sets and functions notation year 10 maths

Question 1

What is a set in mathematics?

Answer 1

A collection of distinct objects considered as a whole.

Question 2

How is a set usually denoted?

Answer 2

By curly braces, e.g., {a, b, c}.

Question 3

What does it mean if an element ‘x’ belongs to a set ‘A’?

Answer 3

It is denoted as x ∈ A.

Question 4

True or False: The set {1, 2, 2, 3} contains three elements.

Answer 4

False.

Question 5

What is the empty set?

Answer 5

A set that contains no elements, denoted as ∅.

Question 6

What is the union of two sets A and B?

Answer 6

The set of elements that are in A, in B, or in both, denoted as A ∪ B.

Question 7

What is the intersection of two sets A and B?

Answer 7

The set of elements that are in both A and B, denoted as A ∩ B.

Question 8

What is the complement of a set A?

Answer 8

The set of all elements not in A, usually denoted as A’.

Question 9

What is a subset?

Answer 9

A set A is a subset of B if every element of A is also an element of B, denoted as A ⊆ B.

Question 10

What is a proper subset?

Answer 10

A set A is a proper subset of B if A ⊆ B and A ≠ B.

Question 11

What symbol is used to denote ‘is not an element of’?

Answer 11

The symbol is ‘∉’.

Question 12

Fill in the blank: The power set of a set A is the set of all __________ of A.

Answer 12

subsets

Question 13

How many elements are in the power set of a set with n elements?

Answer 13

2^n.

Question 14

What is a function?

Answer 14

A relation that assigns exactly one output for each input.

Question 15

How is a function typically denoted?

Answer 15

By f(x), where f is the function and x is the input.

Question 16

What is the domain of a function?

Answer 16

The set of all possible inputs for the function.

Question 17

What is the range of a function?

Answer 17

The set of all possible outputs of the function.

Question 18

True or False: A function can have multiple outputs for a single input.

Answer 18

False.

Question 19

What is a one-to-one function?

Answer 19

A function where each output is mapped from a unique input.

Question 20

What does it mean for a function to be onto?

Answer 20

Every element in the range is mapped from at least one element in the domain.

Question 21

What is a composite function?

Answer 21

A function formed by applying one function to the results of another, denoted as (f ∘ g)(x) = f(g(x)).

Question 22

Fill in the blank: The notation f: A → B indicates a function from set A to set __________.

Answer 22

B

Question 23

What is the notation for the inverse of a function f?

Answer 23

It is denoted as f⁻¹.

Question 24

What is a relation in mathematics?

Answer 24

A set of ordered pairs.

Question 25

What does the notation A × B represent?

Answer 25

The Cartesian product of sets A and B.

Question 26

True or False: The Cartesian product A × B contains all ordered pairs (a, b) where a ∈ A and b ∈ B.

Answer 26

True.

Question 27

What is the notation for the cardinality of a set?

Answer 27

It is denoted as |A|.

Question 28

Fill in the blank: If A = {1, 2, 3}, then |A| = __________.

Answer 28

3

Question 29

What is the notation for the intersection of three sets A, B, and C?

Answer 29

It is denoted as A ∩ B ∩ C.

Question 30

What is the notation for the union of three sets A, B, and C?

Answer 30

It is denoted as A ∪ B ∪ C.

Question 31

What is a finite set?

Answer 31

A set with a limited number of elements.

Question 32

What is an infinite set?

Answer 32

A set with an unlimited number of elements.

Question 33

True or False: The set of natural numbers is finite.

Answer 33

False.

Question 34

What is a function's vertical line test?

Answer 34

A way to determine if a graph represents a function; if any vertical line intersects the graph more than once, it is not a function.

Question 35

What is a linear function?

Answer 35

A function that can be expressed in the form f(x) = mx + b.

Question 36

Fill in the blank: A function is __________ if it can be represented by a straight line.

Answer 36

linear

Question 37

What is the slope of a line in a linear function?

Answer 37

The rate of change of the function, denoted as 'm'.

Question 38

What does the 'b' represent in the linear function f(x) = mx + b?

Answer 38

The y-intercept of the function.

Question 39

What is the notation for the domain of a function?

Answer 39

It is often denoted as D(f) or dom(f).

Question 40

What is the notation for the range of a function?

Answer 40

It is often denoted as R(f) or ran(f).

Question 41

True or False: A function can have a domain that includes negative numbers.

Answer 41

True.

Question 42

What does it mean for a function to be continuous?

Answer 42

It means there are no breaks, jumps, or holes in the graph of the function.

Question 43

What is the notation for a function evaluated at a point x?

Answer 43

It is denoted as f(x).

Question 44

What is a piecewise function?

Answer 44

A function defined by different expressions for different intervals of the domain.

Question 45

Fill in the blank: A __________ function can be represented by multiple formulas over its domain.

Answer 45

piecewise

Question 46

What is the notation for the image of a function?

Answer 46

It is often denoted as f(A) for a set A.

Question 47

What is a function's limit?

Answer 47

The value that a function approaches as the input approaches a certain point.

Question 48

What is a quadratic function?

Answer 48

A function that can be expressed in the form f(x) = ax² + bx + c.

Question 49

Fill in the blank: A __________ function has a degree of 2.

Answer 49

quadratic

Question 50

What is the notation for the range of a quadratic function?

Answer 50

It is often denoted as R(f) or ran(f).

Question 51

True or False: The range of a quadratic function is always all real numbers.

Answer 51

False.

Question 52

What is a constant function?

Answer 52

A function that always returns the same value, regardless of the input.

Question 53

What is the notation for a constant function?

Answer 53

It is often denoted as f(x) = c, where c is a constant.

Question 54

What is the notation for the domain of a constant function?

Answer 54

It is usually all real numbers, denoted as ℝ.

Question 55

What is the difference between a function and a relation?

Answer 55

A function assigns exactly one output for each input, while a relation can assign multiple outputs.

Question 56

What does the notation f(x) = g(x) signify?

Answer 56

It signifies that the functions f and g are equal for all x in their domain.