Patterns and Relationships

Question 1

What is a pattern in mathematics?

Answer 1

A pattern is a sequence or arrangement that follows a specific rule or formula.

Question 2

True or False: Patterns can only be numerical.

Answer 2

False

Question 3

Fill in the blank: A __________ is a number that is added to itself a certain number of times.

Answer 3

multiple

Question 4

What is the next number in the sequence: 2, 4, 6, 8, ___?

Answer 4

10

Question 5

Define a linear pattern.

Answer 5

A linear pattern is a sequence of numbers that increases or decreases by a constant amount.

Question 6

What is the formula for the nth term of an arithmetic sequence?

Answer 6

a_n = a_1 + (n - 1)d

Question 7

Identify the common difference in the sequence: 5, 8, 11, 14.

Answer 7

3

Question 8

True or False: A geometric pattern multiplies by a constant factor.

Answer 8

True

Question 9

What is the first term of the geometric sequence: 3, 6, 12, 24?

Answer 9

3

Question 10

What is the common ratio in the sequence: 2, 6, 18, 54?

Answer 10

3

Question 11

Fill in the blank: The __________ of a sequence is the difference between consecutive terms.

Answer 11

common difference

Question 12

What is a quadratic pattern?

Answer 12

A pattern where the difference between consecutive terms is not constant but the second difference is constant.

Question 13

What is the general form of a quadratic equation?

Answer 13

y = ax^2 + bx + c

Question 14

Identify the type of sequence: 1, 4, 9, 16, 25.

Answer 14

Quadratic sequence

Question 15

True or False: The Fibonacci sequence starts with 0 and 1.

Answer 15

True

Question 16

What is the next number in the Fibonacci sequence: 0, 1, 1, 2, 3, 5, ___?

Answer 16

8

Question 17

What is a function in mathematics?

Answer 17

A function is a relation where each input has exactly one output.

Question 18

True or False: The output of a function can be the same for different inputs.

Answer 18

False

Question 19

What is the x-intercept of a linear function?

Answer 19

The point where the graph intersects the x-axis.

Question 20

Identify the slope in the equation y = 3x + 2.

Answer 20

3

Question 21

What is the y-intercept in the equation y = -2x + 5?

Answer 21

5

Question 22

Fill in the blank: The __________ of a function is its set of inputs.

Answer 22

domain

Question 23

What is the range of a function?

Answer 23

The set of possible outputs of the function.

Question 24

True or False: A relation can be a function if it has multiple outputs for a single input.

Answer 24

False

Question 25

What does it mean for two quantities to be proportional?

Answer 25

They have a constant ratio.

Question 26

What is the formula for direct variation?

Answer 26

y = kx, where k is a constant.

Question 27

Identify the constant of variation in the equation y = 4x.

Answer 27

4

Question 28

What is the difference between a relation and a function?

Answer 28

A function is a specific type of relation where each input has one output.

Question 29

Fill in the blank: In a linear equation, the __________ indicates how steep the line is.

Answer 29

slope

Question 30

What kind of relationship do scatter plots typically show?

Answer 30

The relationship between two variables.

Question 31

What does a positive correlation in a scatter plot indicate?

Answer 31

As one variable increases, the other variable also increases.

Question 32

What does a negative correlation in a scatter plot indicate?

Answer 32

As one variable increases, the other variable decreases.

Question 33

True or False: A scatter plot can show a nonlinear relationship.

Answer 33

True

Question 34

What is the purpose of finding the mean in a data set?

Answer 34

To determine the average value.

Question 35

What is the median in a data set?

Answer 35

The middle value when the data is arranged in order.

Question 36

Fill in the blank: The __________ is the most frequently occurring value in a data set.

Answer 36

mode

Question 37

What is the range of a data set?

Answer 37

The difference between the highest and lowest values.