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The set includes profit and proportion problems, equation solving, backward reasoning and number puzzles, reasoning-required questions with clear explanation steps, geometry involving parallel lines, midpoints and angles, and algebra with variables and ratio relationships. 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Your place will be determined by the grade you achieve at GCSE.  \nYour whole paper will be considered for signs of mathematical reasoning. You are better off completing half the test well than the whole test badly.  \nYou will not be given a score, you will be placed into one of three categories:  \n1) You are an excellent fit for the Maths School  \n2) You are a good fit for the Maths School, focus on getting a grade 8 or above in your GCSE and read around the subject  \n3) We have some concerns as to whether you would cope at a Maths School – work hard to secure a grade 8 or above, and try to develop your fluency  \nSome questions will be straightforward tests of the mathematics you know. These questions will probably be like the ones you do at school. They may well test your mental arithmetic/basic operation skills such as long multiplication/division  \n1. Sami buys 25 mugs for £0 .84 each. He gives away 4 of them and sells the rest at £1 .40 each.  \nWhat percentage profit does he make?  \n2. A Finest cream dessert is sold in tubs of 450ml which contain 125ml of cream. A Superb cream dessert is sold in tubs of 375ml which contain 105ml of cream.  \nWhich cream dessert contains the greater proportion of cream?  \n3. Solve the equations:  \na) ~~ ~~16~~ ~~ 􀕠 − ~~ ~~14~~ ~~(􀕠 − 5) = 1  \nb) ~~ ~~􀕠1~~ ~~ = ~~ ~~􀕠􀕠12~~ ~~  \nSome questions might expect you to work backwards through a problem. For example, you could probably work out the area of this trapezium easily enough  \nbut question 4 asks you to work backwards through a similar problem  \n4. The area of this trapezium is 117cm2. What is the length x cm of its base?  \nSome questions might be puzzles, which just expect you to be prepared to play intelligently with numbers:  \n5. The five-digit numbers 91723 and 85604 use all ten digits between them. The difference between these numbers is 91723 – 85604 = 6119.  \nFind two five-digit numbers which use all ten digits between them and which have the smallest possible difference.  \n6. Find three different whole numbers A, B and C, so that  \n● B is the average of A and C  \n● A2 is the average of B2 and C2  \nNote that not all of the numbers can be positive  \nSome questions might expect you to explain your reasoning, as well as just give an answer.  \n7. A boy counts on his fingers, backward and forwards across his right hand as follows: thumb, 1st finger, 2nd finger, 3rd finger, little finger, 3rd finger, 2nd finger, 1st finger, thumb, 1st finger, and so on.  \nIf he starts counting at one on his thumb, which finger will he be on when he reaches two thousand and thirteen? Explain clearly how you decided.  \nGeometry questions will definitely need you to explain how you came up with your solution – keep the explanations short, stating the angle fact you are using.  \n8. In the diagram, line CD is parallel to line AB, and M is the midpoint of line XZ.  \nAngle DXM = 50° and angle MZA = 25°  \nFind angles i) MAZ  \nii) CXA  \nshowing and explaining each step in your working.  \nYou may need to add additional lines to a diagram you are given.  \n9. The diagram shows an irregular pentagon. The lengths of four of the sides are shown in the diagram. Three of the angles in the pentagon are right angles, as shown.  \nFind the length of the side marked s.  \nSome questions will ask you to use the algebra that you have learnt. Question 10 is probably familiar to you from questions you have done at school, question 11 is harder and involves ratios. Question 12 requires you to call something ‘x’ without explicitly telling you to do so.  \n10. Five bananas and two kiwi fruit cost £2 .30, and four bananas and three kiwi fruit cost £2 .47.  \nHow much would it cost to buy two bananas and one kiwi fruit?  \n11. In September, there were three times as many boys as girls in a class.  \nIn October, two new girls joined the class and one of the boys was expelled. Now there were only twice as many boys as girls in the c","cbCaikggUN0t4eqK","https://ap.wps.com/l/cbCaikggUN0t4eqK","pdf",114342,"English","# Instructions and placement criteria\n## Mathematics reasoning and working through problems\n# Sample questions (1-13)\n## Profit, proportion and equations\n## Number puzzles and averages\n## Reasoning explanations and geometry\n## Algebra, ratios, variables and defined operations","[{\"question\":\"Are these sample aptitude test questions a pass/fail exam?\",\"answer\":\"No. The document states it is not a pass/fail test; placement is determined by the grade achieved at GCSE.\"},{\"question\":\"How are applicants placed into the Maths School categories?\",\"answer\":\"They are placed into one of three categories based on the signs of mathematical reasoning shown and the grade achieved at GCSE.\"},{\"question\":\"What kinds of problem types are included in the sample questions?\",\"answer\":\"The samples include straightforward mathematics, mental arithmetic and basic operations, backwards reasoning, number puzzles, questions requiring explained reasoning, geometry with angles and parallel lines, and longer multi-step or algorithm-style questions.\"}]","Aptitude Test Sample Questions - Practice | PDF"]