Favourite Exam Questions and Topics

Below you will find 27 Favourite Topics that seem to appear regularly.

In each table you can see exactly which Year, what Paper and what Question number where that topic appeared. So, for example, you can follow through the Question links to every question on Pythagoras asked since 1999.

NOTE: this page has been optimised to display in Firefox or Internet Explorer 7. If it does not display properly on your computer click here to open a PDF version of the page.

Questions involving Pythagoras

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 7 none Question 19 none

2005

Question 4 none Question 19 none

2004

Questions 9 & 18 none Question 20 none

2003

Question 1 none Question 12 none

2002

Question 7 none Question 18 none

2001

Question 5 none Question 16 none

2000

none none none none

1999

Question 5 none none none


Comment: As you can see Pythagoras is a real favourite in the calculator papers - there has been at least one questionon this topic every year since 2001.

Questions involving Dimensions of Expressions

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none none none none

2005

none Question 8 none Question 20

2004

none Question 2 none Question 15

2003

none Question 8 none Question 21

2002

none Question 9 none Question 17

2001

none Question 10 none Question 24

2000

none Question 12 none Question 26

1999

none Question 8 none Question 15


Comment: Another favourite, this time of the non-calculator papers. As you can see there has been one question on this topic almost every year since 1999.

Questions involving Trial & Improvement

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none none none none

2005

Question 3 none Question 17 none

2004

Question 4 none Question 15 none

2003

Question 4 none Question 15 none

2002

Question 6 none Question 13 none

2001

Question 6 none Question 17 none

2000

Question 2 none Question 14 none

1999

none Question 3 none Question 11


Comment: As you can see this has been asked almost every year since 1999 so it is well worth revising thoroughly.

Questions involving Vectors

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 13 Question 17 none none

2005

none Question 22 none none

2004

none Question 17 none none

2003

none Question 23 none none

2002

none Question 16 none none

2001

none Question 16 none none

2000

none Question 20 none none

1999

none Question 13 none none


Comment: Another topic which has been asked every year since 1999 in the Higher non-calculator papers - a MUST for revision!

Questions involving Transformations

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 10 Question 24 Question 22 Question 10

2005

Question 20 Questions 3 & 20 none Questions 1 & 14

2004

none Questions 12 & 20 none Question 10

2003

Question 20 Questions 6 , 21 & 24 none Questions 7 & 19

2002

none Questions 7 & 17 none Questions 1, 7 & 20

2001

Question 20 Question 15 Question 11 none

2000

none Question 6 none Question 22

1999

none Question 12 none Question 2

Comment: Another extremely popular question. But dont forget Transformations can mean transformations of graphs,enlargements, reflections, rotations, stretches etc. As you can see there has been a question on this topic every year since 1999. In the Higher tier in 2003 there were 4 Questions involving transformations in some form oranother! Another MUST for revision.

Questions involving Algebra

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Questions 6, & 20 Questions 10, 18, 22 & 23 Questions 2, 4, 18 & 27 Questions 8, 12 & 22

2005

Questions 1, 6, 12 & 18 Questions 1, 4 & 21 Questions 4, 9 & 21 Questions 3, 6, 11 & 15

2004

Question 21 Questions 7 & 19 Question 14 Questions 2, 11, 13 & 22

2003

Questions 15 & 18 Questions 11 & 20 Questions 5 & 6 Questions 1, 8, 11 & 27

2002

Question 20 Questions 6 & 12 Question 12 Questions 6 & 11

2001

Question 11 Questions 8, 14 & 20 Questions 5 & 22 Questions 5 & 22

2000

Questions 5 ,12 & 17 Question 5 Questions 3 & 20 Questions 3 & 24

1999

Questions 4 , 8 & 14 Question 5 Questions 13 & 17 Question 5

Comment:As you can see Algebra is examined every year without fail. This is essential revision.

Questions involving Trigonometry

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Questions 12 & 23 none Question 23 none

2005

Questions 10 & 19 none Question 25 none

2004

Questions 9 & 18 none Question 20 none

2003

Questions 10 & 14 none Question 21 none

2002

Question 12 none Question 22 none

2001

Question 10 none none none

2000

Question 9 none Question 22 none

1999

Question 5 none Question 16 none

Comment: In the Higher calculator Paper 6, Trigonometry has come up every year since 1999. These are the sameharder questions that you find near the end of Intermediate Paper 4.

Questions involving Standard Form

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none Question 9 none Question 21

2005

Question 9 none Question 24 none

2004

Question 5 none Question 16 none

2003

Question 9 Question 10 Question 20 Question 23

2002

Question 11 none Question 21 none

2001

Question 8 Question 6 Question 19 Question 21

2000

none Question 2 none Question 21

1999

none none none Question 17

Comment:This is a favourite of both papers and has come up every year since 1999.

Questions involving a Circle Problem

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none Question 15 none Question 27

2005

none Question 14 none Question 26

2004

Question 17 Question 16 none Question 25

2003

none Question 12 none Question 25

2002

none Question 13 none none

2001

none Question 17 none none

2000

none Question 17 none none

1999

Question 15 none none Question 9

Comment: Another favourite. In the Higher papers it has been examined at least once every year since 1999.

Questions involving Histograms

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none Question 19 none none

2005

none none none none

2004

none Question 14 none none

2003

none Question 19 none none

2002

Question 17 none none none

2001

none Question 12 none none

2000

Question 11 none none none

1999

none Question 16 none none

Comment: A favourite only of the Higher Papers - with the exception of 2005, there has beenone Histogram question every year since 1990.

Questions involving Probability

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 18 Question 5 Question 24 Question 15

2005

Question 16 Questions 9 & 13 Question 10 Questions 2, 21 & 23

2004

Question 14 Question 3 Question 23 Question 16

2003

Questions 11 & 19 Question 22 Question 22 none

2002

Questions 9 & 20 Question 8 Question 19 Question 10

2001

Question 21 Question 11 Question 1 Questions 4, 7& 25

2000

Question 7 Questions 7 & 13 Question 18 Questions 17 & 25

1999

Question 7 Question 6 Questions 7 & 18 Questions 6 & 13

Comment: An extremely popular topic with at least one question in both calculator and non-calculator papers. A real MUST for revision.

Questions involving Percentages

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 5 Question 13 Questions 5 & 17 Questions 3 & 23

2005

Questions 2, 7 & 14 none Questions 14, 18 & 22 Question 5

2004

Question 12 none Question 24 Question 5

2003

none Question 2 none Question 15

2002

none none Questions 7 & 16 Question 8

2001

Questions 3 & 4 none Questions 8 & 14 Questions 2 & 14

2000

Question 8 none Questions 7 & 19 Question 11

1999

Question 3 Question 9 Questions 3 & 5 Questions 1, 4 & 17

Comment: As you can see Percentagequestions are everywhere in the Intermediate papers. They are also quite popular in the Higher papers too. Essential revision.

Questions involving Simultaneous Equations

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 11 none Question 27 none

2005

Question 8 none Question 23 none

2004

Question10 none Question 21 none

2003

Question 7 none Question 18 none

2002

Question 8 none Question 17 none

2001

Question 9 none Question 20 none

2000

none none none none

1999

none Question 7 none Question 14

Comment: Every year since 2001 there has been a question on Simultaneous Equations - so they are another favourite.

Questions involving Area and/or Perimeter

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 22 none Questions 2 & 10 Questions 4 & 8

2005

Questions 4 & 13 Question 7 Questions 9, 12 & 19 Questions 5 & 19

2004

Question 16 Question 9 none Questions 1 & 21

2003

Questions 5, 13 & 14 none Questions 8, 9 & 16 none

2002

Question 5 none Questions 6 & 15 Question 9

2001

Questions 1 & 15 none Questions 9 & 12 Question 11

2000

none none Questions 1 & 5 none

1999

Question 2 & 9 Question 11 Questions 9 & 13 Question 16

Comment: A very popular topic as you can see. In 2003 there were even three questions concerning Area and/or Perimeter. The questions can mix in a bit of Algebra, Trigonometry, or Circle properties, especially in the Higher Papers.

Questions involving Solving Equations

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 21 Questions 1 & 10 Question 13 Questions 12, 13 & 22

2005

Questions 12 & 15 Question 4 Question 9 Question 16

2004

Question 19 none Question 13 none

2003

none Question 3 none Question 16

2002

Question 3 none none none

2001

Questions 2 & 11 Question 19 Question 13 none

2000

none none none Question 13

1999

none Question 2 none Question 8

Comment: In some form or another being able to Solve an Equation is at the very heart of mathematics - and the examiners are very keen to test you on this. As you can see, since 2001 there has been a question on the Higher Paper each year. You have to know how to solve equations.

Questions involving Volume

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none Question 3 none Question 14

2005

none none none none

2004

Question 8 Question 6 Question 19 Question 19

2003

Questions 1 & 12 none Question 12 none

2002

Question 22 none none none

2001

none Question 9 none Questions 8

2000

Questions 4 & 10 none Question 17 & 21 none

1999

Question 9 Question 15 none none

Comment: Another very popular topic because it can test so much. For example, can you find the volumes of a cube? a cuboid? a prism? a pyramid? a sphere? a hemisphere? a cone? a cone with a hemisphere stuck to the base? And do you know how to recognise the dimensions of a volume?

Questions involving Straight Line Equations

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 17 Question 12 none Question 26

2005

none Question 12 none Question 25

2004

none Question 10 Question 3 Question 24

2003

Question 6 none Question 17 none

2002

Question 10 none Question 20 none

2001

Question 19 none none none

2000

none none none none

1999

none none Question 8 none

Comment:In the Higher papers there has been one question on this topic every year since 2001. Its a very important topic because of the overlap with science. Many experiments in science produce straight line graphs and scientists need to understand how to find the equations from the lines. So it is regularly tested.

Questions involving Cumulative Frequency

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 16 Question 14 Question 28 Question 25

2005

Question 5 none Question 20 none

2004

none Question 13 none Question 23

2003

none none none none

2002

none Question 10 none Question 18

2001

none none Question 18 none

2000

none Question 14 none Question 29

1999

none Question 10 none Question 18

Comment: As you can see, in the Higher Papers Cumulative Frequencyhas come up 6 times in eight years, whereas in the Intermediate Papers it has come 7 times in the past eight years. Its quite a favourite because it can test how strong your understanding of statistics really is.

Questions involving Finding the nth Term Formula

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none none Question 6 none

2005

none none none none

2004

Question 7 none Question 18 none

2003

none Question 5 Question 7 Question 2

2002

none none none Question 2

2001

none Question 13 none none

2000

none Questions 8 & 15 Question 6 Questions 1 & 15

1999

Question 16 none none none

Comment: Intermediate paper - 8 Questionsin 7 years. Higher Paper - 6 Questionsin 6 years. A must for revision.

Questions involving Fractions & Ratio

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Questions 2 & 14 none Questions 5 & 20 Questions 3, 5 & 7

2005

none Question 5 none Question 18

2004

none none Questions 7 & 10 Question 6

2003

none none Question 4 Questions 3, 5 & 9

2002

none none none none

2001

none none Question 8 Question 12

2000

none none Question 15 Questions 2 & 12

1999

none Question 1 Questions 3 & 11 Questions 4 & 10

Comment: A real favourite of the Intermediate Papers as you can see, with 22 Questions in the past 8 years. A good understanding of Fractions & Ratio is assumed at the Higher level.

Questions involving Scatter Graphs

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none none Question 11 none

2005

none none none Question 8

2004

none none Question 9 none

2003

none none none none

2002

none none Question 11 none

2001

none Question 1 none Question 15

2000

Question 3 none Question 11 Question 6

1999

Question 1 none Question 12 none

Comment: More popular in the Intermediate papers with 8 questions in the past 8 years.

Questions involving Quadratics

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 21 Questions 1 & 2 none Questions 13, 16 & 22

2005

Question 15 none none none

2004

Question 17 none none none

2003

Questions 18 & 13 none none none

2002

Question 13 none none none

2001

Question 11 none none none

2000

none none none none

1999

Question 14 none none none

Comment: This is an absolute must for Higher candidates. Being able to recognise and, more especially, to solve a Quadraticequation is a fundamental skill at GCSE.

Questions involving Similar Shapes

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none Question 11 none Question 24

2005

Question 11 Question 18 Question 26 none

2004

Question 11 none Question 22 none

2003

Question 8 none Question 19 none

2002

none none none none

2001

Question 12 none Question 23 none

2000

none Question 10 none Question 28

1999

none Questions 11 & 15 none Question 16

Comment: A popular question on both Higher & Intermediate papers, with almost one question each year.

Questions involving Prime Numbers & Factors

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 4 Question 1 Question 16 Question 13

2005

none Question 11 none Question 24

2004

none Question 4 none Question 17

2003

Question 2 none Question 13 none

2002

none none none none

2001

none none none none

2000

none none none none

1999

Question 16 none none none

Comment: Often these Questions are connected to finding the HCF and the LCM , and for the last four years there has been something concerning Prime Numbers

Questions involving Tessellations

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none none none none

2005

none none none none

2004

none none Question 6 none

2003

none none none none

2002

none none none Question 7

2001

none none none Question 3

2000

none none none Question 5

1999

none none none none

Comment: Often a favourite in the Intermediate papers.

Questions involving Cosine & Sine Rules

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

none none none none

2005

Question 19 none none none

2004

Question 16 none none none

2003

none none none none

2002

Question 18 none none none

2001

Question 14 none none none

2000

Question 16 none none none

1999

Question 13 none none none

Comment: These are asked only in the Higher calculator papers, but apart from 2003 and 2006 they have appeared every year since.

Questions involving Upper & Lower Bounds

 

HIGHER

INTERMEDIATE

Year

Paper 6 (calculator)

Paper 5 (non-calculator)

Paper 4 (calculator)

Paper 3 (non-calculator)

2006

Question 19 none none Question 17

2005

Question 17 none none none

2004

Question 20 none none none

2003

Question 16 none none none

2002

Question19 none none none

2001

Question 17 none none none

2000

none Question 3 none Question 19

1999

none none Question 19 none

Comment: Another regular topic - it has appeared in the Higher papers every year since 2000.