Worksheet Library
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1. Numbers & Number System
Examiner's Note: Mastering fundamentals like Prime Factorization and Upper/Lower Bounds is essential for students aiming for a Level 9 in 2026. These topics form the bedrock for advanced Algebra.
| Topic | Key Concepts | Difficulty | Action |
|---|---|---|---|
| 1.1 Integers | BIDMAS, directed numbers | - | Download PDF (+ Answers) |
| 1.2 Factors and Multiples | Prime factorization, HCF, LCM | - | Download PDF (+ Answers) |
| 1.3 Fractions | Equivalency, ordering, mixed numbers | - | Download PDF (+ Answers) |
| 1.4 Decimals | Recurring decimals to fractions | Higher Tier (H) | Download PDF (+ Answers) |
| 1.5 Powers and Roots | Indices laws, negative/fractional | Higher Tier (H) | Download PDF (+ Answers) |
| 1.6 Set Language | Venn Diagrams, Notation ∩ ∪ | - | Download PDF (+ Answers) |
| 1.7 Percentages | Compound interest, Reverse percentages | - | Download PDF (+ Answers) |
| 1.8 Ratio and Proportion | Direct/Inverse proportion | Higher Tier (H) | Download PDF (+ Answers) |
| 1.9 Degree of Accuracy | Upper/lower bounds | Higher Tier (H) | Download PDF (+ Answers) |
| 1.10 Standard Form | Scientific Notation | - | Download PDF (+ Answers) |
| 1.11 Surds | Rationalizing denominator | Higher Tier (H) | Download PDF (+ Answers) |
2. Equations, Formulae, Identities
Examiner's Note: Fluency in Algebraic Proof and Completing the Square distinguishes top-tier students. Examiners frequently test these in the final 20% of the paper.
| Topic | Key Concepts | Difficulty | Action |
|---|---|---|---|
| 2.1 Algebraic Manipulation | Expanding, Factorizing quadratics | Higher Tier (H) | Download PDF (+ Answers) |
| 2.2 Algebraic Fractions | Simplifying, Solving | Higher Tier (H) | Download PDF (+ Answers) |
| 2.3 Formulae | Changing the subject, complex cases | Higher Tier (H) | Download PDF (+ Answers) |
| 2.4 Linear Equations | Solving unknowns | - | Download PDF (+ Answers) |
| 2.5 Simultaneous Equations | Linear/Quadratic solving | Higher Tier (H) | Download PDF (+ Answers) |
| 2.6 Quadratic Equations | Formula, Completing the square | Higher Tier (H) | Download PDF (+ Answers) |
| 2.7 Inequalities | Quadratic inequalities, Graphical | Higher Tier (H) | Download PDF (+ Answers) |
| 2.8 Algebraic Proof | Formal proof logic | Higher Tier (H) | Download PDF (+ Answers) |
Stuck on Harder Factorization?
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3. Sequences, Functions, Graphs
Examiner's Note: Understanding Function Notation (fg(x)) and Calculus Gradients is mandatory for 2026 higher papers. Graph transformations often catch students out.
| Topic | Key Concepts | Difficulty | Action |
|---|---|---|---|
| 3.1 Sequences | nth term quadratic | Higher Tier (H) | Download PDF (+ Answers) |
| 3.2 Functions | Composite fg(x), Inverse f⁻¹(x) | Higher Tier (H) | Download PDF (+ Answers) |
| 3.3 Linear Graphs | y=mx+c, Perpendicular lines | Higher Tier (H) | Download PDF (+ Answers) |
| 3.4 Graphs of Functions | Cubic, Reciprocal, Exponential, Trig | Higher Tier (H) | Download PDF (+ Answers) |
| 3.5 Solving Equations Graphically | Intersections | - | Download PDF (+ Answers) |
| 3.6 Real-Life Graphs | Velocity-time, Acceleration | - | Download PDF (+ Answers) |
| 3.7 Calculus | Differentiation, Gradients, Kinematics | Higher Tier (H) | Download PDF (+ Answers) |
| 3.8 Transformations of Graphs | y=f(x)+a, etc. | Higher Tier (H) | Download PDF (+ Answers) |
4. Geometry & Trigonometry
Examiner's Note: Questions on Circle Theorems and 3D Mensuration carry heavy marks. Ensure you can apply the Sine/Cosine rules in non-right-angled contexts.
| Topic | Key Concepts | Difficulty | Action |
|---|---|---|---|
| 4.1 Angles and Lines | Parallel lines, Polygons | - | Download PDF (+ Answers) |
| 4.2 Polygons | Interior/Exterior angles | - | Download PDF (+ Answers) |
| 4.3 Mensuration 2D | Circles, Sectors | - | Download PDF (+ Answers) |
| 4.4 Mensuration 3D | Pyramids, Spheres, Cones | - | Download PDF (+ Answers) |
| 4.5 Similarity and Congruence | Area/Volume scale factors | Higher Tier (H) | Download PDF (+ Answers) |
| 4.6 Pythagoras and Basic Trig | SOH CAH TOA | - | Download PDF (+ Answers) |
| 4.7 Advanced Trig | Sine/Cosine Rule, Area of Triangle | Higher Tier (H) | Download PDF (+ Answers) |
| 4.8 3D Geometry | 3D Trigonometry | Higher Tier (H) | Download PDF (+ Answers) |
| 4.9 Circle Theorems | Tangents, Chords, Cyclic Quads | Higher Tier (H) | Download PDF (+ Answers) |
5. Vectors & Transformation
Examiner's Note: Vector Geometry proofs are notoriously difficult. You must be able to prove collinearity using vector paths to succeed in this section.
| Topic | Key Concepts | Difficulty | Action |
|---|---|---|---|
| 5.1 Transformations | Reflection, Rotation, Translation, Enlargement | - | Download PDF (+ Answers) |
| 5.2 Vectors | Arithmetic, Magnitude | - | Download PDF (+ Answers) |
| 5.3 Vector Geometry | Proofs, Collinearity | Higher Tier (H) | Download PDF (+ Answers) |
Stuck on Vector Proofs?
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6. Statistics & Probability
Examiner's Note: Precision is key in Conditional Probability and Histograms. Ensure you understand Frequency Density versus Frequency for data representation.
| Topic | Key Concepts | Difficulty | Action |
|---|---|---|---|
| 6.1 Data Representation | Histograms, Cumulative Frequency | - | Download PDF (+ Answers) |
| 6.2 Statistical Measures | Mean, Median, Mode | - | Download PDF (+ Answers) |
| 6.3 Advanced Analysis | Box plots, IQR | Higher Tier (H) | Download PDF (+ Answers) |
| 6.4 Probability | Tree Diagrams, Sample Space | - | Download PDF (+ Answers) |
| 6.5 Combined Events | Conditional Probability | Higher Tier (H) | Download PDF (+ Answers) |