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Mathematics · Self Assessment

Practice Test: Sets & Matrices

A 100-mark paper covering "Sets: Notation, Venn Diagrams & Set Operations" and "Matrices: Operations, Determinants & Transformations" — multiple choice, true/false, fill-in-the-blank, column matching, and short answer, all auto-graded instantly.

EDUSAMBAM Editorial Team · 45 questions · 100 marks · Instant self-assessment

Questions

100

Marks

Sections

100%

Auto-Graded

Section	Questions	Marks Each	Total
A — Multiple Choice	15	2	30
B — True / False	10	2	20
C — Fill in the Blank	10	2	20
D — Column Matching	5 pairs	2	10
E — Short Answer	5	4	20
Total	45	—	100

Fill-in-the-blank and short-answer questions are checked automatically against accepted answers — exact wording doesn't need to match, but the key term should be present.

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Section A — Multiple Choice

30 marks

15 questions · 2 marks each.

1.The symbol ∈ means:Basic2 pts

A. Is a subset of

B. Is not equal to

C. Union

D. Is an element of

2.n(A) represents:Basic2 pts

A. The complement of A

B. The number of elements in A

C. The universal set

D. The empty set

3.The universal set is written:Basic2 pts

A. ξ

B. ∅

C. ∈

D. ⊂

4.A = {1, 2, 3}, B = {1, 2, 3, 4, 5}. Is A ⊂ B?Intermediate2 pts

A. No

B. Cannot be determined

C. Yes

D. Only if A = B

5.A = {2, 4, 6}, B = {4, 6, 8}. Find A ∪ B.Basic2 pts

A. {2, 4, 6, 8}

B. {4, 6}

C. {2, 8}

D. {2, 4, 4, 6, 6, 8}

6.A = {2, 4, 6}, B = {4, 6, 8}. Find A ∩ B.Basic2 pts

A. {2, 4, 6, 8}

B. {2}

C. {4, 6}

D. {8}

7.The counting formula for two sets is:Intermediate2 pts

A. n(A ∪ B) = n(A) + n(B)

B. n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

C. n(A ∪ B) = n(A) × n(B)

D. n(A ∪ B) = n(A ∩ B)

8.The order of a matrix with 2 rows and 3 columns is written:Basic2 pts

A. 3 × 2

B. 6

C. 5

D. 2 × 3

9.Two matrices can only be added if:Basic2 pts

A. They are both square

B. They both have determinant 0

C. They have the same order

D. Neither has any negative numbers

10.Matrix multiplication is performed using:Intermediate2 pts

A. Row times column, then sum the products

B. Element-by-element multiplication

C. Adding corresponding elements

D. Dividing corresponding elements

11.A = (1 0 over 2 3), B = (2 1 over 0 1). Find the top-left element of AB.Advanced2 pts

A. 0

B. 1

C. 3

D. 2

12.Matrix multiplication is:Intermediate2 pts

A. Always commutative

B. Generally NOT commutative

C. The same as addition

D. Only defined for square matrices

13.The determinant of (3 2 over 1 4) is:Intermediate2 pts

A. 14

B. 10

C. 2

D. 12

14.A matrix with a determinant of zero is called:Intermediate2 pts

A. An identity matrix

B. Symmetric

C. Invertible

D. Singular

15.To find the inverse of (a b over c d), the formula is:Advanced2 pts

A. (d b over c a)

B. det(A) × (a b over c d)

C. 1/det(A) × (d −b over −c a)

D. (a b over c d) itself

Section B — True / False

20 marks

10 questions · 2 marks each.

16.The empty set is written ∅ or { }.Basic2 pts

True

False

17.Every set is a subset of the empty set.Intermediate2 pts

True

False

18.A ∪ B contains elements in A, B, or both.Basic2 pts

True

False

19.A ∩ B contains elements only in A, not B.Basic2 pts

True

False

20.n(A′) means the number of elements NOT in A, within ξ.Intermediate2 pts

True

False

21.Two matrices of different orders can always be multiplied together.Intermediate2 pts

True

False

22.The identity matrix behaves like the number 1 in ordinary multiplication.Basic2 pts

True

False

23.A matrix with a non-zero determinant has an inverse.Intermediate2 pts

True

False

24.Matrix addition requires multiplying corresponding elements.Basic2 pts

True

False

25.Simultaneous equations written as AX = B can be solved using X = A⁻¹B.Intermediate2 pts

True

False

Section C — Fill in the Blank

20 marks

10 questions · 2 marks each. Type the missing word or term.

26.The symbol for "is an element of" is ______.Basic2 pts

27.A set with no elements is called the ______ set.Basic2 pts

28.Elements common to both A and B form the ______ of A and B.Intermediate2 pts

29.The complement of A, written A′, contains elements not in A but in the ______ set.Intermediate2 pts

30.Filling a Venn diagram from a word problem should start with the most ______ region.Advanced2 pts

31.The order of a matrix is given as rows × ______.Basic2 pts

32.Multiplying every element of a matrix by a number is called ______ multiplication.Intermediate2 pts

33.The determinant of a 2×2 matrix (a b over c d) is ad − ______.Intermediate2 pts

34.A matrix with a determinant of zero has no ______.Intermediate2 pts

35.The matrix that leaves any compatible matrix unchanged when multiplied is called the ______ matrix.Basic2 pts

Section D — Column Matching

10 marks

Match each term to its correct definition. Use the ▲▼ buttons to reorder Column B.

36–40.Match each term to its correct definition.Advanced10 pts

Column A

Union

Intersection

Complement

Determinant

Identity matrix

Column B

Elements in ξ that are not in A

Elements in A, B, or both

Leaves any compatible matrix unchanged when multiplied

Elements in both A and B

ad − bc for a 2×2 matrix

Section E — Short Answer

20 marks

5 questions · 4 marks each. Answer in one or two sentences.

41.Explain how to use the counting formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B) in a survey problem.Advanced4 pts

42.Describe the order in which you should fill in a three-set Venn diagram from a word problem.Advanced4 pts

43.Explain the difference between matrix addition and matrix multiplication.Advanced4 pts

44.Describe how to find the determinant and inverse of a 2×2 matrix.Advanced4 pts

45.Explain how matrices can be used to solve a pair of simultaneous equations.Advanced4 pts

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