Expressions and Equations: Master the Basics of Algebra

Question 1

Find the slope of the line represented by the equation y = -2x + 3

Accepted Answer

-2

Answer

2

Answer

3

Answer

-3

Question 2

Which graph represents the equation x = 2?

Accepted Answer

Vertical line through (2, 0)

Answer

Horizontal line through (0, 2)

Answer

Diagonal line through (0, 2)

Answer

Parabola through (2, 0)

Question 3

Determine the domain of the function: f(x) = √(x - 3)

Accepted Answer

(3, ∞)

Answer

[0, ∞)

Answer

(-∞, 3)

Answer

All real numbers

Question 4

Simplify the algebraic expression: 2x + 3y - 4

Accepted Answer

2(x + y) - 4

Answer

6xy - 1

Answer

2x - 3y + 4

Answer

4x + 6y - 8

Question 5

Find the value of 2x + 5 when x equals 3.

Accepted Answer

11

Answer

5

Answer

15

Answer

20

Question 6

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

Accepted Answer

x = 8

Answer

x = 10

Answer

x = 12

Answer

x = 14

Question 7

Which step is NOT used to solve the equation: 5x - 12 = 3x + 6?

Accepted Answer

Multiply both sides by 10.

Answer

Add 12 to both sides.

Answer

Subtract 3x from both sides.

Answer

Divide both sides by 2.

Question 8

Graph the equation y = 3x - 2.

Accepted Answer

A straight line through (0, -2) and (2, 4)

Answer

A straight line through (0, 2) and (4, -2)

Answer

A parabola opening up

Answer

A hyperbola

Question 9

Evaluate the expression: 5 + 2 * (3 - 1)

Accepted Answer

8

Answer

5

Answer

6

Answer

10

Question 10

Solve the equation: 2x - 5 = 10

Accepted Answer

x = 7

Answer

x = 2

Answer

x = 5

Answer

x = 10

Question 11

Factor the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

(x - 18)(x + 18)

Answer

Cannot be factored

Question 12

Solve the inequality: 3x - 5 < 14

Accepted Answer

x < 6

Answer

x < 3

Answer

x > 6

Answer

x > 3

Question 13

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

Accepted Answer

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

Answer

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

Answer

A parabola opening upwards

Answer

A circle

Question 14

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 15

Which of the following is an example of a polynomial expression?

Accepted Answer

2x^2 + 3x - 1

Answer

x^(1/2) + 2

Answer

log(x) + e^x

Answer

sin(x) + cos(x)

Question 16

Which of the following is the domain of the function f(x) = 1/x?

Accepted Answer

All real numbers except 0

Answer

All real numbers except -1 and 1

Answer

All positive real numbers

Answer

All rational numbers

Question 17

Solve for x: 2(x - 3) = 10?

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 18

Factor the quadratic expression x^2 - 5x + 6

Accepted Answer

(x - 2)(x - 3)

Answer

(x - 3)(x + 2)

Answer

(x + 2)(x + 3)

Answer

(x - 1)(x + 6)

Question 19

Determine the inverse of the function f(x) = 2x + 1.

Accepted Answer

g(x) = x/2 - 1

Answer

g(x) = x - 2/1

Answer

g(x) = 1/2x + 1

Answer

g(x) = 2x - 1

Question 20

Which of the following expressions is equivalent to 2ab + 3a - 5b?

Accepted Answer

a(2b + 3) - 5b

Answer

a(2b - 3) + 5b

Answer

(2a + 3)b - 5b

Answer

(2a - 3)b + 5b

Question 21

What is the slope of the line represented by the equation y = 2x - 1?

Accepted Answer

2

Answer

-1

Answer

1

Answer

3

Question 22

Which of the following is the graph of the inequality x + y > 3?

Accepted Answer

A shaded region above the line x + y = 3

Answer

A shaded region below the line x + y = 3

Answer

A shaded region to the left of the line x + y = 3

Answer

A shaded region to the right of the line x + y = 3

Question 23

Which of the following is the absolute value of -7?

Accepted Answer

7

Answer

-7

Answer

0

Answer

1

Question 24

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

Accepted Answer

27x^6y^3

Answer

9x^5y^3

Answer

9x^6y^3

Answer

27x^5y^3

Question 25

Graph the line with the 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 26

Solve for x: 2x^2 - 5x - 3 = 0

Accepted Answer

x = 1/2 or x = -3

Answer

x = -1/2 or x = 3

Answer

x = 1 or x = -3

Answer

x = -1 or x = 3

Question 27

Graph the inequality: y < 2x + 1

Accepted Answer

The region below a line with a slope of 2 and a y-intercept of 1

Answer

The region above a line with a slope of 2 and a y-intercept of 1

Answer

The region below a line with a slope of -2 and a y-intercept of 1

Answer

The region above a line with a slope of -2 and a y-intercept of 1

Question 28

Which of the following is a system of equations in two variables?

Accepted Answer

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

Answer

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

Answer

x = 2, y = 3

Answer

y = 2x, x = 3

Question 29

What is the order of operations used in mathematics?

Accepted Answer

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Answer

Parentheses, Exponents, Addition, Subtraction, Multiplication, Division

Answer

Exponents, Parentheses, Multiplication, Division, Addition, Subtraction

Answer

Parentheses, Multiplication, Division, Exponents, Addition, Subtraction

Question 30

Graph the linear equation: y = 2x + 1

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 31

Find the least common multiple of 6 and 12

Accepted Answer

24

Answer

2

Answer

6

Answer

12

Question 32

Find the greatest common factor of 12 and 18

Accepted Answer

6

Answer

1

Answer

2

Answer

3

Question 33

Which of the following is the correct order of operations in mathematics?

Accepted Answer

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Answer

Parentheses, Multiplication/Division, Exponents, Addition/Subtraction

Answer

Parentheses, Addition/Subtraction, Multiplication/Division, Exponents

Question 34

Evaluate the mathematical expression: 5 + 2 * 4 - 3^2

Accepted Answer

11

Answer

15

Answer

7

Answer

1

Question 35

Solve for x in the equation: 3x - 7 = 14

Accepted Answer

5

Answer

7

Answer

3

Answer

1

Question 36

The equation of a line is given as y = -2x + 5. What is its slope?

Accepted Answer

-2

Answer

2

Answer

-5

Answer

5

Question 37

Which of the following expressions is equivalent to (x + 3)(x - 2)?

Accepted Answer

x^2 + x - 6

Answer

x^2 - x - 6

Answer

x^2 + 5x - 6

Answer

x^2 - 5x - 6

Question 38

Find the solution to the inequality: x - 5 > 1

Accepted Answer

x > 4

Answer

x < -4

Answer

x < 4

Answer

x > -4

Question 39

Which transformation will move the graph of y = x^2 two units up?

Accepted Answer

y = x^2 + 2

Answer

y = x^2 - 2

Answer

y = (x - 2)^2

Answer

y = (x + 2)^2

Question 40

Solve the equation: 2x - 5 = 11

Accepted Answer

8

Answer

6

Answer

12

Answer

10

Question 41

Rationalize the denominator of the expression: 1 / (√2 - 1)

Accepted Answer

√2 + 1

Answer

√2 - 1

Answer

-1

Answer

2

Question 42

Which of the following expressions is equivalent to 2(x + 3)?

Accepted Answer

2x + 6

Answer

2x + 3

Answer

4x + 6

Answer

4x + 3

Question 43

The graph of the linear equation y = 2x + 1 passes through the point:

Accepted Answer

(0, 1)

Answer

(1, 0)

Answer

(0, 2)

Question 44

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

Accepted Answer

x<sup>2</sup> - 4

Answer

x - 4

Answer

x + 4

Answer

x<sup>2</sup> + 4

Question 45

Which of the following inequalities is true for x > 0?

Accepted Answer

x + 1 > 1

Answer

x + 1 < 1

Answer

x - 1 > 1

Answer

x - 1 < 1

Question 46

What is the value of the expression 3x - 2y when x = 3 and y = -2?

Accepted Answer

13

Answer

1

Answer

-7

Answer

7

Question 47

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

Accepted Answer

x + 3y

Answer

5x - y

Answer

-x + 3y

Answer

x - 3y

Question 48

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

Accepted Answer

2x - 6

Answer

x - 6

Answer

2x + 6

Question 49

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

Accepted Answer

[Image of a line with a slope of 2 and a y-intercept of 1]

Answer

[Image of a line with a slope of 1 and a y-intercept of 2]

Answer

[Image of a line with a slope of -2 and a y-intercept of 1]

Question 50

Solve for x in the inequality: x - 5 < 3

Accepted Answer

x < 8

Answer

x < 3

Answer

x > 8

Answer

x > 3

Question 51

Which of these expressions is a monomial?

Accepted Answer

3x^2

Answer

(x + y)^2

Answer

2x + 3y

Question 52

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

Accepted Answer

x^6y^3

Answer

x^3y^9

Answer

x^2y^3

Answer

x^3y^3

Question 53

What are the solutions to the equation: |x - 2| = 5?

Accepted Answer

x = 7 or x = -3

Answer

x = 5

Answer

x = 0

Answer

x = -5

Question 54

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 9)(x - 9)

Answer

Cannot be factored