GCSE Mathematics:
      90 maths problem solving questions
      The new Maths GCSE has an increased focus on problem solving.
      So that you can help your students practice this type of question, 
      we’ve refreshed our 90 maths problems resource so that it’s 
      relevant to the new GCSE.
      Visit All About Maths aqa.maths.aqa.org.uk our free maths 
      resource website to access other resources and guidance.
                                   Great support
                                   Great resources
                                +
                                 AQA Maths GCSE
       aqamaths.aqa.org.uk
       
      You can get further copies of this Teacher Resource from: 
      The GCSE Mathematics Department 
      AQA 
      Devas Street 
      Manchester 
      M16 6EX 
       
      Or, you can download a copy from our All About Maths website (http://allaboutmaths.aqa.org.uk/). 
       
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      centres for AQA are permitted to copy material from this specification booklet for their own internal 
      use. 
       
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      (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX. 
       
       
 
                                                                                                                           
                                      
            
          Contents 
 
          1      Introduction                                                      2 
          1a     Origin                                                            2 
          1b     Purpose                                                           2 
          1c     Problem solving in GCSE Mathematics                               3 
          2      Teaching strategies                                               4 
          2a     General strategies for problem solving in mathematics             4 
          2b     The five strategies of the resource                               5 
          2c     Teaching using the resource                                       6 
          2d     Organisation of teaching                                          6 
          2e     The relevance of mathematics learning                             7 
          2f     A progression in student problem solving                          7 
          3      The Problems                                                      8 
          4      The Commentaries                                                99 
          5      Answers                                                        154 
          6      Classification of Problems                                     161 
          7      Classification Table by Strategy                               162 
          8      Classification Table by Content Area                           166 
 
 
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                                                                                                   Introduction 
 
                                                   1a  Origin                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          
                                                   This resource was originally produced by Leeds                                                                                                                                                                                                                           The approach taken to problem solving in the pilot 
                                                   University’s Assessment and Evaluation Unit to                                                                                                                                                                                                                           qualification formed the basis for AQA’s approach 
                                                   support teachers in developing approaches to the                                                                                                                                                                                                                         to the assessment of AO3 in the GCSE 
                                                   type of problem solving questions that appeared                                                                                                                                                                                                                          Mathematics specifications, for which first 
                                                   in the pilot GCSE in Additional Mathematics. This                                                                                                                                                                                                                        teaching began in September 2010 (for exams up 
                                                   pilot was part of the QCDA funded Curriculum                                                                                                                                                                                                                             until June 2016), and the problems in this 
                                                   Pathways Project. We are grateful to QCDA for                                                                                                                                                                                                                            document remain highly relevant in approaching 
                                                   giving their permission to reproduce these                                                                                                                                                                                                                               problem solving in the new AQA GCSE 
                                                   resources to support teachers of GCSE                                                                                                                                                                                                                                    Mathematics specification for first examination in 
                                                   Mathematics.                                                                                                                                                                                                                                                             2017. Hence, we hope that this resource will be 
                                                                                                                                                                                                                                                                                                                            useful to all teachers of mathematics in 
                                                                                                                                                                                                                                                                                                                            developing problem solving strategies for lessons.  
 
                                                   1b  Purpose                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
                                                   This resource is designed to support teaching and                                                                                                                                                                                                                              In the remainder of the introductory pages there                                                                                                                                                                                                                     
                                                   preparation for the problem solving requirement                                                                                                                                                                                                                                are descriptions of: 
                                                   (AO3) of the new AQA GCSE in Mathematics                                                                                                                                                                                                                                                    •                  problem solving in the GCSE Additional 
                                                   (8300) as well as the previous GCSEs in                                                                                                                                                                                                                                                                        Mathematics  
                                                   Mathematics (Linear; 4365 and unitised 4360)                                                                                                                                                                                                                                                •                  general strategies for problem solving in 
                                                   and the Linked-Pair pilot GCSEs in Methods in                                                                                                                                                                                                                                                                  Mathematics 
                                                   Mathematics (9365) and Applications of 
                                                   Mathematics (9370)                                                                                                                                                                                                                                                                          •                  five strategies that are helpful in solving 
                                                                                                                                                                                                                                                                                                                                                                  the kinds of problems that are set in the 
                                                   The resource consists of:                                                                                                                                                                                                                                                                                      examination papers for the GCSE in 
                                                                                                                                                                                                                                                                                                                                                                  Additional Mathematics 
                                                                     •                  these introductory pages                                                                                                                                                                                                                               •                  teaching using the resource 
                                                                     •                  90 examples of problem solving questions                                                                                                                                                                                                               •                  a progression in student problem solving 
                                                                     •                  extended commentaries for 30 of the                                                                                                                                                                                                                    •                  the information given in the resource 
                                                                                        problem solving questions                                                                                                                                                                                                                                                 about all problems 
                                                                     •                  answers to the 90 questions                                                                                                                                                                                                                            •                  the elements of the commentaries on the 
                                                                     •                  summary lists linking questions both to                                                                                                                                                                                                                                   30 questions. 
                                                                                        process skills and to content areas. 
                                                   The problem solving questions can also be found 
                                                   as separate problem sheets within the resources 
                                                   available as part of AQA All About Maths 
                                                   http://allaboutmaths.aqa.org.uk  
 
 
 
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