TopicGeneral Maths
Number · SS1
Sets & Venn diagrams
Grouping things into sets and using Venn diagrams to count what belongs where.
- Before this
- Number foundations & fractions
- Leads to
- LogicProbabilitySets & logic
Learn
- 1Sets and set notationListing and describing sets, the universal set and the empty set, subsets, and reading union, intersection and complement from a Venn diagram, for two sets and three.Done16 min
- 2Venn diagram problemsCounting with Venn diagrams: the two-set formula, filling a three-set diagram from the centre outwards, forming an equation for an unknown region, and probabilities read from the diagram.Done18 min
Practise
Answer sets & venn diagrams questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.
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Past questions (78)
From 1992–2025: 40 WAEC, 4 NECO, 34 JAMB. Theory questions first, then objective, newest first.
Theory (30)
- WAEC 2025 · Paper 2 · Q1Factorize .
- WAEC 2023 · Paper 2 · Q6, where is a counting number. Write down all the elements in .
- WAEC 2022 · Paper 2 · Q5Given that and , simplify, without using a calculator, , leaving the answer in the form …
- WAEC 2022 · Paper 2 · Q1In a school, 100 students indicated their interest in the following sports: football, volleyball and hockey. 48 liked football, 42 liked volleyball …
- WAEC 2022 · Paper 2 · Q6Given that , and , where is an integer, find: (i) ; (ii) …
- WAEC 2022 · Paper 2 · Q8In a class of 60 students, 30 read Literature and 35 read Government. All the students read at least one of the subjects. If a student is …
- WAEC 2022 · Paper 2 · Q9In a class of 50 students, 18 play football, 20 volleyball and 21 handball. 9 play football and volleyball, 6 football and handball, 11 volleyball …
- WAEC 2021 · Paper 2 · Q6In a class of 80 students, study Biology and study Physics. If each student studies at least one of the subjects: …
- WAEC 2021 · Paper 2 · Q1A school advertised for Mathematics, Physics and Chemistry tutors and received applications from 10 people. Of these, 3 applied to teach Mathematics …
- WAEC 2021 · Paper 2 · Q13There are 20 men on a public bus. Of these, 15 wear glasses and 10 wear wrist watches. If one man is chosen at random from the bus, what is the …
- WAEC 2020 · Paper 2 · Q1If , and are subsets of , …
- WAEC 2020 · Paper 2 · Q8In a class, students were taught French, Mathematics and Economics. The teachers observed that 5 liked all the 3 subjects, 9 French and Mathematics, …
- WAEC 2020 · Paper 2 · Q5A number is selected at random from the set . Find the probability that the number selected is:
- WAEC 2019 · Paper 2 · Q9A survey of 40 students showed that 23 students study Mathematics, 5 study Mathematics and Physics, 8 study Chemistry and Mathematics, 5 study …
- WAEC 2019 · Paper 2 · Q9A selection interview was conducted for 110 students into various subjects in a Science department. 25 were selected for Physics, 45 for Biology …
- WAEC 2018 · Paper 2 · Q6In a road-worthiness test on 240 cars, passed. The cars that failed had faults in Clutch, Brakes and Steering as follows: Clutch only …
- WAEC 2017 · Paper 2 · Q5Out of 120 customers in a shop, 45 bought bags and shoes. All the customers bought either bags or shoes, and 11 more customers bought shoes than …
- WAEC 2017 · Paper 2 · Q11Sets and are subsets of . If a number is selected …
- WAEC 2017 · Paper 2 · Q7If , express in terms of .
- WAEC 2016 · Paper 2 · Q6Find the sum of the Arithmetic Progression (A.P.) .
- WAEC 2014 · Paper 2 · Q9In the Venn diagram, , and are subsets of the universal set . The regions are: only , only , only …
- WAEC 2014 · Paper 2 · Q4Without using tables or a calculator, evaluate .
- WAEC 2013 · Paper 2 · Q13Given that and , illustrate on the number line.
- WAEC 2012 · Paper 2 · Q6A boy had dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister's share was equal to of , …
- WAEC 2012 · Paper 2 · Q2Given that , and , find: (i) ; (ii) .
- WAEC 2011 · Paper 2 · Q6In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 Mathematics and Accounts only, 6 Mathematics only, …
- WAEC 2010 · Paper 2 · Q1, and are subsets of the universal set . Find …
- WAEC 2010 · Paper 2 · Q6In a class of 50 students, 30 offered History, 15 offered History and Geography while 3 did not offer any of the two subjects. (i) Represent …
- WAEC 2009 · Paper 2 · Q4Out of 30 candidates applying for a post, 17 have degrees, 15 have diplomas and 4 have neither a degree nor a diploma. How many of them have …
- WAEC 2008 · Paper 2 · Q10In a class of 200 students, 70 offered Physics, 90 Chemistry and 100 Mathematics, while 24 did not offer any of the three subjects. Twenty-three …
Objective (48)
- WAEC 2025 · Paper 1 · Q10In the Venn diagram, the shaded portion is represented by which set expression?
- WAEC 2025 · Paper 1 · Q8If and , find .
- NECO 2024 · Paper 1 · Q10In a class of 80 students, every student studies Mathematics or Geography or both. If 65 students study Mathematics and 50 study Geography, how …
- NECO 2024 · Paper 1 · Q2If , find .
- WAEC 2024 · Paper 1 · Q2Given that , where is an integer, and , where is a multiple of , find .
- NECO 2023 · Paper 1 · Q10Given sets , and , find .
- NECO 2023 · Paper 1 · Q13The Venn diagram shows the number of students who wrote Biology, Physics and Mathematics in a school. Find the number of students who wrote at …
- WAEC 2023 · Paper 1 · Q2There are 30 students in a class. 15 study woodwork and 13 study metalwork. 6 study neither of the two subjects. How many students study woodwork …
- WAEC 2022 · Paper 1 · Q3Given that and are sets such that , and , find .
- WAEC 2022 · Paper 1 · Q43A local community has two newspapers, the Morning Times and the Evening Dispatch. The Morning Times is read by of the households and the …
- WAEC 2021 · Paper 1 · Q20Consider the statements : all students offering Literature () also offer History (); : students offering History do not offer Geography …
- WAEC 2021 · Paper 1 · Q6If and , where is an integer, find .
- WAEC 2020 · Paper 1 · Q2If and are subsets of , find .
- WAEC 2019 · Paper 1 · Q6If and are subsets of and is an integer, find .
- JAMB 2017 · UTME · Q40In a class of 60 students, 30 offer physics and 40 offer chemistry. If a student is picked at random from the class, what is the probability …
- JAMB 2017 · UTME (set 2) · Q1Given and , find .
- JAMB 2017 · UTME (set 2) · Q3If , and , …
- JAMB 2014 · UTME · Q10If and , list the elements in .
- JAMB 2014 · UTME · Q11From the Venn diagram, the shaded parts represent
- JAMB 2013 · UTME · Q10If and , find .
- JAMB 2013 · UTME · Q9, and are subsets of the universal set . Which Venn diagram shows the relationship ?
- JAMB 2012 · UTME · Q10In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games, how many play neither?
- JAMB 2012 · UTME · Q9If is the set of all prime factors of 30 and is the set of all factors of 18 less than 10, find .
- JAMB 2011 · UTME · Q10From the Venn diagram, the complement of the set is given by
- JAMB 2011 · UTME · Q50In a class of 60 students, 30 offer Physics and 40 offer Chemistry. If a student is picked at random from the class, what is the probability …
- JAMB 2010 · UTME · Q12In a survey of 50 newspaper readers, 40 read Champion and 30 read Guardian. How many read both papers?
- JAMB 2004 · UME · Q10In a class of 40 students, each student offers at least one of Physics and Chemistry. If the number that offer Physics is three times the number …
- JAMB 2004 · UME · Q9The shaded region in the Venn diagram is
- JAMB 2003 · UME · Q8Given , and , …
- JAMB 2003 · UME · Q9In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither. How many offer both Mathematics and Physics?
- JAMB 2002 · UME · Q25In a class of 80 students, offer Music only, offer both Music and History, offer History only and 20 offer neither. If …
- JAMB 2002 · UME · Q4In a school, 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 offer Mathematics. How many offer Biology but not Mathematics?
- JAMB 2000 · UME · Q1Let , and . Determine .
- JAMB 2000 · UME · Q4In a youth club with 94 members, 60 like modern music and 50 like traditional music. The number of members who like both is three times the number …
- JAMB 2000 · UME · Q45If , and , …
- JAMB 1999 · UME · Q4If , , and , list the elements of .
- JAMB 1999 · UME · Q9A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain; 5 sell plantain …
- JAMB 1998 · UME · Q8Given the universal set and the sets , and , find .
- JAMB 1998 · UME · Q9In the Venn diagram, the shaded region is
- JAMB 1997 · UME · Q10A survey of 100 students in an institution shows that 80 students speak Hausa and 20 speak Igbo, while only 9 speak both languages. How many …
- JAMB 1995 · UME · Q10If , then is equal to
- JAMB 1995 · UME · Q9Four members of a school's first eleven cricket team are also members of the first fourteen rugby team. How many boys play for at least one of …
- JAMB 1994 · UME · Q50In a survey, 20 students read newspapers and 35 read novels. If 40 of the students read either newspapers or novels, what is the probability …
- JAMB 1994 · UME · Q7In a science class of 42 students, each offers at least one of Mathematics and Physics. If 22 students offer Physics and 28 offer Mathematics, …
- JAMB 1994 · UME · Q8Given that for sets and in a universal set , , then is
- JAMB 1993 · UME · Q9The shaded portion in the Venn diagram is
- JAMB 1992 · UME · Q8If and , the elements of and respectively …
- JAMB 1992 · UME · Q9If is the universal set, and , find , …