Algebra Basics: Expressions and Equations - 6th Grade Math Quiz

Question 1

In the expression 5x + 12, which part represents the variable and which part represents the constant?

Accepted Answer

5x is the variable and 12 is the constant.

Answer

12 is the variable and 5x is the constant.

Answer

Both 5x and 12 are variables.

Question 2

What is the distributive property of multiplication over addition?

Accepted Answer

a(b + c) = ab + ac

Answer

(a + b)c = ac + bc

Answer

a(bc) = abc

Answer

a + b = b + a

Question 3

Which of the following is a constant?

Accepted Answer

5

Answer

x

Answer

y

Answer

2a

Question 4

Simplify the expression: 5(2x + 3)

Accepted Answer

10x + 15

Answer

5x + 3

Answer

10x + 3

Answer

2x + 15

Question 5

Which of the following is a coefficient?

Accepted Answer

2

Answer

x

Answer

y + 5

Answer

3xy

Question 6

Write an equation that represents the perimeter of a rectangle with length l and width w.

Accepted Answer

P = 2l + 2w

Answer

P = l + w

Answer

P = l * w

Answer

P = 2lw

Question 7

Which equation represents the fact that the sum of two numbers is 15?

Accepted Answer

x + y = 15

Answer

x - y = 15

Answer

xy = 15

Answer

x/y = 15

Question 8

Which expression is the simplified form of (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 9

Solve the equation 2y + 6 = 16.

Accepted Answer

y = 4

Answer

y = 5

Answer

y = 6

Answer

y = 7

Question 10

Which of the following is NOT a step in solving the equation 4x - 8 = 12?

Accepted Answer

Multiply both sides by 4.

Answer

Add 8 to both sides.

Answer

Divide both sides by 4.

Answer

Subtract 8 from both sides.

Question 11

Which of the following is the solution to the inequality x - 3 < 2?

Accepted Answer

x < 1

Answer

x < 5

Answer

x > 1

Answer

x > 5

Question 12

Which of the following is an algebraic expression that includes a variable and operations?

Accepted Answer

10 + x

Answer

ten plus x

Answer

x = 5

Answer

the sum of two numbers

Question 13

Translate the phrase "the sum of a number and 5" into an algebraic expression.

Accepted Answer

x + 5

Answer

3x + 5

Answer

5x + 3

Answer

x + 3 + 5

Question 14

Simplify the expression x^2 * x^3 using the laws of exponents.

Accepted Answer

x^6

Answer

x^5

Answer

2x^5

Answer

2x^6

Question 15

Which of the following represents the area of a rectangle with a length of 6 cm and a width of 4 cm?

Accepted Answer

24 cm²

Answer

10 cm

Answer

24 cm

Answer

100 cm²

Question 16

Which graph shows the equation y = x + 2?

Accepted Answer

A line with a slope of 1 and a y-intercept of 2

Answer

A line with a slope of 2 and a y-intercept of 1

Answer

A line with a slope of 1 and a y-intercept of -2

Question 17

What does the expression '2x + 5' represent?

Accepted Answer

The sum of twice a number and 5

Answer

The difference of twice a number and 5

Answer

The product of twice a number and 5

Answer

The quotient of twice a number and 5

Question 18

Which of the following is NOT an algebraic expression?

Accepted Answer

10

Answer

2x + 5

Answer

y - 3

Answer

(a + b) / 2

Question 19

Write an algebraic equation to represent the statement: 'The sum of twice a number and 5 is 15'.

Accepted Answer

2x + 5 = 15

Answer

2x - 5 = 15

Answer

x + 5 = 15

Answer

x - 5 = 15

Question 20

Which of the following is NOT a valid step when solving the equation 2(x - 3) = 10?

Accepted Answer

Subtract 2 from both sides

Answer

Distribute the 2

Answer

Add 3 to both sides

Answer

Divide both sides by 2

Question 21

Represent the numbers greater than or equal to -5 using an inequality.

Accepted Answer

x ≥ -5

Answer

x > -5

Answer

x < -5

Answer

x ≤ -5

Question 22

Which of the following represents the sum of x and y?

Accepted Answer

x + y

Answer

x - y

Answer

x multiplied by y

Answer

x divided by y

Question 23

Which expression is the same as 2(x + 3)?

Accepted Answer

2x + 6

Answer

4x + 3

Answer

6x + 2

Answer

x + 6

Question 24

What is the solution to the equation x - 5 = 10?

Accepted Answer

15

Answer

5

Answer

10

Answer

20

Question 25

Which expression represents '5 more than twice a number'?

Accepted Answer

2x + 5

Answer

2 - 5x

Answer

5 - 2x

Answer

5x + 2

Question 26

A library has 250 books. They buy 35 new books each week. Which equation shows the total number of books (y) after x weeks?

Accepted Answer

y = 250 + 35x

Answer

y = 250 - 35x

Answer

y = 35 + 250x

Answer

y = 35x - 250

Question 27

What are the solutions for x in the inequality x + 5 > 10?

Accepted Answer

x > 5

Answer

x < 5

Answer

x < 10

Question 28

Which equation represents the sentence: 'The sum of twice a number and 5 is greater than 12'?

Accepted Answer

2x + 5 > 12

Answer

2x + 5 < 12

Answer

5x + 2 > 12

Question 29

Which of the following expressions is equivalent to 2x + 5?

Accepted Answer

5 + 2x

Answer

2 * (x + 2.5)

Answer

10 + x

Answer

x^2 + 5

Question 30

Find the value of the expression 3(x - 2) when x = 5.

Accepted Answer

9

Answer

15

Answer

6

Answer

3

Question 31

Which of the following is a one-step equation?

Accepted Answer

x - 5 = 10

Answer

(x + 3)(x - 2) = 0

Answer

x^2 + 2x = 0

Answer

x - y = 5

Question 32

Solve for x: x + 7 = 15

Accepted Answer

8

Answer

7

Answer

22

Answer

15

Question 33

Provide a real-world example of an algebraic expression.

Accepted Answer

The perimeter of a rectangle with length x and width 5 is 2x + 10.

Answer

The Pythagorean theorem is a^2 + b^2 = c^2.

Answer

The volume of a cube with side length s is s^3.

Question 34

What is the distributive property?

Accepted Answer

a(b + c) = ab + ac

Answer

(a + b) + c = a + (b + c)

Answer

a - b = b - a

Question 35

Simplify the expression: 2(x + 3) - 5

Accepted Answer

2x + 1

Answer

x - 5

Answer

2x - 7

Answer

x + 1

Question 36

What is the inverse operation of multiplication?

Accepted Answer

Division

Answer

Addition

Answer

Exponentiation

Answer

Subtraction

Question 37

Which of the following is a variable?

Accepted Answer

x

Answer

=

Answer

5

Answer

+

Question 38

An algebraic expression is a mathematical phrase that contains variables, constants, and operations. Which of the following is an example of an algebraic expression?

Accepted Answer

2x + 5

Answer

x

Answer

x + 5 = 10

Answer

5 = x

Question 39

To solve a one-step equation, we isolate the variable on one side of the equation by performing inverse operations. Solve for x: x + 5 = 10

Accepted Answer

5

Answer

15

Answer

10

Answer

-5

Question 40

In the equation 2y = 12, the variable y is multiplied by 2 to get the result 12. What is the value of y?

Accepted Answer

6

Answer

2

Answer

12

Question 41

A variable represents an unknown value in an algebraic expression. In the expression 2x - 5, which term is the variable?

Accepted Answer

x

Answer

5

Answer

2x

Answer

2

Question 42

Simplifying an algebraic expression means combining like terms. Simplify the expression 2x + 3x - x:

Accepted Answer

4x

Answer

5x

Answer

2x

Answer

x

Question 43

When solving word problems that involve algebraic expressions, we need to translate the problem into an equation. The sum of two numbers is 10. If we let the larger number be x, what is the expression for the smaller number?

Accepted Answer

10 - x

Answer

x - 10

Answer

x + 10

Answer

x

Question 44

Solving an equation means finding the value of the variable that makes the equation true. Solve the equation x - 5 = 10

Accepted Answer

15

Answer

-5

Answer

5

Answer

25

Question 45

Translating word problems into equations requires understanding the mathematical relationships described in the problem. Which of the following situations can be represented by the equation 2x + 5 = 15?

Accepted Answer

Twice a number plus five equals fifteen

Answer

Fifteen less than a number is two

Answer

A number divided by five equals fifteen

Question 46

Simplifying expressions with parentheses requires distributing the factor outside the parentheses to each term inside the parentheses. Simplify the expression 4(x + 2):

Accepted Answer

4x + 8

Answer

8x + 4

Answer

2x + 8

Answer

x + 8

Question 47

Find the value of y that makes the equation true: y + 7 = 15

Accepted Answer

8

Answer

7

Answer

9

Question 48

Which expression represents the perimeter of a rectangle with length x and width 5?

Accepted Answer

2x + 10

Answer

x + 5

Answer

5x + 2

Question 49

Simplify the expression: 2(3x - 4) + 5x:

Accepted Answer

11x - 8

Answer

11x + 8

Answer

5x + 8

Answer

5x - 8