These ‘Grade 9’ practice papers are designed to practice the highest end of the GCSE specification and stretch the most able students. These would be excellent practice for A Level students too and any mathematicians looking for some fun with algebra, geometry and problem solving. There are 3 papers - One non-calculator and 2 calculator papers and I have endeavored to include all elements of the specification within the 3 papers. Included in downloads are the full paper, a concise version to save on printing and full solutions. Paper 1 is a non-calculator paper and so numerical skills and arithmetic will be tested. The topics covered in Practice Paper 1 are: Factorising/solving quadratics Expanding 3 brackets Rules of indices - solving equations Solving linear simultanous equations Ratio Completing the square - solving equations and max/min points Surds -rationalising the denominator Coordinate geometry - straight lines, gradient, distance. Compound interest Sectors/Arc Lengths Surface area of a prism Area of a triangle - exact trigonometric values Quadratic sequences Probability - Tree diagrams Graph sketching - reciprocal and cubic equations Vectors Functions - inverse functions The topics covered in Practice Paper 2 are: Recurring decimals and fractions Quadratic inequalities Ratio - Areas of circles, squares and Pythagoras Cumulative frequency and estimation of mean Bounds Rules of indices and quadratic equations Proof of circle theorems Histograms Trigonometry - right-angle Algebraic fractions Trig graphs and transformations Bearings Trigonometry - cosine rule Proportion Construction of angles Probability - Venn diagrams and conditional probability Iterative sequences Quadratic simultaneous equations Tangent to a circle The topics covered in Practice Paper 3 are: Laws of indices Siolving quadratic equations - factoring in 3 ways Mean, Median, Mode and Range Forming and solving linear simultaneous equations Speed/distance/time - problem solving Rates Problem solving - solving quadratic equations Speed/time graphs Standard form - Estimation Composite Functions Surface Area and Ratio - Spheres and Cones Pythagoras - 3D Problem Solving - solving equations Regions, straight lines and inequalities Coordinate geometry of straight lines - area and intersections Angles in a polygon - problem solving Conditional probability Set notation These papers are brand new, hot off the press, with all questions written by myself (it was a big task!) so all feedback is extremely valuable and much appreciated so please review if you can :)