Solving Quadratic Equations GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Solving Quadratic Equations GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Practise every GCSE method for solving quadratics, from simple square roots to the quadratic formula and completing the square. What’s included • Foundation Tier practice booklet: 30 questions, 86 marks (15 pages) • Higher Tier practice booklet: 30 questions, 122 marks (16 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Solving equations of the form x² = k and x² + c = k • Solving by factorising (a = 1), including x² + bx = 0 • Solving quadratics using a graph Higher Tier covers • Factorising where a > 1 • The quadratic formula, with answers to 2 decimal places • Completing the square, with answers in surd form • Forming and solving quadratics from area problems Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Straight-Line Graphs GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Straight-Line Graphs GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Everything on y = mx + c, from plotting lines to perpendicular bisectors. Graph questions include printed grids for students to draw on. What’s included • Foundation Tier practice booklet: 30 questions, 81 marks (23 pages) • Higher Tier practice booklet: 30 questions, 93 marks (21 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Plotting straight-line graphs from tables of values • Gradient and y-intercept from y = mx + c • Finding the gradient between two points and the midpoint of a line segment • Equation of a line through two points and of a parallel line • Reading values and intersections from a graph Higher Tier covers • Equation of a line through two points • Plotting lines of the form ax + by = c • Perpendicular gradients and equations of perpendicular lines • Length of a line segment • Intersections found algebraically and graphically • Equation of a perpendicular bisector Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Angles & Parallel Lines GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Angles & Parallel Lines GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Angle facts practice with clear diagrams for every question. Students work out missing angles and, at Higher, form and solve equations from angle facts. What’s included • Foundation Tier practice booklet: 30 questions, 64 marks (30 pages) • Higher Tier practice booklet: 30 questions, 110 marks (31 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Angles around a point and on a straight line • Vertically opposite angles • Alternate and co-interior angles in parallel lines • Interior and exterior angles of regular polygons Higher Tier covers • Forming and solving equations from angle facts • Angles in parallel lines with algebraic expressions • Finding the number of sides of a regular polygon from its interior angle • Exterior angles given as algebraic expressions Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Area & Perimeter GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Area & Perimeter GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Area and perimeter of 2D shapes and circles, with a labelled diagram for every question. What’s included • Foundation Tier practice booklet: 30 questions, 80 marks (29 pages) • Higher Tier practice booklet: 30 questions, 104 marks (31 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Area and perimeter of rectangles, triangles and trapezia • Perimeter of compound (L-shaped) figures • Circumference and area of circles • Finding a missing length from a given area Higher Tier covers • Circles with answers to significant figures • Arc length and sector area • Finding the angle of a sector from its area • Finding the radius of a circle from its area • Perimeters of compound shapes Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Bounds & Error Intervals GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Bounds & Error Intervals GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Clear, structured practice on error intervals and bounds, including truncation and bounds in calculations. What’s included • Foundation Tier practice booklet: 30 questions, 55 marks (12 pages) • Higher Tier practice booklet: 30 questions, 85 marks (17 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Error intervals from rounding (to the nearest 10, 1 decimal place or significant figures) • Error intervals from truncation • Smallest and largest possible values • Deciding which values could be the actual measurement Higher Tier covers • Upper and lower bounds • Error intervals using inequality notation • Bounds in calculations with density, speed and subtraction • Bounds in formulae such as v = (p − q) ÷ r Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Congruence & Similarity GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Congruence & Similarity GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Practice on congruent and similar shapes, from identifying congruence conditions to area and volume scale factors and formal congruence proofs. What’s included • Foundation Tier practice booklet: 30 questions, 75 marks (21 pages) • Higher Tier practice booklet: 30 questions, 100 marks (25 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Identifying congruent triangles using SSS, SAS and ASA • Matching corresponding vertices and sides • Finding missing lengths in similar triangles and rectangles • Deciding whether two shapes are similar Higher Tier covers • Similar triangles with algebraic side lengths • Area and volume scale factors • Congruence proofs with parallelograms, rectangles and isosceles triangles (including RHS) Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Constructions, Loci & Bearings GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Constructions, Loci & Bearings GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Bearings, scale drawings and loci practice, with diagrams to support each question. What’s included • Foundation Tier practice booklet: 30 questions, 75 marks (21 pages) • Higher Tier practice booklet: 30 questions, 102 marks (20 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Converting compass directions into three-figure bearings • Back bearings • Angles between two bearings • Map scales and scale drawings Higher Tier covers • Multi-stage journeys on bearings • Back bearings • Describing loci • Loci problems such as an animal tethered by a rope • Scale drawings with bearings • Regions defined by more than one condition Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Pythagoras & Trigonometry GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Pythagoras & Trigonometry GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Right-angled triangle work at Foundation and non-right-angled trigonometry at Higher, with a diagram for every question. What’s included • Foundation Tier practice booklet: 30 questions, 83 marks (28 pages) • Higher Tier practice booklet: 30 questions, 106 marks (31 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Finding the hypotenuse and a shorter side using Pythagoras • Ladder and real-life Pythagoras problems • Using SOHCAHTOA to find missing sides • Angles of elevation Higher Tier covers • Pythagoras’ theorem • The sine rule • The cosine rule • Area of a triangle using ½ab sin C Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Circle Theorems GCSE Maths Higher Booklet + Mark SchemeQuick View
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Circle Theorems GCSE Maths Higher Booklet + Mark Scheme

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A Higher Tier booklet on circle theorems, with a diagram for every question and an emphasis on giving correct reasons. What’s included • Higher Tier practice booklet: 30 questions, 89 marks (31 pages) • Full mark scheme for the booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Topics covered • Angle at the centre is twice the angle at the circumference • Angles in the same segment • Opposite angles in a cyclic quadrilateral • Isosceles triangles formed by radii • Tangent and radius, and two tangents from an external point • Stating geometric reasons for each step Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Transformations & Vectors GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Transformations & Vectors GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Transformations drawn on printed grids, plus column vector practice. What’s included • Foundation Tier practice booklet: 30 questions, 74 marks (28 pages) • Higher Tier practice booklet: 30 questions, 103 marks (29 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Reflections, rotations, translations and enlargements on a grid • Describing transformations • Adding, subtracting and multiplying column vectors Higher Tier covers • Enlargements, including fractional scale factors • Rotations, reflections and translations • Describing a single transformation fully • Position vectors and the vector between two points Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Volume & Surface Area GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Volume & Surface Area GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Volume and surface area of 3D shapes, with a labelled diagram for every question. What’s included • Foundation Tier practice booklet: 30 questions, 90 marks (31 pages) • Higher Tier practice booklet: 30 questions, 123 marks (31 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Volume and surface area of cuboids • Triangular prisms • Volume and surface area of cylinders • Finding a missing dimension from the volume Higher Tier covers • Cuboids, prisms and cylinders to significant figures • Volume and surface area of cones • Volume of spheres • Finding the radius of a sphere from its volume Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Solving Linear Equations GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Solving Linear Equations GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Graded practice in solving equations, building from one-step equations to unknowns on both sides, fractions and brackets. What’s included • Foundation Tier practice booklet: 30 questions, 86 marks (15 pages) • Higher Tier practice booklet: 30 questions, 112 marks (16 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • One-step and two-step equations • Equations with brackets • Unknowns on both sides • Equations involving fractions, e.g. x/4 + 3 = 7 Higher Tier covers • Brackets on both sides • Equations with fractions, e.g. (a − 3)/4 = 5 and y/2 + y/3 = 10 • Equations with algebraic fractions • An extension into solving quadratics by factorising Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Simultaneous Equations GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Simultaneous Equations GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Solve simultaneous equations by graph, elimination and substitution, then apply them to worded problems. Graph questions include printed grids. What’s included • Foundation Tier practice booklet: 30 questions, 113 marks (25 pages) • Higher Tier practice booklet: 30 questions, 130 marks (27 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Substituting values into pairs of expressions • Solving simultaneous equations from a graph, and drawing the graphs from tables • Solving by elimination and by substitution • Worded problems (e.g. the cost of burgers and drinks) Higher Tier covers • Elimination where both equations must be multiplied • Graphical solutions • Solving a linear and a quadratic equation simultaneously • Forming and solving equations from worded problems Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Show That Algebraic Arguments GCSE Maths Foundation Booklet + Mark SchemeQuick View
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Show That Algebraic Arguments GCSE Maths Foundation Booklet + Mark Scheme

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A Foundation Tier booklet that teaches students to lay out “show that” answers properly, showing each step instead of jumping to the answer. What’s included • Foundation Tier practice booklet: 30 questions, 84 marks (16 pages) • Full mark scheme for the booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Topics covered • Showing that expressions simplify to a given result • Expanding single brackets and collecting like terms • Perimeter and area of shapes with algebraic side lengths • Expanding double brackets to reach a given expression • Rewriting expressions in factorised form Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Sequences GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Sequences GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Practise finding and using nth term rules for linear and quadratic sequences, including the classic question of whether a number is a term in the sequence. What’s included • Foundation Tier practice booklet: 30 questions, 80 marks (15 pages) • Higher Tier practice booklet: 30 questions, 118 marks (16 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Finding the next terms of a sequence • Finding and using the nth term of a linear sequence • Deciding whether a number is a term in a sequence, with a reason • Pattern problems with matchsticks, tiles and dots Higher Tier covers • nth term of linear sequences • Finding the nth term of a quadratic sequence • Finding a given term of a quadratic sequence • Deciding whether a number is a term of a quadratic sequence Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Real-Life Graphs GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Real-Life Graphs GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Interpret graphs in context, from conversion graphs and cost graphs to distance-time and velocity-time graphs. Every graph is drawn on a printed grid. What’s included • Foundation Tier practice booklet: 30 questions, 99 marks (31 pages) • Higher Tier practice booklet: 30 questions, 136 marks (31 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Conversion graphs (pounds and euros, Celsius and Fahrenheit) • Cost graphs: completing tables, plotting and interpreting (taxi fares, call-out charges, bike hire, phone plans) • Distance-time graphs for journeys with stops • Two-person distance-time graphs: when and where one overtakes the other Higher Tier covers • Cost and conversion graphs in context • Distance-time graphs and average speed • Speed-time and velocity-time graphs: acceleration and distance travelled • Estimating the area under a curve using strips • Estimating gradients on curved graphs by drawing a tangent Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Quadratic, Cubic & Reciprocal Graphs GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Quadratic, Cubic & Reciprocal Graphs GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Plot, read and interpret non-linear graphs. Every graph question comes with a printed grid, so students can work straight on the page. What’s included • Foundation Tier practice booklet: 30 questions, 105 marks (30 pages) • Higher Tier practice booklet: 30 questions, 99 marks (27 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Completing tables of values and plotting quadratic graphs • Reading roots, turning points and y-intercepts from a graph • Using a graph to estimate solutions of equations • Recognising the shapes of linear, quadratic, cubic and reciprocal graphs Higher Tier covers • Plotting quadratic and reciprocal graphs • Completing the square to find a turning point • Finding roots by factorising • Cubic graphs from factorised form • Solving equations by drawing a suitable straight line • Exponential graphs Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Non-Linear Simultaneous Equations GCSE Maths Higher Booklet + Mark SchemeQuick View
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Non-Linear Simultaneous Equations GCSE Maths Higher Booklet + Mark Scheme

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Higher Tier practice on solving a linear and a non-linear equation together, both algebraically and graphically. What’s included • Higher Tier practice booklet: 30 questions, 134 marks (25 pages) • Full mark scheme for the booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Topics covered • Solving a linear and a quadratic equation by substitution • Graphical solutions using a drawn line and curve • Showing a line is a tangent to a curve and finding the point of contact • Estimating intersections of a line and a circle x² + y² = r² Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Iteration GCSE Maths Higher Booklet + Mark SchemeQuick View
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Iteration GCSE Maths Higher Booklet + Mark Scheme

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A complete Higher Tier booklet on iterative methods, a topic that regularly appears near the end of the calculator paper. What’s included • Higher Tier practice booklet: 30 questions, 106 marks (22 pages) • Full mark scheme for the booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Topics covered • Showing a root lies between two values using a change of sign • Rearranging cubic equations into the form x = ∛(px + q) • Using an iteration formula to find x₁, x₂ and x₃ • Finding a root to a given degree of accuracy Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Inequalities GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Inequalities GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Everything from number-line notation to quadratic inequalities and shaded regions, with plenty of practice at showing solutions clearly. What’s included • Foundation Tier practice booklet: 30 questions, 79 marks (16 pages) • Higher Tier practice booklet: 30 questions, 101 marks (20 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Reading and drawing inequalities on a number line • Listing integer values that satisfy an inequality • Solving one- and two-step linear inequalities • Double inequalities and negative coefficients of x • Forming and solving an inequality from a worded problem Higher Tier covers • Inequalities with brackets, fractions and unknowns on both sides • Double inequalities shown on a number line • Solving quadratic inequalities • Identifying and shading regions that satisfy several inequalities on a grid Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.
Expressions, Substitution & Simplifying GCSE Maths Booklets | Foundation & Higher + Mark SchemesQuick View
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Expressions, Substitution & Simplifying GCSE Maths Booklets | Foundation & Higher + Mark Schemes

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Core algebra skills practised step by step, from substitution and collecting like terms through to factorising quadratics and simplifying algebraic fractions. What’s included • Foundation Tier practice booklet: 30 questions, 70 marks (13 pages) • Higher Tier practice booklet: 30 questions, 102 marks (16 pages) • Full mark scheme for each booklet, giving the answer and worked method for every question Questions are grouped into three difficulty bands (Developing, Secure and Greater Depth), so students move from fluency to exam-style problem solving. Each question shows its mark allocation and has working space underneath. Foundation Tier covers • Substituting into expressions, including negatives and squared terms • Collecting like terms • Expanding single brackets • Factorising into a single bracket • Expanding and simplifying double brackets Higher Tier covers • Expanding double brackets with coefficients, e.g. (3y − 2)(2y + 5) • Expanding three-factor products such as 2(x + 3)(x − 1) • Factorising quadratics where a = 1 and a > 1 • Difference of two squares • Simplifying algebraic fractions Use it for revision, homework, intervention groups, cover lessons or independent practice. Suitable for AQA, Edexcel and OCR GCSE (9–1) Maths. Print-ready PDFs.