In this blog, Emma discusses the skills needed to successfully approach the Radley 13+ Maths Scholarship papers.
I have a large bank of past 13+ ISEB Common Entrance and 13+ ISEB Scholarship papers. I have also collected a large number of sample 13+ and 13+ Scholarship papers from independent schools around the Country. I was astounded by the depth of algebraic knowledge that is expected of a twelve/thirteen year old in the 13+ Radley Scholarship examinations. The questions are fantastic examples of what would be expected in the new and rigorous GCSE Mathematics syllabus at the highest grades and would challenge even a competent Higher tier student.
There seems to be a common format in their Paper 1 and Paper 2 Scholarship papers. Paper 1 starts off by testing numerical skills in the first two questions. Students need to be confident in multiplying and dividing numbers together with up to three decimal places. There is then a section on fractions, which is reasonably straightforward if students have good skills and are well practised. They need to be confident in all four operations with fractions, including mixed numbers, and should be prepared to apply BODMAS skills whilst working through their calculations. The remaining questions test algebraic skills.
Paper 1 is very much about testing specific skills, whereas Paper 2 is much more about problem solving. The Radley website is extremely helpful and provides copies of their past papers going back as far as 2006. These are a fantastic revision tool and will help you identify exactly what you need to know, particularly on Paper 1.
Before starting their preparation for the Radley 13+ Scholarship examinations, students need to ensure they are fully confident in the following topic areas within algebra: collecting like terms, expanding and simplifying single brackets involving negatives, fractions and indices, factorising expressions into a single bracket involving negatives, forming and solving equations to include negatives, fractions and letters on both sides, solving simultaneous linear equations, substitution of values into expressions to include negatives, changing the subject of a formula, plotting and drawing linear graphs, nth terms of linear sequences.
Students will need to be able to solve a range of equations involving algebraic fractions, be able to carry out all four operations with algebraic fractions, and solve complex simultaneous equations, which can include square roots and fractional values of x and y. They need to be able to expand and simplify two brackets (quadratic expansion) and maybe even three brackets on occasion. They also need to be able to factorise quadratic expressions, including the difference of two squares and where the coefficient of x-squared is not one. There will be questions where they need to solve quadratic equations by factorising first. They should be able to change the subject of a formula where the subject appears twice. They need to be prepared to draw the graphs of quadratic functions and identify their features. Students also need to be able to generate terms of quadratic sequences and know how to generate terms of Fibonacci/iterative sequences.
To solve many of the geometry based questions, a good working knowledge of Pythagoras will be key. Be prepared to leave answers in square root form. To access these types of question students will need to be able to calculate confidently the area and surface area of all common 2D shapes – the formulas will not be given to them. Many questions involve circles and quarter circles inside squares and rectangles. They can be complex and challenging even for very capable Higher tier GCSE students.
Students need to know how to apply percentage increases and decreases using a multiplier. Given two amounts, they need to be able to work out the percentage increase/decrease/profit/loss. They should also be able to calculate reverse percentages where you work backwards to find the original amount. There are lots of good questions to test out their knowledge in the past papers.
Have a range of resources to help your son prepare for these challenging Scholarship examinations. One or two different GCSE Higher tier textbooks will be essential to provide examples and practice questions to work through. The MathsWatch revision CD is a fantastic resource which GCSE students up and down the country use to help prepare for their examinations. It contains hundreds of clips covering every topic which last between three and eight minutes each. A teacher introduces the topics via a video clip, providing examples, practice questions and exam type questions for students to work through together. Students pause the CD whilst working through the questions and then press play to go over the method and answers. It would provide a really useful support to your other work, and I feel provides better explanations than a textbook alone. The MathsWatch CD costs just £4.00 and is only available to buy through Schools and Colleges. The GCSE Bitesize website will also be able to provide useful revision and practice questions.
Preparing for these examinations is not for the feint-hearted! I cannot emphasise how challenging these scholarship papers are. Even a typical GCSE student would find a number of questions difficult to complete. They have been designed for a reason, for Radley to attract the top students in the country. If you are a confident mathematician who absolutely loves a challenge and enjoys the thrill of mastering complex skills typically suited to a 15 or 16 year old, then these Scholarship examinations are right for you. Go for it and enjoy them.
If you are finding it difficult to help your son prepare for these scholarship examinations, arrange for a tutor to help support them with their preparation. They will be able to assess their current knowledge and come up with a plan to work on any weak areas that they may have.