UKMT Maths Challenge Practice Questions

UKMT Maths Challenge Practice Questions

The UKMT (United Kingdom Mathematics Trust) is a leading organization in the UK that promotes and supports mathematical education. It organizes various mathematical competitions, including the Junior Mathematical Challenge (JMC), the Intermediate Mathematical Olympiad (IMO), and the British Mathematical Olympiad (BMO).

At IITian Academy you will have practice Questions and ukmt past questions by topics.

UKMT Maths Challenge Overview

UKMT Maths Challenge Practice Questions

Junior Competitions (Year 8 or Below)

Intermediate Competitions(Year 11 or Below)

  • UKMT Intermediate Maths Challenge
  • UMKT Senior Maths Challenge

UKMT Mathematical Challenges

The United Kingdom Mathematics Trust (UKMT) was founded in 1996 and stands as a registered charity, whose charitable aim is to advance the education of young people in mathematics by offering a wide range of national-level competitions and activities for students from 11 to 18 years old in the UK.

UKMT encourages mathematical reasoning, precision of thought, and fuency in using basic mathematical techniques to solve interesting problems.

Among many mathematical challenges organized by UKMT, their biggest competitions are the Junior, Intermediate and Senior Mathematical Challenge(JMC/IMC/SMC), which have over 700,000 entries from 6,000 schools each year, and are the UK’s most popular school Mathematical Challenges.

To recognize the highest performers in the Challenge, UKMT Mathematical Challenges award the top-scoring 50%-66% (JMC/IMC with 50%, SMC with 66%) of participants Bronze, Silver and Gold certifcates in the ratio 3:2:1.

  • The UK’s most popular school Mathematical Challenges
  • Over 700,000 participants all over the world annually
  • Three levels suitable for different age groups
  • Up to  50%-66% award ratio

UKMT Mathematical Challenges- JMC (junior Mathematical Challenge)

First-round Challenges

First round Challenges consist of the Junior, Intermediate and Senior Mathematical Challenges.

Junior Mathematical Challenge

  • Time limit
    • 60 minutes
  • Age group
    • England, Wales and Overseas: Year 8 and below
    • Scotland: S2 or below
    • Northern Ireland: Year 9 or below
  • Competition Date
    • Thursday 1st May 2025
  • Scoring

Scoring rules for the Junior Mathematical Challenge are as follows:

      • 5 marks are awarded for each correct answer to questions 1 – 15
      • 6 marks are awarded for each correct answer to questions 16 – 25
      • In the Junior Mathematical Challenge you will NOT lose marks for getting questions wrong Answers left blank will be marked as 0

Follow-on Round –Junior Kangaroo

The Junior Kangaroo is an invitation-only competition open exclusively to UK schools. Students qualify based on their performance in the Junior Maths Challenge (JMC), with several thousand students making the cut annually

Time limit

  • 60 minutes

Age group

  • England and Wales: Year 8 and below
  • Scotland: S2 or below
  • Northern Ireland: Year 9 or below

Scoring

Scoring rules for the Junior Kangaroo are as follows:

  • 5 marks are awarded for each correct answer to questions 1 – 15
  • 6 marks are awarded for each correct answer to questions 16 – 25
  • In the Junior Kangaroo you will NOT lose marks for getting questions wrong Answers left blank will be marked as 0

Awards and Thresholds

The top-scoring 25% of participants each receive a Certificate of Merit. Each participant below this thresholds receives a Certificate of Qualification or Participation depending on their entry route.

YearJunior Kangaroo Certification Thresholds’
2024103
202390
202297
202197
2020N/A

Follow-on Round-Junior Mathematical Olympiad

Entry to the Junior Olympiad is by invitation based on a qualifying JMC score, or by discretionary entry. Around 1,200 students qualify from the JMC each year.

  • Time limit
    • 2 hours
  • Age group
    • England, Wales and Overseas: Year 8 and below
    • Scotland: S2 or below
    • Northern Ireland: Year 9 or below
  • Competition Date
    • Tuesday 10th June 2025
  • Scoring

Scoring rules for the Junior Mathematical Olympiad are as follows:

    • Each question in Section A is worth 1 point
    • Each question in Section B is worth up to 10 points
    • Answers in Section B can be awarded partial marks depending on on the clarity of the participants Mathematical presentation.
YearJunior Mathematical Olympiad Qualification
MeritDistinctionBronze MedalSilver MedalGold Medal
2024 20 38 38 43 50
20232136364451
20221629344148
20211237374757
2020N/AN/AN/AN/AN/A

UKMT Mathematical Challenges- Intermediate Competitions

First-round Challenges- IMC

UKMT Intermediate Challenges are aimed at students year 11 and below. Starting with the Intermediate Maths Challenge, with the Kangaroos and Olympiads as follow-on rounds, these are designed to challenge and engage your students

Intermediate Mathematical Challenge

  • Time limit
    • 60 minutes
  • Age group
    • England, Wales and Overseas: Year 11 and below
    • Scotland: S4 or below
    • Northern Ireland: Year 12 or below
  • Competition Date
    • Wednesday 29th January 2025
  • Scoring

Scoring rules for the Intermediate Mathematical Challenge are as follows:

    • 5 marks are awarded for each correct answer to questions 1 – 15
    • 6 marks are awarded for each correct answer to questions 16 – 25
    • Each incorrect answer to questions 16 – 20 loses 1 mark
    • Each incorrect answer to questions 21 – 25 loses 2 marks Answers left blank will be marked as 0

Awards and Thresholds

To recognize the highest performers in the Challenge, we award the top-scoring 50% of participants Bronze, Silver and Gold certificates in the ratio 3:2:1. Students that are ‘Best in Year’ or ‘Best in School’ will also receive a badge to denote this on their certificates. Students not amongst the high scorers will receive a Certificate of Participation.

Year

Certificates

 

Bronze

Silver

Gold

Grey Kangaroo Qualification

Pink Kangaroo Qualification

Cayley Olympiad Qualification

Hamilton Olympiad Qualification

Maclaurin Olympiad Qualification

2024

47

61

77

72

84

101

106

110

2023

42

55

71

67

77

95

100

103

2022

50

65

81

65

81

101

111

117

2021

55

68

86

68

86

100

110

118

2020

60

72

89

80

89

110

117

120

 Follow-on Rounds – Grey and Pink Kangaroos

Entry to the Grey and Pink Kangaroos is by invitation based on a qualifying IMC score, or by discretionary entry. Several thousand UK-based students qualify from the IMC each year. Open to UK schools only

Grey and Pink Kangaroos

  • Time limit
    • 60 minutes
  • Age group
    • Grey Kangaroo:
      England and Wales: Year 9 and below
      Scotland: S2 or below
      Northern Ireland: Year 10 or below

      Pink Kangaroo:
      England and Wales: Year 10 and 11
      Scotland: S3 and S4
      Northern Ireland: Year 11 or 12

  • Competition Date
    • Thursday 20th March 2025
  • Scoring

Scoring rules for the Grey & Pink Kangaroos are as follows:

        • 5 marks are awarded for each correct answer to questions 1 – 15
        • 6 marks are awarded for each correct answer to questions 16 – 25 In the
        • Grey Kangaroo / Pink Kangaroo: you will NOT lose marks for getting questions wrong. Answers left blank will be marked as 0

Awards and Thresholds

The top-scoring 25% of participants each receive a Certificate of Merit

Year

Grey Kangaroo Merit

Pink Kangaroo Merit

2024

89

74

2023

84

84

2022

78

86

2021

82

74

2020

101

101

 Follow-on Rounds – Cayley, Hamilton and Maclaurin Mathematical Olympiads

Entry to the Intermediate Olympiads is by invitation based on a qualifying IMC score, or by discretionary entry. Around 1,800 students qualify from the IMC each year.

Cayley, Hamilton and Maclaurin Mathematical Olympiads

  • Time limit
    • 2 hours
  • Age group
    • Cayley Maths Olympiad:
      England, Wales and Overseas: Year 9 and below
      Scotland: S2 or below
      Northern Ireland: Year 10 or below

      Hamilton Maths Olympiad:
      England, Wales and Overseas: Year 10
      Scotland: S3
      Northern Ireland: Year 11

      Maclaurin Maths Olympiad:
      England, Wales and Overseas: Year 11
      Scotland: S4
      Northern Ireland: Year 12

  • Competition Date
    • Thursday 20th March 2025
  • Scoring

Scoring rules for the Cayley, Hamilton & Maclaurin Maths Olympiads are as follows:

    • Each question is worth 10 points
    • Answers can be awarded partial marks depending on the clarity of the participants Mathematical presentation

Awards and Thresholds

Each qualifying student receives a Certificate of Qualification or Participation depending on their entry route. The highest-scoring participants each receive Certificates of Distinction and Merit.

Each of the top 20 scorers receive a gold medal, the next 30 a silver medal and the next 50 a bronze medal. All medalists will also be awarded a book prize; the title varies from year to year.

Previous Cayley Thresholds 

Year

Merit

Distinction

Bronze 

Silver 

Gold 

2024

14

26

31

38

45

2023

12

31

35

42

50

2022

20

33

38

44

51

2021

10

28

31

2020

N/A

N/A

N/A

N/A

N/A

Previous Hamilton Thresholds 

Year

Merit

Distinction

Bronze 

Silver 

Gold 

2024

14

29

33

40

50

2023

18

34

38

44

52

2022

13

28

31

36

44

2021

10

23

27

2020

N/A

N/A

N/A

N/A

N/A

Previous Maclaurin Thresholds 

Year

Merit

Distinction

Bronze 

Silver 

Gold 

2024

14

27

33

39

46

2023

18

29

33

39

47

2022

10

24

29

36

44

2021

10

29

23

2020

N/A

N/A

N/A

N/A

N/A

UKMT Mathematical Challenges- Senior Competitions

First-round Challenges- Senior Mathematical Challenge

UKMT Senior Mathematical Challenge first round  aimed at students year 13 or below. The problems on the Senior Maths Challenge are designed to make students think. Stimulating problems for both beginners and experienced problem-solvers

Intermediate Mathematical Challenge

  • Time limit
    • 60 minutes
  • Age group
    • England, Wales and Overseas: Year 13 and below
    • Scotland: S6 or below
    • Northern Ireland: Year 14 or below
  • Competition Date
    • TBD
  • Scoring

Scoring rules for the Senior Mathematical Challenge are as follows:

      • All participants start with 25 points
      • 4 marks are awarded for each correct answer
      • 1 mark is deducted for each incorrect answer
      • Answers left blank will be marked as 0

Awards and Thresholds

To recognize the highest performers in the Challenge, we award the top-scoring 66% of participants Bronze, Silver and Gold certificates in the ratio 3:2:1. Students that are ‘Best in Year’ or ‘Best in School’ will also receive a badge to denote this on their certificates. Students not amongst the high scorers will receive a Certificate of Participation.

Previous Thresholds

Year

Certificates

Senior Kangaroo

Qualification

BMO1 

Qualification

Bronze

Silver

Gold

2024

49

66

83

83

110

2023

49

64

80

80

106

2022

48

62

76

76

100

2021

49

66

85

85

108

2020

59

73

91

91

108

First-round Challenges- Andrew Jobbings Senior Kangaroo

Entry to the Andrew Jobbings Senior Kangaroo is by invitation based on a qualifying Senior Mathematical Challenge score, or by discretionary entry. Several thousand UK-based students qualify from the SMC each year. Open to UK schools only.

Intermediate Mathematical Challenge

  • Time limit
    • 60 minutes
  • Age group
    • England and Wales: Year 13 and below
    • Scotland: S6 or below
    • Northern Ireland: Year 14 or below
  • Competition Date
    • Wednesday 20th November 2024
  • Scoring

Scoring rules for the Andrew Jobbings Senior Kangaroo are as follows:

    • 5 marks are awarded for each correct answer
    • In the Senior Kangaroo you will NOT lose marks for getting questions wrong

Awards and Thresholds

Each participant receives a Certificate of Qualification or Participation, depending on their entry route, and the top-scoring 25% of participants each receive a Certificate of Merit.

Previous Thresholds

Year

Senior Kangaroo Qualification

 

Merit

2024

2023

50

2022

40

2021

45

First-round Challenges- British Mathematical Olympiad Round 1

As a follow-on Round to the Senior Mathematical Challenge (SMC), the British Mathematical Olympiad Round 1 (BMO1) is a 3.5 hour Olympiad consisting of six problems requiring full written solutions.

As well as challenging high-scorers from the SMC, the British Mathematical Olympiad is an entry point to the training and selection programme for international competitions.

The competition is open to eligible students. UKMT invites around 1000 qualifying students from the SMC, those who did not participate in the SMC can be entered at the discretion of their schools

British Mathematical Olympiad Round 1

  • Time limit
    • 3.5 hours
  • Age group
    • England, Wales and Overseas: Year 13 and below
    • Scotland: S6 or below
    • Northern Ireland: Year 14 or below
  • Competition Date
    • Wednesday 20th November 2024
  • Scoring

Scoring rules for the British Mathematical Olympiad Round 1 (BMO1) are as follows:

      • Each question carries 10 marks
      • Partial marks are awarded depending on the clarity of the participants Mathematical presentation. We advise working in rough first, then writing up your best attempt.
      • One complete solution will gain more credit than several unfinished attempts.

Awards and Thresholds

The top scoring students will receive a Certificate of Distinction or a Certificate of Merit depending on their score.

Each of the top 20 scorers receive a gold medal, the next 30 a silver medal and the next 50 a bronze medal. All medalists will also be awarded a book prize; the title varies from year to year. Each qualifying student receives a Certificate of Qualification or Participation depending on their entry route.

Previous Thresholds

Year

BMO Round 1 

 

Merit

Distinction

BMO2 invite

Bronze 

Silver 

Gold 

2024

2023

13

30

Y13: 43

Y12: 42

Y11: 39

Y10: 37

44

49

58

2022

12

25

Y13: 38

Y12: 36

Y11: 34

Y10: 33

39

43

51

2021

11

21

Y13: 33

Y12: 32

Y11: 31

Y10: 29

33

38

45

2020

10

18

Y13: 27

Y12: 26

Y11: 24

Y10: NA

29

34

40

First-round Challenges- British Mathematical Olympiad Round 2

As a follow-on Round to the BMO1 , as  well as challenging high-scorers from the SMC, the British Mathematical Olympiad is an entry point to the training and selection programme for international competitions. UKMT invites around 100 qualifying students from BMO1, those who did not participate in BMO1 can be entered at the discretion of their schools

British Mathematical Olympiad Round 1

  • Time limit
    • 3.5 hours
  • Age group
    • England, Wales and Overseas: Year 13 and below
    • Scotland: S6 or below
    • Northern Ireland: Year 14 or below
  • Competition Date
    • Wednesday 22 January 2025
  • Scoring

Scoring rules for the British Maths Olympiad Round 2 are as follows:

    • Each question, which require full written solutions, is worth 10 points
    • Marks awarded depend on the clarity of the participants Mathematical presentation. We advise working in rough first, then writing up your best attempt
    • One or two complete solutions will gain far more credit than partial attempts for all four questions

Awards and Thresholds

The top scoring students will receive a Certificate of Distinction or a Certificate of Merit depending on their score.

Each qualifying student receives a Certificate of Qualification or Participation depending on their entry route.

Previous Thresholds

Year

BMO Round 2

 

Merit

Distinction

2024

6

15

2023

7

11

2022

10

17

2021

6

18

2020

7

15

UKMT Mathematical Challenges- Mathematical Olympiad for Girls

First-round Challenges- Mathematical Olympiad for Girls

The Mathematical Olympiad for Girls is aimed at girls and young women across the UK and consists of five challenging problems.

Entry to MOG is by discretionary entry

British Mathematical Olympiad Round 1

  • Time limit
    • 2.5 hours
  • Age group
    • England and Wales: Year 13 and below (younger students may be entered at the school’s discretion)
    • Scotland: S6 and below
    • Northern Ireland: Year 14 and below
  • Competition Date
    • Wednesday 25th September 2024
  • Scoring

Scoring rules for the Mathematical Olympiad for Girls as follows:

      • Each question carries 10 marks
      • Partial marks may be awarded for incomplete or partially correct answers
      • One fully correct answer will gain you more credit than several guesses
      • There are no negative marks for incorrect answers

Awards and Thresholds

The top scoring students will receive a Certificate of Distinction or a Certificate of Merit depending on their score. The top 30 scorers will also be awarded a book prize; the title varies from year to year. Each student receives a Certificate of Participation.

Previous Thresholds

Year

Merit

Distinction

Book Prize

2024

2023

16

26

43

2022

20

36

50

2021

10

23

43

2020

N/A

N/A

N/A

 
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