Master Linear Equations and Inequalities: Practice Quiz for Twelfth Graders

Question 1

Which inequality represents the statement 'A number y is less than or equal to 10'?

Accepted Answer

y ≤ 10

Answer

y < 10

Answer

y > 10

Answer

y ≥ 10

Question 2

Which of the following is an equation of the line parallel to y = 2x + 1 and passing through the point (3, 5)?

Accepted Answer

y = 2x + 5

Answer

y = 2x + 7

Answer

y = 2x - 1

Answer

y = 2x + 3

Question 3

Which of the following is NOT a step in solving a compound inequality?

Accepted Answer

Use the distributive property

Answer

Isolate the variable term

Answer

Reverse the inequality symbol if multiplying or dividing by a negative

Answer

Combine like terms

Question 4

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

Accepted Answer

y = 2x + 8

Answer

y = 2x - 8

Answer

y = -2x - 8

Answer

y = -2x + 8

Question 5

Solve the inequality: 3x - 4 > 13.

Accepted Answer

x > 5.7

Answer

x < -3

Answer

x < 5.7

Answer

x > -3

Question 6

Graph the linear equation: y = 2x - 1.

Accepted Answer

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

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

Answer

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

Question 7

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

Accepted Answer

y = 3x + 2

Answer

y = 2x + 3

Answer

y = x + 5

Answer

y = 3x - 2

Question 8

A farmer has 100 feet of fencing to enclose a rectangular area. Determine the maximum possible area that can be enclosed.

Accepted Answer

5000 square feet

Answer

2500 square feet

Answer

10000 square feet

Answer

20000 square feet

Question 9

Which step is NOT involved in solving linear equations?

Accepted Answer

Using guess-and-check method

Answer

Isolating the variable on one side of the equation

Answer

Combining similar terms

Answer

Multiplying or dividing by the same number on both sides

Question 10

Solve the linear equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7

Question 11

Graph the inequality: y > 2x + 1 on the coordinate plane.

Accepted Answer

A line with a slope of 2 and y-intercept of 1, shaded above the line

Answer

A line with a slope of -2 and y-intercept of 1, shaded above the line

Answer

A line with a slope of 2 and y-intercept of 1, shaded below the line

Answer

A line with a slope of -2 and y-intercept of 1, shaded below the line

Question 12

Find the solution to the system of linear equations: x + y = 3, x - y = 1

Accepted Answer

(x = 2, y = 1)

Answer

(x = 1, y = 2)

Answer

(x = 3, y = 0)

Answer

The system has no solution

Question 13

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

Accepted Answer

2x + 4

Answer

x + 4

Answer

x + 8

Answer

2x + 8

Question 14

Which statement accurately describes the graph of the equation y = -x + 2?

Accepted Answer

The slope is -1 and the y-intercept is 2

Answer

The slope is 1 and the y-intercept is -2

Answer

The slope is -2 and the y-intercept is 1

Answer

The slope is 2 and the y-intercept is -1

Question 15

Identify the linear inequality in two variables:

Accepted Answer

x + y > 5

Answer

x^2 + y^2 = 1

Answer

|x - y| < 3

Answer

e^(x+y) = 10

Question 16

Calculate the slope of the line passing through the points (2, 3) and (5, 7)

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 17

Solve the quadratic equation by factoring: (x - 2)(x + 3) = 0

Accepted Answer

x = 2 or x = -3

Answer

x = -2 or x = 3

Answer

x = 1 or x = -4

Answer

The equation has no solution

Question 18

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

Accepted Answer

2x² - 3x + 3

Answer

2x² + x - 3

Answer

2x² - x + 3

Answer

2x² + 3x - 3

Question 19

Factor the expression: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)²

Answer

(x + 3)²

Answer

Cannot be factored

Question 20

Which of the following is a quadratic equation?

Accepted Answer

x² - 3x + 2 = 0

Answer

x + y = 5

Answer

2x - 1 > 5

Answer

y = 2x + 3

Question 21

Solve the inequality 3x - 4 > 10.

Accepted Answer

x > 2

Answer

x < -2

Answer

x < 2

Answer

x > -2

Question 22

What is the slope-intercept form of a linear equation?

Accepted Answer

y = mx + b

Answer

y = x + b

Answer

y = mx

Answer

y = b

Question 23

Which of the following is the equation of a line parallel to the x-axis?

Accepted Answer

y = 2

Answer

y = x

Answer

y = 2x

Answer

y = -2x

Question 24

Which of the following is used to determine if a point lies on a given line?

Accepted Answer

Point-slope form

Answer

Slope-intercept form

Answer

Standard form

Answer

None of these

Question 25

What is the domain of the inequality x > 5?

Accepted Answer

(5, ∞)

Answer

(-∞, 5)

Answer

[5, ∞)

Answer

(-∞, ∞)

Question 26

Which of the following equations is in slope-intercept form (y = mx + b)?

Accepted Answer

y = mx + b

Answer

Ax + By = C

Answer

x = my + b

Answer

y = mx - b

Question 27

Which inequality is represented by the graph below?

[Image of a graph showing the shaded area below the line y = 2x - 1]

Accepted Answer

y < 2x - 1

Answer

y > 2x - 1

Answer

y ≤ 2x - 1

Answer

y ≥ 2x - 1

Question 28

Which system of equations has no solution?

Accepted Answer

x - y = 3
y = -x

Answer

x + y = 5
y = 2

Answer

2x + 3y = 6
y = -2x + 2

Answer

x + 2y = 4
y = -x + 1

Question 29

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

Accepted Answer

y = -1/2x + 8

Answer

y = 1/2x + 8

Answer

y = -2x + 11

Answer

y = 2x + 11

Question 30

Solve the system of inequalities:
x ≥ 2
y ≤ 3x - 1?

Accepted Answer

x ≥ 2, y ≤ 3x - 1

Answer

x ≥ 2, y ≥ 3x - 1

Answer

x ≤ 2, y ≤ 3x - 1

Answer

x ≤ 2, y ≥ 3x - 1

Question 31

Which of the following is the slope-intercept form of a linear equation, where 'm' represents the slope and 'b' represents the y-intercept?

Accepted Answer

y = mx + b

Answer

Ax + By = C

Answer

x = my + b

Answer

y = mx - b

Question 32

Solve the linear equation: 3x - 5 = 10.

Accepted Answer

x = 7

Answer

x = 1

Answer

x = 3

Answer

x = 5

Question 33

Find the solution to the inequality x + 2 > 5.

Accepted Answer

x > 3

Answer

x < 3

Answer

x < -3

Answer

x > -3

Question 34

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

Accepted Answer

(x = 3, y = 2)

Answer

(x = 2, y = 3)

Answer

(x = -2, y = -3)

Answer

(x = -3, y = -2)

Question 35

Which operation is the inverse of multiplication when working with linear equations?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Exponentiation

Question 36

Find the equation of the line that passes through point (-2, 5) and has a slope of 3.

Accepted Answer

y = 3x + 11

Answer

y = 3x - 1

Answer

y = -3x + 11

Answer

y = -3x - 1

Question 37

Which system of equations has the solution (-1, 2)?

Accepted Answer

2x + y = 1, x - y = 3

Answer

2x + y = -1, x - y = 3

Answer

2x - y = 1, x + y = 3

Answer

2x - y = -1, x + y = 3

Question 38

Which equation represents a horizontal line?

Accepted Answer

y = 5

Answer

y = 5x

Answer

x = 5

Answer

x = 5y

Question 39

Which graph represents the inequality y < 2x + 1?

Accepted Answer

A shaded region below the line y = 2x + 1

Answer

A shaded region above the line y = 2x + 1

Answer

A shaded region to the left of the line y = 2x + 1

Answer

A shaded region to the right of the line y = 2x + 1

Question 40

Which formula calculates the distance between two points (x1, y1) and (x2, y2)?

Accepted Answer

√((x1 - x2)² + (y1 - y2)²)

Answer

√((x2 - x1)²)

Answer

√((x2 - x1)² + (y2 - y1)²)

Answer

√((y2 - y1)²)

Question 41

Which equation represents a line perpendicular to y = 2x - 1?

Accepted Answer

y = -1/2x + 3

Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = 1/2x + 3

Question 42

What is the graph of the linear equation *y* = -2*x* + 1?

Accepted Answer

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

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

Answer

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

Question 43

Solve the inequality: 3*x* - 4 < 10

Accepted Answer

x < 4.67

Answer

x < 2

Answer

x > 4.67

Answer

x > 2

Question 44

What are the solutions for *x* in the equation: |*x* - 3| = 5?

Accepted Answer

x = 8 or x = -2

Answer

x = 3 or x = -3

Answer

x = 2 or x = -2

Answer

x = 5 or x = -5

Question 45

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

Accepted Answer

y = x + 2

Answer

y = -x + 2

Answer

y = -x - 2

Answer

y = x - 2

Question 46

Solve for *x* in the equation: 2*x* + 5 = 15

Accepted Answer

x = 5

Answer

x = 20

Answer

x = 10

Answer

x = 1

Question 47

What is the graph of the inequality *y* > 2*x* - 3?

Accepted Answer

A line with a slope of 2 and a *y*-intercept of -3, shaded above the line.

Answer

A line with a slope of 2 and a *y*-intercept of -3, shaded below the line.

Answer

A line with a slope of -2 and a *y*-intercept of 3, shaded below the line.

Answer

A line with a slope of -2 and a *y*-intercept of -3, shaded above the line.

Question 48

What is the solution region for the system of inequalities:  x + y ≤ 5 and y ≥ -x + 1?

Accepted Answer

The shaded region below the line y = -x + 1 and to the left of the line x + y = 5.

Answer

The shaded region below the line y = -x + 1 and to the right of the line x + y = 5.

Answer

The shaded region above the line y = -x + 1 and to the right of the line x + y = 5.

Question 49

What is the equation of the line that passes through the points (2, 5) and (-1, 1)?

Accepted Answer

y = x + 3

Answer

y = -x - 3

Answer

y = x - 3

Answer

y = -x + 3

Question 50

What are the solutions to the absolute value equation |x - 3| = 5?

Accepted Answer

x = -2, 8

Answer

x = 2, 8

Answer

x = 2, -8

Answer

x = -2, -8

Question 51

Which inequality represents the statement "The sum of two numbers, x and y, is less than or equal to 10"?

Accepted Answer

x + y ≤ 10

Answer

x - y ≥ 10

Answer

x + y ≥ 10

Answer

x - y ≤ 10

Question 52

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

Accepted Answer

-1/2

Answer

2

Answer

1/2

Answer

-2

Question 53

Which of the following describes the graph of the equation y = -2x² + 4x - 3?

Accepted Answer

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

Answer

A parabola opening upwards with a vertex at (-1, 1).

Answer

A straight line with a positive slope.

Question 54

What is the equation of the circle with center (3, -2) and radius 5?

Accepted Answer

(x - 3)² + (y + 2)² = 25

Answer

(x + 3)² + (y - 2)² = 5

Answer

(x - 3)² + (y + 2)² = 5

Answer

(x + 3)² + (y - 2)² = 25