Algebra Learning Quizzes: Master Equations, Inequalities, and More

Question 1

Which of the following is NOT a practical application of algebra?

Accepted Answer

Creating art

Answer

Solving real-world problems

Answer

Predicting patterns

Answer

Developing computer programs

Question 2

Determine the equation of the line passing through the points (2, 5) and (-1, 9).

Accepted Answer

y = -2x + 9

Answer

y = x + 9

Answer

y = 2x + 9

Answer

y = -2x + 5

Question 3

Simplify the expression: (3x^2y)^-3

Accepted Answer

1/(27x^6y^3)

Answer

x^6y^3

Answer

x^6y^3/27

Answer

27x^6y^3

Question 4

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x + 3)

Answer

(x + 3)

Answer

(x + 9)(x - 9)

Question 5

Solve the linear equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 3

Question 6

Factor the quadratic expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x + 3)^2

Answer

(x - 3)^2

Question 7

Evaluate the polynomial expression: 3x^2 - 2xy + y^2, when x = 2 and y = 1

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 8

Which of the following is a linear function?

Accepted Answer

f(x) = 2x + 5

Answer

f(x) = x^2 + 2x + 1

Answer

f(x) = e^x

Answer

f(x) = 1/x

Question 9

Solve for *x* in the equation: 3*x* + 5 = 14

Accepted Answer

x = 3

Answer

x = 6

Answer

x = 1

Answer

x = -3

Question 10

Which of the following values of *x* satisfies the inequality 2*x* - 3 > 7?

Accepted Answer

x = 6

Answer

x = 5

Answer

x = 2

Answer

x = -2

Question 11

Find the solution to the system of equations: 2*x* + *y* = 7 and *x* - *y* = 1

Accepted Answer

x = 3, y = 1

Answer

x = 1, y = 5

Answer

x = 2, y = 3

Answer

x = 4, y = -1

Question 12

Simplify the expression: (*x*² + 3*x* - 4) - (*x*² - 2*x* + 1)

Accepted Answer

5*x* - 5

Answer

*x*² + *x* - 3

Answer

*x*² + 5*x* - 5

Answer

2*x* - 3

Question 13

Factor the expression: *x*² - 9

Accepted Answer

(*x* + 3)(*x* - 3)

Answer

(*x* + 9)(*x* - 1)

Answer

(*x* - 9)(*x* + 1)

Answer

(*x* - 3)²

Question 14

Which of the following equations is a quadratic equation?

Accepted Answer

2*x*² + 5*x* - 3 = 0

Answer

*x*³ - 2*x* + 1 = 0

Answer

*x* + *y* = 5

Answer

3*x* + 7 = 12

Question 15

Solve the quadratic equation: *x*² - 4*x* + 3 = 0

Accepted Answer

x = 1, x = 3

Answer

x = -1, x = -3

Answer

x = 2, x = 1

Answer

x = 4, x = -1

Question 16

The graph of a linear equation is always a:

Accepted Answer

Straight line

Answer

Hyperbola

Answer

Circle

Answer

Parabola

Question 17

What is the slope of the line represented by the equation *y* = 2*x* + 3?

Accepted Answer

2

Answer

-3

Answer

3

Answer

-2

Question 18

A rectangular garden has a length of (*x* + 5) meters and a width of (*x* - 2) meters. What is the area of the garden in terms of *x*?

Accepted Answer

*x*² + 3*x* - 10

Answer

*x*² + 7*x* + 10

Answer

*x*² - 10

Answer

2*x* + 3

Question 19

Which of the following is the solution to the linear equation 2x + 5 = 13?

Accepted Answer

x = 4

Answer

x = 6

Answer

x = 3

Answer

x = 5

Question 20

Solve the inequality: |x - 2| > 4

Accepted Answer

x < -2 or x > 6

Answer

x > -2 or x < 6

Answer

x > 2 or x > 6

Answer

x < 2 or x > 6

Question 21

Find the value of x in the equation system: 2x + y = 5, x - y = 1

Accepted Answer

x = 2

Answer

x = 4

Answer

x = 3

Answer

x = 1

Question 22

Factor the polynomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x + 3)(x - 3)

Answer

Cannot be factored

Question 23

Solve the quadratic equation: x^2 + 5x + 6 = 0

Accepted Answer

x = -2 or x = -3

Answer

x = 2 or x = 3

Answer

x = 1 or x = -4

Answer

x = -1 or x = 4

Question 24

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

Accepted Answer

2x^2 - x - 6

Answer

2x^2 + x - 6

Answer

x^2 - x - 6

Question 25

Find the slope of the line passing through the points (2, 3) and (5, 9)

Accepted Answer

2

Answer

4

Answer

1

Answer

3

Question 26

Which of the following is the equation of the line with slope 2 and y-intercept 3?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

y = x + 3

Question 27

Find the domain of the function: f(x) = sqrt(x - 4)

Accepted Answer

x ≥ 4

Answer

x ≤ 4

Answer

x > 4

Answer

x < 4

Question 28

Simplify the expression: (x + 2)/(x - 2) + (x - 2)/(x + 2)

Accepted Answer

4/(x^2 - 4)

Answer

0

Answer

x/(x^2 - 4)

Answer

x^2/(x^2 - 4)

Question 29

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 6

Answer

x = 8

Question 30

Which inequality represents the solution set of the graph?

Accepted Answer

y > 2x + 1

Answer

y > -2x + 1

Answer

y < 2x + 1

Answer

y < -2x + 1

Question 31

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

Accepted Answer

x = 3, y = 2

Answer

x = 1, y = 4

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Question 32

Simplify the polynomial: (2x^2 - 3x + 5) + (x^2 - 2x + 1)

Accepted Answer

3x^2 - 5x + 6

Answer

2x^2 - 5x + 4

Answer

3x^2 + x + 6

Question 33

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x + 3)^2

Answer

(x - 3)^2

Question 34

Solve the quadratic equation: x^2 - 5x + 6 = 0

Accepted Answer

x = 2 or x = 3

Answer

x = -2 or x = 3

Answer

x = -2 or x = -3

Answer

x = 2 or x = -3

Question 35

What is the slope of the line passing through the points (2, 5) and (4, 9)?

Accepted Answer

2

Answer

1

Answer

-1

Answer

-2

Question 36

Which point does NOT lie on the line y = 2x + 1?

Accepted Answer

(3, 5)

Answer

(1, 3)

Answer

(2, 5)

Answer

(4, 9)

Question 37

What is the distance between the points (1, 2) and (5, 6)?

Accepted Answer

5 units

Answer

3 units

Answer

6 units

Answer

4 units

Question 38

What is the area of the rectangle with length 4 cm and width 3 cm?

Accepted Answer

12 cm^2

Answer

16 cm^2

Answer

24 cm^2

Answer

8 cm^2