Algebra 1 Quizzes: Master the Fundamentals of Algebra

Question 1

Consider the linear equation y = 2x - 5. Which statement accurately describes the line represented by this equation?

Accepted Answer

The line crosses the y-axis at (0, -5).

Answer

The line's slope is -5.

Answer

The line runs parallel to the x-axis.

Question 2

Simplify the polynomial expression (2x + 3)(x - 5).

Accepted Answer

2x^2 - 10x + 3

Answer

2x^2 + 10x - 3

Answer

2x^2 - 10x - 3

Answer

2x^2 + 10x + 3

Question 3

Write the equation of the line that passes through the point (3, -4) and has a slope of 2.

Accepted Answer

y = 2x - 2

Answer

y = 2x - 10

Answer

y = -2x - 10

Answer

y = -2x - 2

Question 4

Which of the following is a polynomial of the third degree (cubic)?

Accepted Answer

x^3 - 2x^2 + x - 3

Answer

x^2 + 2x - 1

Answer

2x^4 - 3x^3 + 4x^2 - 5x + 6

Answer

5x^5 - 4x^4 + 3x^3 - 2x^2 + x - 1

Question 5

Solve the inequality: 2x - 5 > 7.

Accepted Answer

x > 6

Answer

x < 6

Answer

x > -6

Answer

x < -6

Question 6

The graph of the inequality y < 2x + 1 is a straight line.

Accepted Answer

True, and the line is shaded below.

Answer

True, and the line is shaded above.

Answer

False, the line is vertical.

Answer

False, the line is horizontal.

Question 7

What is the degree of the polynomial 3x^4 - 2x^3 + 5?

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 8

Which of these is a quadratic equation?

Accepted Answer

x^2 - 3x + 2 = 0

Answer

x + 2 = 5

Answer

y = 2x - 1

Answer

x^3 + 2x = 0

Question 9

What is the slope of the line that passes through the points (1, 3) and (3, 7)?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 10

Solve the equation: 2(x + 1) - 5 = 11

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 11

Factor the polynomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

(x - 1)(x + 9)

Answer

Cannot be factored

Question 12

Solve the system of equations: x + y = 10, x - y = 2

Accepted Answer

x = 6, y = 4

Answer

x = 4, y = 6

Answer

x = 2, y = 8

Answer

x = 8, y = 2

Question 13

Write the inequality that represents the statement: "The number x is greater than or equal to 5"

Accepted Answer

x ≥ 5

Answer

x ≤ 5

Answer

x < 5

Answer

x > 5

Question 14

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

Accepted Answer

x^6y^-6

Answer

x^6y^6

Answer

x^3y^6

Answer

x^3y^-6

Question 15

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

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 + 7x - 15

Answer

2x^2 - 17x + 15

Answer

2x^2 + 17x + 15

Question 16

Factor the polynomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)^2

Answer

(x - 3)^2

Answer

Cannot be factored

Question 17

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

Accepted Answer

10x + 2

Answer

10x - 2

Answer

14x + 2

Answer

14x - 2

Question 18

Determine the slope of the line passing through the points (2, 3) and (5, 10).

Accepted Answer

2

Answer

1

Answer

-1

Answer

-2

Question 19

For the function f(x) = |x - 2| + 1, determine its domain and range.

Accepted Answer

Domain: (-∞, ∞); Range: [1, ∞)

Answer

Domain: (2, ∞); Range: [1, ∞)

Answer

Domain: (-∞, ∞); Range: (1, ∞)

Question 20

Which of the following is NOT a property of inequalities?

Accepted Answer

If a plus b is greater than c, then a is greater than c.

Answer

If a is greater than b and b is greater than c, then a is greater than c.

Answer

If a is greater than b, then -a is less than -b.

Answer

If both a and b are positive, then their product ab is also positive.

Question 21

Factor the following expression: x squared minus 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(x + 2)(x - 4)

Answer

(x - 2) squared

Question 22

What is the domain of the function f(x) = the square root of x - 2?

Accepted Answer

[2, ∞)

Answer

[-2, ∞)

Answer

[-∞, 2]

Answer

[2, ∞]

Question 23

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 6

Answer

x = 4

Answer

x = 8

Answer

x = 10

Question 24

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

Accepted Answer

6a + 2b

Answer

6a - 8b

Answer

8a - 2b

Answer

8a + 8b

Question 25

Factor the quadratic trinomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 2)(x + 2)

Answer

(x - 1)(x + 1)

Answer

(x - 4)(x + 4)

Question 26

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 4 = 0

Answer

x + y = 5

Answer

y = 3x + 2

Answer

x - 2y = 1

Question 27

Simplify the algebraic expression: (2x - 3) + (5x + 7)

Accepted Answer

7x + 4

Answer

3x + 4

Answer

3x - 10

Answer

7x - 10

Question 28

Factor the quadratic polynomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

(x - 3)^2

Question 29

Which inequality represents the graph below? [Image of a graph of y < 2x + 3]

Accepted Answer

y < 2x + 3

Answer

y > 2x + 3

Answer

y ≥ 2x + 3

Answer

y ≤ 2x + 3

Question 30

Factor the polynomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)^2

Answer

(x - 3)^2

Answer

Cannot be factored

Question 31

Which of the following is NOT a characteristic of a linear function?

Accepted Answer

Range of all real numbers

Answer

Constant rate of change

Answer

Straight line graph

Answer

Domain of all real numbers

Question 32

Which of the following is the slope of the line passing through the points (2, 3) and (4, 7)?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 33

Solve for x: |x - 4| = 6

Accepted Answer

x = 2, x = 10

Answer

x = 10

Answer

x = -2, x = -10

Answer

No solution

Question 34

Which of the following is a quadratic equation?

Accepted Answer

x^2 + 2x - 3 = 0

Answer

x^3 - 2x + 1 = 0

Answer

x^2 - x^3 + 2 = 0

Answer

x^4 + x^2 - 1 = 0

Question 35

Evaluate the expression: 2^3 - 5 * (-2)

Accepted Answer

23

Answer

3

Answer

-3

Answer

15

Question 36

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

Accepted Answer

A straight line with a positive slope

Answer

A circle

Answer

A parabola

Answer

A straight line with a negative slope

Question 37

Which equation below represents a linear equation?

Accepted Answer

y = 2x + 3

Answer

y = x^2 + 2x - 1

Answer

y = (x - 1)^2

Answer

y = sin(x)

Question 38

Solve the linear equation: 2x - 5 = 11

Accepted Answer

x = 8

Answer

x = 3

Answer

x = -3

Answer

x = -8

Question 39

Identify the quadratic inequality:

Accepted Answer

x^2 + 2x - 3 > 0

Answer

x < 5

Answer

y > x

Answer

2x = 4

Question 40

Factor the quadratic expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Question 41

Solve the linear inequality: 3x - 5 > 10

Accepted Answer

x > 5

Answer

x < 5

Question 42

Calculate the slope of the line joining the points (2, 3) and (-1, -2):

Accepted Answer

-1

Question 43

Write 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

Question 44

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

Accepted Answer

4x^4y^6

Answer

4x^4y^5

Question 45

Find the **solution** to the equation x + 5 = 10.

Accepted Answer

5

Answer

-5

Answer

15

Answer

25

Question 46

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

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(-3, 2)

Answer

(-2, 3)

Question 47

Identify the **quadratic equation**:

Accepted Answer

x^2 + 3x + 2 = 0

Answer

x + 2 = 0

Answer

2x - 5 = 0

Answer

x^3 - 2x + 1 = 0

Question 48

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

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

x < 2

Question 49

Solve the **inequality**: |x - 1| < 3

Accepted Answer

-2 < x < 4

Answer

-4 < x < 2

Answer

x < -4 or x > 2

Answer

x > -2 or x < 4

Question 50

Write the equation of the parabola with **vertex** (2, -3) and **focus** (4, -3):

Accepted Answer

y = (x - 2)^2 - 3

Answer

y = (x + 2)^2 - 3

Answer

y = (x - 4)^2 - 3

Answer

y = (x + 4)^2 - 3

Question 51

What is the equation of the line perpendicular to the line y = 2x + 1 and passing through the point (1, 3)?

Accepted Answer

y = -1/2x + 2.5

Answer

y = 1/2x + 2.5

Answer

y = -2x + 4

Answer

y = 2x + 2

Question 52

Solve the following 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 53

Write the equation of the line with slope -2 and y-intercept 5. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Accepted Answer

y = -2x + 5

Answer

y = 2x + 5

Answer

y = -5x + 2

Answer

y = 5x - 2

Question 54

Factor the polynomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 3)^2

Question 55

Simplify the algebraic expression: 2(x - 1)

Accepted Answer

2x - 2

Answer

x - 2

Answer

2x + 2

Answer

4x - 2

Question 56

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 57

The inequality 'The number y is greater than or equal to -5' can be represented as:

Accepted Answer

y ≥ -5

Answer

y > -5

Answer

y < -5

Answer

y ≤ -5

Question 58

The graph of the equation y = 2x - 1 is a:

Accepted Answer

Line with slope 2 and y-intercept -1

Answer

Line with slope -2 and y-intercept 1

Answer

Parabola with vertex (1, -2)

Answer

Circle with center (0, 1) and radius 2

Question 59

To find the slope of the line passing through the points (2, 5) and (4, 9), we can use the formula:

Accepted Answer

Slope = (change in y) / (change in x)

Answer

Slope = (change in x) / (change in y)

Answer

Slope = (y1 + y2) / 2

Answer

Slope = (x1 + x2) / 2

Question 60

An example of a quadratic equation is:

Accepted Answer

x^2 - 3x + 2 = 0

Answer

x + y = 5

Answer

y = 2x - 1

Answer

x^3 + 2x^2 - 5 = 0

Question 61

To solve the quadratic equation x^2 - 5x + 6 = 0 by factoring, we need to find two numbers that:

Accepted Answer

Multiply to give 6 and add to give -5

Answer

Multiply to give -6 and add to give 5

Answer

Multiply to give 6 and subtract to give 5

Answer

Multiply to give -6 and subtract to give -5

Question 62

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

Accepted Answer

3x^2 + 7x + 4

Answer

3x^2 + 3x + 2

Answer

3x^2 - x + 2

Answer

3x^2 + x + 4

Question 63

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

Accepted Answer

y = -2x + 3

Answer

y = 3x - 2

Answer

y = 2x - 3

Answer

y = -3x + 2

Question 64

Solve the quadratic equation: 2x^2 - 5x + 3 = 0

Accepted Answer

x = 1 or x = 3/2

Answer

x = 2 or x = 3

Answer

x = 1 or x = -3/2

Answer

x = 2 or x = -3