Algebra I Learning Quizzes: Master the Fundamentals of Algebra

Question 1

Solve the inequality: 2x - 5 is greater than 9

Accepted Answer

x is greater than 7

Answer

x is less than 7

Answer

x is greater than 2

Answer

x is less than 2

Question 2

A farmer has x^2 - 5x + 6 square meters of land. To divide it into two equal rectangular plots, what should be the length and width of each plot?

Accepted Answer

(x - 3) meters by (x - 2) meters

Answer

(x + 3)(x - 2) meters by (x - 3) meters

Answer

(x - 3) meters by (x + 2) meters

Answer

(x + 3) meters by (x + 2) meters

Question 3

Factor the quadratic expression: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 3)²

Answer

(x + 3)²

Question 4

Simplify the expression: 4 to the power of negative 3

Accepted Answer

1 over 4 to the power of 3

Answer

Negative 4 to the power of 3

Answer

64

Question 5

Consider the piecewise function:

f(x) = {
  x - 2, if x is less than 0
  2x + 1, if x is greater than or equal to 0
}

At which value of x is the function discontinuous?

Accepted Answer

x = 0

Answer

x = 1

Answer

x = -1

Question 6

Factor the polynomial: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(x + 2)(x + 2)

Answer

(x - 2)(x - 2)

Question 7

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

Accepted Answer

x - 1

Answer

1

Answer

x + 1

Answer

x - 2

Question 8

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = -3, y = -2

Answer

x = -2, y = -3

Question 9

A rectangular garden measures x meters in length and y meters in width. If the garden's perimeter is 30 meters, which equation shows the relationship between x and y?

Accepted Answer

2x + 2y = 30

Answer

x + y = 30

Answer

2x - 2y = 30

Question 10

Which term accurately describes an expression containing only one term?

Accepted Answer

Monomial

Answer

Polynomial

Answer

Binomial

Answer

Trinomial

Question 11

Find the equation of the line parallel to y = 2x + 1 and passes through the point (3, 5)

Accepted Answer

y = 2x + 7

Answer

y = 2x - 1

Answer

y = -2x + 7

Answer

y = -2x - 1

Question 12

Identify the pattern in the sequence: 3, 7, 11, 15, ... Is it arithmetic, geometric, or neither?

Accepted Answer

Arithmetic

Answer

Geometric

Answer

Neither

Answer

Cannot be determined

Question 13

Factor the polynomial x³ - 8 using the difference of cubes formula.

Accepted Answer

(x - 2)(x² + 2x + 4)

Answer

x² + 2x + 4

Answer

x³ + 2x + 4

Question 14

Solve the linear equation 3x - 5 = 14:

Accepted Answer

x = 7

Answer

x = 3

Answer

x = 6

Answer

x = 10

Question 15

Simplify the radical expression √(25x⁴y⁶):

Accepted Answer

5x²y³

Answer

5x²y⁶

Answer

x²y³

Answer

x²y⁶

Question 16

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

Accepted Answer

1 - 2/(x + 3)

Answer

1 + 2/(x + 3)

Answer

(x - 5)/(x + 3)

Answer

Cannot be simplified

Question 17

Factor the polynomial x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Answer

(x + 3)^2

Question 18

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

Accepted Answer

16x^6y^3

Answer

8x^5y^3

Answer

8x^6y^3

Answer

16x^5y^3

Question 19

Which of the following is the standard form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0

Answer

x^2 + by + c = 0

Answer

ax + by + c = 0

Answer

x^2 + bx + c = 0

Question 20

Which of the following is NOT a characteristic of an exponential function?

Accepted Answer

Its rate of change is constant

Answer

It is non-linear

Answer

Its graph increases rapidly

Answer

Its domain is all real numbers

Question 21

Calculate the slope of the line passing through the points (2, 5) and (4, 9).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 22

Find the equation of the line that goes through the point (2, -3) and is parallel to the line y = 2x + 1.

Accepted Answer

y = 2x - 7

Answer

y = -2x - 7

Answer

y = 2x + 1

Answer

y = -2x + 1

Question 23

Find the volume of a rectangular prism with a length of 5 cm, a width of 3 cm, and a height of 2 cm.

Accepted Answer

30 cubic centimeters

Answer

10 cubic centimeters

Answer

15 cubic centimeters

Question 24

Solve the inequality: **3x - 7 > 2**.

Accepted Answer

x > 3

Answer

x < 3

Answer

x < 9

Answer

x > 9

Question 25

Solve the inequality: x + 2 > 5

Accepted Answer

x > 2

Answer

x > 3

Answer

x < 2

Answer

x < 3

Question 26

What is the slope of the line perpendicular to the line y = -2x + 5?

Accepted Answer

2

Answer

-2

Answer

1/2

Answer

-1/2

Question 27

Which of these is the equation of the line with x-intercept 2 and y-intercept -3?

Accepted Answer

y = -2x - 3

Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 3

Question 28

Which of the following functions is a rational function?

Accepted Answer

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

Answer

f(x) = √x

Answer

f(x) = x^3 + 2x

Answer

f(x) = sin(x)

Question 29

Solve the equation: 2(x - 3) = 10

Accepted Answer

8

Answer

12

Answer

10

Answer

5

Question 30

What is the slope of the line represented by the equation: y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 31

Solve the equation: |x - 3| = 5

Accepted Answer

x = 8 or x = -2

Answer

x = 2 or x = -2

Answer

x = -8 or x = 2

Answer

x = 5 or x = -5

Question 32

Solve for x in the equation: 3x - 5 = 10

Accepted Answer

5

Answer

-5

Answer

3

Answer

15

Question 33

Factor the expression: x^2 - 9

Accepted Answer

(x + 3) * (x - 3)

Answer

x * (x - 9)

Answer

3 * (x^2 - 3)

Answer

(x - 3) * (x + 9)

Question 34

Find the domain of the function f(x) = √(x - 2)

Accepted Answer

[2, ∞)

Answer

(-∞, ∞)

Answer

(-∞, 2]

Answer

[0, ∞)

Question 35

Which inequality represents the statement "7 is at least three less than x"?

Accepted Answer

x ≥ 10

Answer

x > 10

Answer

x < 10

Answer

x ≤ 10

Question 36

Which of the following equations has a graph that is perpendicular to the x-axis?

Accepted Answer

y = 4

Answer

y = 2x + 1

Answer

y = x^2 - 1

Answer

y = -x + 3

Question 37

Calculate the slope of the line passing through the points (2, 5) and (4, 9)

Accepted Answer

2

Answer

-2

Answer

1

Question 38

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

x(x - 9)

Answer

(x + 3)^2

Answer

(x - 3)^2

Question 39

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 40

Identify the domain of the function: f(x) = 1/(x - 2)

Accepted Answer

All real numbers except 2

Answer

Only negative real numbers

Answer

All real numbers

Answer

Only positive real numbers

Question 41

Find the solution to the equation: 2x + 5 = 13

Accepted Answer

4

Answer

3

Answer

6

Answer

5

Question 42

Determine the slope of the line described by the equation: y = -2x + 3

Accepted Answer

-2

Answer

-3

Answer

2

Answer

3

Question 43

Graph the inequality: x + 2y > 4

Accepted Answer

Half-plane above the line x + 2y = 4

Answer

Half-plane below the line x + 2y = 4

Answer

Circle centered at (4, 2) with radius 2

Answer

Square with vertices at (4, 6), (6, 4), (4, 2), and (2, 4)

Question 44

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

Accepted Answer

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

Answer

A circle with center at (0, 1) and radius 2.

Answer

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

Answer

A parabola opening upward with a vertex at (0, 1).

Question 45

Factor the expression x^2 - 4:

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

(x + 4)(x - 1)

Question 46

Evaluate the expression sqrt(16 + 9):

Accepted Answer

5

Answer

4

Answer

-5

Answer

25

Question 47

Which of the following is a quadratic equation?

Accepted Answer

x^2 + 2x - 3 = 0

Answer

sqrt(x) + 1 = 0

Answer

2x + 3y = 6

Answer

x - 3 = 0

Question 48

Which of the following graphs represents the inequality y > 2x - 1?

Accepted Answer

A shaded region above a line

Answer

A line with a dashed boundary

Answer

A line with a solid boundary

Answer

A shaded region below a line

Question 49

Factor the following polynomial expression completely: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 9)(x - 1)

Answer

Cannot be factored

Answer

(x - 3)^2

Question 50

Simplify the following expression using exponent rules: (2x^2y)^3

Accepted Answer

8x^6y^3

Answer

6x^6y^3

Answer

8x^5y^3

Question 51

Determine the equation of the line with a slope of -2 and a y-intercept of 3

Accepted Answer

y = -2x + 3

Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = -2x - 3

Question 52

Find the domain of the following function: f(x) = sqrt(x - 5)

Accepted Answer

[5, ∞)

Answer

(-∞, ∞)

Answer

[0, ∞)

Answer

(-∞, 5]

Question 53

Identify which of the following is a quadratic equation:

Accepted Answer

x^2 + 2x - 3 = 0

Answer

x + 2y = 5

Answer

sqrt(x) = 2

Question 54

Solve for *x* in the equation: 3(*x* - 2) = 15

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 55

Which graph represents the equation *y* = 2*x* + 1?

Accepted Answer

(Image of a line with a slope of 2 and y-intercept of 1)

Answer

(Image of a line with a slope of -2 and y-intercept of 1)

Answer

(Image of a line with a slope of 1 and y-intercept of 2)

Answer

(Image of a parabola opening upward)

Question 56

Simplify the radical expression: √(25*x²)

Accepted Answer

5*x

Answer

5*x²

Answer

x/5

Answer

x²/5

Question 57

Which equation represents a line perpendicular to *y* = 3*x* + 2?

Accepted Answer

y = - (1/3)x + b

Answer

y = 3x + b

Answer

y = -3x + b

Answer

y = (1/3)x + b

Question 58

What is the solution to the equation 3(*x* + 2) - 5 = 4*x* - 1?

Accepted Answer

x = 2

Answer

x = -4

Answer

x = 4

Answer

x = -2

Question 59

Simplify the expression: 2*x² + 3*x - 5 + 4*x² - *x* + 2

Accepted Answer

6*x² + 2*x - 3

Answer

6*x² + 4*x - 3

Answer

6*x⁴ + 2*x² - 3

Answer

10*x² + 2*x - 3

Question 60

What is the slope of the line represented by the equation *y* = -2*x* + 5?

Accepted Answer

-2

Answer

5

Answer

2

Answer

-5

Question 61

Which inequality represents the statement: 'Five less than twice a number is at least fifteen'?

Accepted Answer

2*x* - 5 ≥ 15

Answer

5 - 2*x* ≥ 15

Answer

5 - 2*x* ≤ 15

Answer

2*x* - 5 ≤ 15

Question 62

The area of a rectangular garden is represented by the expression (*x* + 3)(*x* - 2). If the length is (*x* + 3), what is the width?

Accepted Answer

x - 2

Answer

x + 6

Answer

x + 2

Answer

x - 3

Question 63

What is the *y*-intercept of the line that passes through the points (2, 5) and (4, 11)?

Accepted Answer

-1

Answer

2

Answer

3

Answer

1

Question 64

What is the solution to the inequality 4x - 7 < 9?

Accepted Answer

x < 4

Answer

x ≥ 4

Answer

x ≤ 4

Answer

x > 4