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 :)
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