from a total surface area given as a decimal or in terms of π working from a curved surface area an algebraic question where the height is a multiple of the radius two illustrated real-life problems: painting the inside of an open farm water tank, where only one circle is used, and an advert wrapped around a shopping-mall pillar, which uses the curved surface only TIEF (Real-life challenge): one extended, illustrated problem about painting a water tank on a villa roof in Dubai. Students choose which surfaces to include, account for two coats, convert area into litres of paint, and compare tin sizes and prices to find the cheapest way to buy the paint. The worked solutions set out every step for all 19 questions. They show exact answers in terms of π alongside decimal answers, keep full calculator values until the final step, and highlight common pitfalls such as forgetting to halve the diameter, including both circles on an open tank, or rounding down the number of paint tins. Skills covered: surface area of cylinders, circumference and area of circles, nets of 3D shapes, working with π, rearranging to find unknown lengths, unit conversion, rounding, and problem solving in context.

Volume of a Cylinder – Differentiated Worksheet with Worked Solutions (KS3 and GCSE) This printable resource helps students build confidence in finding the volume of a cylinder, from first practice through to real-life problem solving. It suits KS3 learners meeting the topic for the first time and GCSE students (Foundation and Higher) who need consolidation, exam-style practice or revision. Each level is colour-coded, so students can start at the right point and work their way up, which makes it easy to use in mixed-ability classes. The worksheet has five levels. Green (Practice) gives straightforward questions using V = πr²h, with dimensions given as either the radius or the diameter. Amber (Further Practice) adds decimal measurements, cylinders standing up and lying on their side, everyday contexts such as tins, logs and fuel tanks, and rounding to 3 significant figures. Red (Further Developing Understanding) moves on to half cylinders, quarter cylinders and a three-quarter cylinder in different orientations, so students have to reason about fractions of a full cylinder. TIF (Problem Solving) asks students to work backwards from a given volume to find a missing height or radius. This includes rearranging formulae, using square and cube roots, and comparing two cylinders with equal volume. TIEF (Challenge) has two multi-step real-life problems, a rooftop water tank and a juice factory filling cans. These involve converting to litres, deciding when to round down, and working with money. Every question has a colourful labelled diagram and a squared grid for working, which encourages clear, well-set-out methods. A separate answer booklet gives full worked solutions showing every step, from substitution to the rounded final answer. It also includes a teacher note on common rounding mistakes, so it works well for self-assessment, peer marking or homework. The resource is ideal for classwork, homework, intervention, revision lessons or independent practice. It covers key skills in the KS3 and GCSE curriculum: volume of prisms, rounding to decimal places and significant figures, rearranging formulae, and applying maths to real-world contexts.

GCSE Surface area

Solving Problems Involving Ratio suitable for KS3/KS4.

This lesson introduces the key probability formulae required for Edexcel A-Level Statistics, linking them to real-life applications such as weather forecasting, medical testing, quality control, insurance, and sports analytics. Students begin with a starter activity that revisits prior knowledge of probability and explores how probabilities are used to support decision-making in everyday situations. The lesson develops understanding of probability notation and the main formulae, including the complement rule, addition laws for mutually exclusive and non-mutually exclusive events, multiplication laws for independent events, and conditional probability. Visual representations such as Venn diagrams and probability trees are used to help students organise information, identify relationships between events, and select appropriate methods. Students then apply these formulae through progressively challenging practice questions and Edexcel-style examination problems, supported by fully worked solutions that model clear reasoning and effective exam technique. By the end of the lesson, students will be able to confidently choose and apply the correct probability formula in a range of statistical contexts and examination scenarios.

Explore Edexcel A-Level probability formulae using real-life contexts, Venn diagrams and trees, with practice, exam questions and worked solutions.

The graph has been translated, stretched, or reflected from the parent function. The asymptote moves according to the transformation, and the graph retains its characteristic exponential or logarithmic shape.

Bridging the gap between GCSE and A-level workbook for the new Curriculum. AS Assessment included as well.