Master Algebra Basics: Introduction to Algebra Learning Quizzes

Question 1

Which of the following expressions is an algebraic expression?

Accepted Answer

5 + x

Answer

x = 5

Answer

The sum of 5 and x

Answer

5 is greater than x

Question 2

Simplify the algebraic expression: 3x + 2y - x + 5y

Accepted Answer

2x + 7y

Answer

4x + 7y

Answer

2x - 3y

Answer

4x - 3y

Question 3

Which of the following equations is a quadratic equation?

Accepted Answer

x^2 + 2x + 1 = 0

Answer

x + 2 = 5

Answer

x^3 - 2x + 1 = 0

Answer

x^4 + 2x^2 + 1 = 0

Question 4

Simplify the expression by combining like terms: 3x - 2x + 5

Accepted Answer

x + 5

Answer

x - 5

Answer

5x - 2

Answer

2x + 5

Question 5

Which of the following equations represents a line with a slope of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

x = 2y + 3

Answer

3x = 2y + 3

Question 6

Solve the system of equations: 
x + y = 5
x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Question 7

What is a variable?

Accepted Answer

A letter or symbol that represents a changing value

Answer

A fixed value

Answer

An equation

Answer

A graph

Question 8

Which of the following graphs represents the equation $$y = x^2$$?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

A hyperbola

Question 9

Which of the following is an example of an algebraic inequality?

Accepted Answer

$$y > x$$

Answer

$$y = x + 2$$

Answer

$$y^2 = 4$$

Answer

$$x + y = 5$$

Question 10

Determine the equation of the line with a slope of 2 and a y-intercept of -1:

Accepted Answer

y = 2x - 1

Answer

y = -2x + 1

Answer

y = x - 2

Answer

y = -x + 2

Question 11

Which of the following is NOT a term in the algebraic expression '2x + 3y - 5'?

Accepted Answer

-x

Answer

2x

Answer

3y

Answer

5

Question 12

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

Accepted Answer

2x^2 + 5x - 12

Answer

2x^2 - 5x - 12

Answer

2x^2 + 8x - 12

Answer

2x^2 - 8x - 12

Question 13

Solve the system of linear equations: x + y = 5, x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Question 14

Which of the following is NOT a term used in algebra?

Accepted Answer

Coefficient

Answer

Variable

Answer

Constant

Answer

Expression

Question 15

Which of the following is the graph of the equation y = 2x + 1?

Accepted Answer

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

Answer

A horizontal line passing through y = 1

Answer

A vertical line passing through x = 1

Answer

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

Question 16

An algebraic expression contains variables, constants, and mathematical operators. Which of the following is an algebraic expression?

Accepted Answer

x - 2

Answer

5 + 3

Answer

y = 5

Answer

3^2

Question 17

Simplify the algebraic expression: 2x + 5x - 3.

Accepted Answer

7x - 3

Answer

7x + 3

Answer

2x - 3

Answer

2x + 3

Question 18

Solve for x in the equation: x - 5 = 10.

Accepted Answer

x = 15

Answer

x = 5

Answer

x = -5

Answer

x = 2

Question 19

Translate the following word phrase into an algebraic expression: The sum of two numbers.

Accepted Answer

x + y

Answer

2 + x

Answer

(x + y) / 2

Answer

x - y

Question 20

An inequality represents a relationship between two expressions where one is greater than, less than, or equal to the other. Which of the following expressions represents a number greater than 10?

Accepted Answer

10 + z

Answer

x - 2

Answer

y / 5

Answer

15 - a

Question 21

When simplifying algebraic expressions involving exponents, we multiply the coefficients and add the exponents of like terms. Simplify the expression: (x^2 * y^3) / (xy).

Accepted Answer

x * y^2

Answer

x * y

Answer

x^2 * y^2

Answer

x^3 * y^3

Question 22

A linear equation is a mathematical equation in which the highest exponent of the variable is 1. Which of the following is a linear equation?

Accepted Answer

2x + 3y = 6

Answer

y = x^2

Answer

y - 1 = 1 / x

Answer

x^3 + 5 = 0

Question 23

Factor the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)

Answer

x(x - 9)

Answer

(x^2 - 3)

Question 24

Solve this inequality: 2x - 5 < 11

Accepted Answer

x < 8

Answer

x > 8

Answer

x < -3

Answer

x > -3

Question 25

Solve for x in the equation: 2x - 5 = 15

Accepted Answer

x = 10

Answer

x = 20

Answer

x = -5

Answer

x = 5

Question 26

Which of the following is a variable?

Accepted Answer

x

Answer

+

Answer

5

Question 27

Identify the coefficient in the expression: 5x - 2

Accepted Answer

5

Answer

-2

Answer

x

Question 28

Which of the following is a constant term?

Accepted Answer

5

Answer

2x

Answer

x

Question 29

Find an equivalent expression to 2(x + 3):

Accepted Answer

2x + 6

Answer

x + 6

Answer

x + 3

Answer

4x + 3

Question 30

Identify the algebraic expression below:

Accepted Answer

2x + 5

Answer

The sum of two numbers

Answer

A fraction

Question 31

Identify the quadratic equation:

Accepted Answer

x^2 + 2x - 3 = 0

Answer

y = 2x + 1

Answer

x + 2 = 3

Answer

2x = 6

Question 32

Factor the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 4)(x - 4)

Answer

(x - 2)(x - 2)

Question 33

Solve the inequality: 2x - 5 > 11

Accepted Answer

x > 8

Answer

x > -8

Answer

x < 8

Answer

x < -8

Question 34

A rental company charges a monthly fee of $20 plus $0.10 per mile driven. Express the total cost of renting a car for m miles algebraically:

Accepted Answer

20 + 0.10m

Answer

20m + 0.10

Answer

0.10 + 20m

Answer

0.10m + 20

Question 35

Identify the rational number:

Accepted Answer

-3/4

Answer

π

Answer

√2

Question 36

In the equation y = 2x + 3, what does the variable 'y' represent?

Accepted Answer

An unknown number

Answer

The coefficient of x

Answer

The steepness of the line

Answer

The starting value of y

Question 37

Which expression is equivalent to (2x)(3y)?

Accepted Answer

6xy

Answer

x + 3y

Answer

2x * 3y

Question 38

Determine the slope of the line represented by the equation y = -2x + 5:

Accepted Answer

-2

Answer

-5

Answer

2

Answer

5

Question 39

Find the greatest common factor (GCF) of the expression 12x^2y and 18xy^2:

Accepted Answer

6xy

Answer

2x

Answer

y

Question 40

Which equation represents a line that is parallel to the x-axis?

Accepted Answer

y = 3

Answer

y = -x + 5

Answer

y = x^2 - 2

Answer

y = 2x + 1

Question 41

Determine the domain of the function f(x) = sqrt(x - 2):

Accepted Answer

x ≥ 2

Answer

All real numbers

Answer

x ≤ 2

Answer

x > 2

Question 42

Which of the following is an example of an algebraic expression?

Accepted Answer

2x + 5

Answer

sin(θ) = 0.5

Answer

y = 3

Answer

John is 6 feet tall

Question 43

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

Accepted Answer

3x - 1

Answer

x - 11

Answer

9x - 6

Answer

3x - 6

Question 44

What is the solution for *x* in the equation: 2x - 5 = 11?

Accepted Answer

8

Answer

5

Answer

-3

Answer

16

Question 45

In the equation y = 2x + 3, what is the slope of the line?

Accepted Answer

2

Answer

-2

Answer

3

Answer

1

Question 46

What is the factored form of the expression: x² - 9?

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

(x - 3)²

Answer

Cannot be factored

Question 47

What is the value of the expression 3x + 5 when x = 2?

Accepted Answer

11

Answer

16

Answer

8

Question 48

Which of the following is a solution to the equation 2x - 3 = 7?

Accepted Answer

x = 5

Answer

x = -2

Answer

x = 2

Answer

x = -5

Question 49

The perimeter of a rectangle is 20 cm. If the length is 7 cm, what is the width?

Accepted Answer

3 cm

Answer

10 cm

Answer

13 cm

Question 50

Which of the following is an example of an algebraic expression?

Accepted Answer

2x + 3

Answer

x > 5

Answer

x = 5

Answer

2 + 3 = 5

Question 51

Simplify the expression: 4x - 2x + 7

Accepted Answer

2x + 7

Answer

2x + 14

Answer

6x + 7

Answer

4x + 9

Question 52

Which of the following is the correct translation of the phrase 'five less than twice a number' into an algebraic expression?

Accepted Answer

2x - 5

Answer

5 - 2x

Answer

5x - 2

Answer

2x + 5

Question 53

Solve for y:  3y - 6 = 12

Accepted Answer

y = 6

Answer

y = -2

Answer

y = 2

Answer

y = -6

Question 54

What is the coefficient of x in the expression 5x + 2?

Accepted Answer

5

Answer

2

Answer

7

Answer

x

Question 55

A store sells apples for $1 each and oranges for $0.50 each. If you buy 'a' apples and 'o' oranges, which expression represents the total cost?

Accepted Answer

a + 0.5o

Answer

a + o

Answer

1.5(a + o)

Answer

0.5a + o

Question 56

Which of the following is an example of a variable?

Accepted Answer

x

Answer

+

Answer

5