Patterns and Functions: Master the Art of Patterns and Functions in Sixth Grade Math

Question 1

Which option is NOT a way to represent a mathematical function?

Accepted Answer

Paragraph

Answer

Table

Answer

Graph

Answer

Equation

Question 2

The pattern 2, 4, 8, 16, ... is an example of what type of pattern?

Accepted Answer

Geometric

Answer

Linear

Answer

Quadratic

Answer

Exponential

Question 3

What is the y-intercept of the function y = -x + 2?

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Question 4

Identify the function that is NOT linear:

Accepted Answer

f(x) = x^2 + 1

Accepted Answer

f(x) = 1/x

Accepted Answer

f(x) = |x|

Answer

f(x) = 2x + 1

Question 5

Which of the following is NOT a type of mathematical pattern?

Accepted Answer

Random

Answer

Arithmetic

Answer

Geometric

Answer

Algebraic

Question 6

Which of the following equations represents the linear pattern: {1, 3, 5, 7, ...}?

Accepted Answer

y = x + 2

Answer

y = 2x + 1

Answer

y = 3x - 2

Answer

y = x - 1

Question 7

The graph of the function y = 2x - 1 has a:

Accepted Answer

Positive slope

Answer

Negative slope

Answer

Zero slope

Answer

Undefined slope

Question 8

What is the y-intercept of the line y = -x + 5?

Accepted Answer

5

Answer

-1

Answer

1

Answer

-5

Question 9

The graph of the inequality y > 2x - 3 is:

Accepted Answer

A shaded area above a line

Answer

A line with a positive slope

Answer

A line with a negative slope

Answer

A shaded area below a line

Question 10

Which graph shows an exponential function?

Accepted Answer

A curve that goes up quickly at first and then slows down

Answer

A straight line going up

Answer

A curve that goes down quickly at first and then slows down

Answer

A circle

Question 11

Which of the following patterns involves numbers?

Accepted Answer

The number of petals on a flower

Answer

The sequence of colors in a rainbow

Answer

The pattern of stripes on a zebra

Answer

The arrangement of leaves on a stem

Question 12

Which of these describes the connection between two things?

Accepted Answer

A function

Answer

A pattern

Answer

A table

Answer

A graph

Question 13

Which graph represents a curved line?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

A triangle

Question 14

Which equation describes a linear function?

Accepted Answer

y = 3x - 1

Answer

y = x^2 + 2

Answer

y = sin(x)

Answer

y = 1/(x+1)

Question 15

What is the slope of the line y = 2x + 3?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 16

What is the y-intercept of the line y = 2x + 3?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 17

Which real-life situation can be represented using a linear function?

Accepted Answer

The cost of renting a car

Answer

The growth of a plant

Answer

The trajectory of a thrown ball

Answer

The amount of water in a leaking tank

Question 18

Which graph represents the function y = 2x + 1?

Accepted Answer

A line passing through (0, 1) with a slope of 2

Answer

A line passing through (0, 0) with a slope of 1

Answer

A parabola opening upward

Answer

A circle centered at (0, 0)

Question 19

The sequence 2, 4, 8, 16, ... follows which pattern?

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Odd numbers

Answer

Fibonacci

Question 20

Which of these equations represents a line parallel to the x-axis?

Accepted Answer

y = 2

Answer

y = 3x

Answer

y = x + 1

Answer

y = 2x - 1

Question 21

What is the y-intercept of the line with the equation y = 4x - 3?

Accepted Answer

-3

Answer

0

Answer

3

Answer

4

Question 22

Which of the following is an example of a linear function?

Accepted Answer

y = 2x + 5

Answer

y = x^2

Answer

y = sin(x)

Answer

y = log(x)

Question 23

Which sequence shows a linear pattern?

Accepted Answer

2, 4, 6, 8, 10

Answer

1, 2, 4, 8, 16

Answer

1, 3, 5, 7, 9

Answer

2, 5, 10, 17, 26

Question 24

Write the equation of the line with a slope of 2 that passes through point (1, 3).

Accepted Answer

y = 2x + 1

Answer

y = 3x + 1

Answer

y = 2x - 1

Answer

y = 3x - 1

Question 25

What is the domain of function f(x) = 1/(x - 2)?

Accepted Answer

All real numbers except 2

Answer

All real numbers greater than 2

Answer

All real numbers less than 2

Answer

Only the number 2

Question 26

Find an equivalent expression to (x + 2)(x - 3).

Accepted Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 - 5x + 6

Answer

x^2 + 5x + 6

Question 27

Find the value of the expression 2^3 + 3^2.

Accepted Answer

17

Answer

13

Answer

23

Answer

29

Question 28

Exponential patterns exhibit a consistent multiplication factor between consecutive terms. Identify the pattern in the sequence: 3, 9, 27, 81, ...

Accepted Answer

Multiplying by 3

Answer

Adding 6

Answer

Squaring each term

Answer

Alternating addition and subtraction

Question 29

Linear patterns can be represented by equations. The first term of a linear pattern is 10, and the common difference is 5. Which equation represents this pattern?

Accepted Answer

y = 10 + 5x

Answer

y = 5x + 10

Answer

y = 10x + 5

Answer

y = 5 + 10x

Question 30

Graphs can visually represent functions. Which of these graphs shows a linear function?

Accepted Answer

[Image of a line with a constant slope]

Answer

[Image of a curved line]

Answer

[Image of a parabola]

Answer

[Image of a circle]

Question 31

Linear patterns can be extended using algebraic expressions. The pattern 7, 11, 15, 19, ... can be continued using the expression:

Accepted Answer

7 + 4n

Answer

7 + n

Answer

7x + n

Answer

7x + 4n

Question 32

Graphs and equations are interconnected. Which graph represents the equation y = 2x - 1?

Accepted Answer

[Image of a line with a positive slope]

Answer

[Image of a line with a negative slope]

Answer

[Image of a parabola]

Answer

[Image of a circle]

Question 33

Which of the following is NOT a trait of linear functions?

Accepted Answer

The graph has a parabolic shape.

Answer

The graph is a straight line.

Answer

The change in output is consistent for every change in input.

Answer

The function can be written as y = mx + b.

Question 34

Which graph represents a quadratic function?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

A square

Question 35

Which pattern can be extended by adding 3?

Accepted Answer

3, 6, 9, 12

Answer

2, 5, 8, 11

Answer

4, 8, 12, 16

Answer

5, 10, 15, 20

Question 36

Which of the following is NOT a method of visualizing a function?

Accepted Answer

Pie chart

Answer

Table

Answer

Equation

Answer

Scatter plot

Question 37

A number sequence begins with 5 and adds 3 to each term to arrive at the next. What is the 7th term in the sequence?

Accepted Answer

23

Answer

17

Answer

20

Answer

26

Question 38

Which of the following is an equation for a linear function?

Accepted Answer

y = 3x - 2

Answer

y = x² + 1

Answer

y = 1/x

Answer

y = |x|

Question 39

The graph of a linear function shows a straight line with a slope of 2. What is the equation of this function with y-intercept 3?

Accepted Answer

y = 2x + 3

Answer

y = -2x + 3

Answer

y = 2x - 3

Answer

y = -2x - 3

Question 40

Which of the following describes a geometric pattern?

Accepted Answer

Multiplying each term by a fixed number

Answer

Adding a fixed number to each term

Answer

Subtracting a varying amount from each term

Answer

Alternating between adding and subtracting fixed numbers

Question 41

Which equation represents the relationship shown in the table?

| Number of Hours Worked (x) | Amount Earned (y) | 
|---|---| 
| 1 | 10 | 
| 2 | 20 | 
| 3 | 30 |

Accepted Answer

y = 10x

Answer

y = x - 10

Answer

y = x + 10

Answer

y = 10/x

Question 42

A pattern starts with the number 2 and follows the rule: 'multiply the previous number by 3 and then subtract 1'. What is the 3rd number in the pattern?

Accepted Answer

17

Answer

5

Answer

20

Answer

14

Question 43

A bakery sells cookies for $1.50 each. Which equation represents the total cost (C) of buying 'n' cookies?

Accepted Answer

C = 1.50n

Answer

C = n - 1.50

Answer

C = 1.50 / n

Answer

C = n + 1.50

Question 44

The table shows the number of students in a class who like different colors. Which color is liked by the most students?

| Color | Number of Students | 
|---|---| 
| Red | 8 | 
| Blue | 12 | 
| Green | 5 |

Accepted Answer

Blue

Answer

Red

Answer

Green

Answer

All colors are liked equally