Algebra for Beginners: Master Variables and Equations

Question 1

Solve the following system of equations using the substitution method:

2x + 3y = 12
x - y = 3

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 3, y = -1

Answer

x = -2, y = -1

Question 2

Which of the following equations is a quadratic equation?

Accepted Answer

x^2 - 4 = 0

Answer

x + 2 = 0

Answer

2x - 3 = 5

Answer

x^3 + 2x^2 - 1 = 0

Question 3

When x equals 3 and y equals negative 2, what is the value of 3x minus 2y?

Accepted Answer

13

Answer

1

Answer

15

Answer

17

Question 4

Which method is NOT used to solve a quadratic equation?

Accepted Answer

Guessing and checking

Answer

Factoring

Answer

Completing the square

Answer

Using the quadratic formula

Question 5

Which property of the real number system states that when you add any two real numbers, the result is also a real number?

Accepted Answer

Closure under Addition

Answer

Additive Inverse

Answer

Associativity of Multiplication

Answer

Commutativity of Division

Question 6

Which equation represents a line?

Accepted Answer

y = 2x + 1

Answer

y = x^2 + 2

Answer

y = 1/x

Answer

y = |x|

Question 7

Solve the inequality: x - 5 is less than 3

Accepted Answer

x < 8

Answer

x > 8

Answer

x < 2

Answer

x > 2

Question 8

Joe has 5 apples. His mom gives him more apples so that he has 10 apples in total. How many apples did his mom give him?

Accepted Answer

5 apples

Answer

10 apples

Answer

15 apples

Answer

20 apples

Question 9

Which topic is not included in the Algebra unit?

Accepted Answer

Geometry

Answer

Solving Linear Equations

Answer

Graphing Linear Equations

Answer

Exponents

Question 10

Factor the expression: x² - 4x + 4

Accepted Answer

(x - 2)²

Answer

(x + 2)²

Answer

x(x - 4)

Answer

Cannot be factored

Question 11

Which graph represents the linear 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 with a vertex at (0, 1)

Answer

A circle with a radius of 1

Question 12

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

Accepted Answer

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

Answer

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

Answer

A parabola opening upwards passing through (0, 1)

Question 13

Which step is NOT used to solve a system of linear equations with two variables?

Accepted Answer

Average the coefficients of the variables in the two equations to find the solution.

Answer

Eliminate a variable using addition or subtraction.

Answer

Substitute one equation into the other to solve for one variable.

Answer

Multiply both equations by the same non-zero number to create equivalent equations.

Question 14

Quadratic functions can open upward or downward, depending on the sign of the leading coefficient. Which equation represents a downward-opening parabola?

Accepted Answer

y = -x^2 + 2x + 1

Answer

y = 2x^2 + 3x + 1

Question 15

Consider the system of equations: y = x + 2 and y = 2x - 1. Which of the following best represents the graphical solution to this system?

Accepted Answer

A single point where the two lines intersect

Answer

Two parallel lines that never intersect

Answer

Two intersecting lines that form a right angle

Answer

An infinite number of points along the line y = x

Question 16

In an algebraic expression, what represents the unknown value?

Accepted Answer

A letter or symbol

Answer

A specific number

Answer

An equation

Answer

A graph

Question 17

Solve the equation: 2 to the power of x equals 16

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 8

Question 18

Which of the following represents a variable?

Accepted Answer

The letter x

Answer

The number 5

Answer

The equation y = 3

Answer

The expression 2 + 3

Question 19

Factor the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 4)(x - 4)

Answer

(x - 2)^2

Answer

(x + 2)^2

Question 20

Determine the equation of a line with a slope of 2 and a y-intercept of -1.

Accepted Answer

y = 2x - 1

Answer

y = 2x + 1

Answer

y = -2x - 1

Answer

y = -2x + 1

Question 21

Which of the following is an example of a quadratic equation?

Accepted Answer

x^2 - 4x + 4 = 0

Answer

x + y = 5

Answer

y = 2x - 1

Answer

2x - 3 > 7

Question 22

Which graph accurately shows 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 with its vertex at (0, 1)

Answer

A circle with a radius of 1

Question 23

When working with polynomial expressions, what should you do with like terms?

Accepted Answer

Add them together

Answer

Subtract them from each other

Answer

Multiply them together

Answer

Divide them by each other

Question 24

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

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = -3x + 2

Answer

y = 3x - 2

Question 25

Solve the system of equations: 
x + y = 7
x - y = 1

Accepted Answer

(3, 4)

Answer

(4, 3)

Answer

(1, 6)

Answer

(6, 1)

Question 26

Identify the polynomial among the given options:

Accepted Answer

x^2 + 2x + 1

Answer

x + 2

Answer

1/x

Answer

√x

Question 27

Which of the following is a variable? A letter or symbol that represents an unknown value

Accepted Answer

x

Answer

5

Answer

y = 2x

Answer

10 + 5

Question 28

Which of the following properties can be used to solve the equation 3(x - 2) = 15?

Accepted Answer

Distributive property

Answer

Associative property

Answer

Commutative property

Answer

Inverse property

Question 29

What is the solution to the inequality x + 5 > 10?

Accepted Answer

x > 5

Answer

x < 5

Answer

x = 5

Answer

x < 10

Question 30

Which of the following is a linear equation in two variables?

Accepted Answer

y = mx + b

Answer

y = x^2

Answer

y = e^x

Answer

y = sin(x)

Question 31

A circular garden has its center at (2, 3) and a radius of 5 units. What is the equation of this circle?

Accepted Answer

(x - 2)² + (y - 3)² = 25

Answer

(x + 2)² + (y + 3)² = 25

Answer

x² + y² = 25

Answer

(x - 3)² + (y - 2)² = 25

Question 32

Find the domain and range of the function f(x) = x^2 - 4.

Accepted Answer

Domain: (-∞, ∞); Range: [0, ∞)

Answer

Domain: (0, ∞); Range: [-4, ∞)

Answer

Domain: (-∞, ∞); Range: (-∞, 0]

Answer

Domain: (0, ∞); Range: (-∞, 0]

Question 33

Given the function f(x) = 3x - 5, find its inverse function.

Accepted Answer

f^(-1)(x) = (x + 5)/3

Answer

f^(-1)(x) = 3x + 5

Answer

f^(-1)(x) = -3x + 5

Answer

f^(-1)(x) = (3x - 5)^-1

Question 34

Which graph shows a parabola with a positive leading coefficient?

Accepted Answer

Upward-opening parabola

Answer

Downward-opening parabola

Answer

Upward-sloping line

Answer

Closed circle

Question 35

What is the degree of the equation: 2x³ - 5x² + x + 3 = 0?

Accepted Answer

3

Answer

1

Answer

2

Question 36

Find the equation of the circle whose center is at (2, 3) and has a radius of 5.

Accepted Answer

(x - 2)² + (y - 3)² = 25

Answer

(x + 2)² + (y + 3)² = 25

Answer

(x - 2)² - (y - 3)² = 25

Question 37

Which of the following represents a variable?

Accepted Answer

x

Answer

5

Answer

y = 2x + 1

Answer

The number of students present

Question 38

Find the slope of the line represented by the equation y = 2x + 1

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 39

Factor the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

(x + 4)(x - 4)

Answer

(x - 4)^2

Question 40

Solve the inequality: x - 5 < 2

Accepted Answer

x < 7

Answer

x > 7

Answer

x < -3

Answer

x > -3

Question 41

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

Accepted Answer

All real numbers except 2

Answer

All real numbers except 0

Answer

All real numbers

Answer

No real numbers

Question 42

Which of the following represents the equation of a circle with center (2, 3) and radius 5?

Accepted Answer

(x - 2)^2 + (y - 3)^2 = 25

Answer

(x - 2)^2 + (y - 3)^2 = 5

Answer

(x + 2)^2 + (y + 3)^2 = 5

Answer

(x + 2)^2 + (y + 3)^2 = 25

Question 43

Which of the following is an example of a variable?

Accepted Answer

x

Answer

5

Answer

+

Answer

=

Question 44

Which of the following is an example of an equation?

Accepted Answer

2x + 5 = 12

Answer

x is a variable

Answer

The sum of two numbers is 10

Answer

x is greater than 5

Question 45

Which of the following is an example of a polynomial?

Accepted Answer

x^2 + 2x - 3

Answer

e^x

Answer

2/x

Answer

sin(x)

Question 46

Which of the following is a rational expression?

Accepted Answer

x/(x - 1)

Answer

sin(x)

Answer

x^2

Answer

sqrt(x)

Question 47

What is the value of 'x' in the equation 2x + 5 = 11?

Accepted Answer

x = 3

Answer

x = -2

Answer

x = 1

Answer

x = 8

Question 48

Which equation represents a straight line on a graph?

Accepted Answer

y = 2x + 1

Answer

y = x² + 2

Answer

y = √x

Answer

y = 1/x

Question 49

In the equation y = -3x + 4, what does the number '-3' represent?

Accepted Answer

Slope of the line

Answer

A point on the line

Answer

Y-intercept of the line

Answer

A constant value

Question 50

What are the values of 'x' and 'y' that solve both equations: 
 1) x + y = 6  
 2) x - y = 2

Accepted Answer

x = 4, y = 2

Answer

x = 3, y = 3

Answer

x = 2, y = 4

Answer

x = 5, y = 1

Question 51

Apples cost $1.50 each, and oranges cost $0.75 each. If you buy 'a' apples and 'o' oranges, which expression represents the total cost?

Accepted Answer

1.5a + 0.75o

Answer

2.25o + a

Answer

2.25a + o

Answer

1.5o + 0.75a

Question 52

Which of the following is an equation?

Accepted Answer

x + 5 = 12

Answer

The sum of two numbers is 10

Answer

The area of a circle is pi * r^2

Answer

y is greater than 7

Question 53

Solve for x: x - 3 = 7

Accepted Answer

10

Answer

7

Answer

4

Answer

-4

Question 54

What does the graph of the equation y = 2x + 1 look like?

Accepted Answer

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

Answer

A parabola with a vertex at (0, 1)

Answer

A circle with a radius of 2

Answer

A horizontal line

Question 55

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

Accepted Answer

x = 3, y = 2

Answer

x = 4, y = 1

Answer

x = 2, y = 3

Answer

x = 1, y = 4

Question 56

Which of the following represents a variable?

Accepted Answer

x

Answer

=

Answer

+

Answer

5

Question 57

Simplify the expression: 3x + 2y - x + 5y

Accepted Answer

2x + 7y

Answer

x + 7y

Answer

2x - 7y

Answer

4x + 7y

Question 58

Solve the inequality: 2x - 5 > 11

Accepted Answer

x > 8

Answer

x > 11

Answer

x < 8

Answer

x < 11

Question 59

What is the slope of the line that passes through the points (2, 3) and (5, 7)?

Accepted Answer

4/3

Answer

3/4

Answer

2

Answer

-1

Question 60

What is the value of 'x' in the equation 2x + 5 = 11?

Accepted Answer

x = 3

Answer

x = 2

Answer

x = 8

Answer

x = 1

Question 61

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

Accepted Answer

Graph with a y-intercept of -1 and a slope of 2

Answer

Graph with a y-intercept of 1 and a slope of -2

Answer

Graph with a y-intercept of -1 and a slope of -2

Answer

Graph with a y-intercept of 1 and a slope of 2

Question 62

If a store sells apples for $1 each and oranges for $0.50 each, what is the total cost of buying 3 apples and 2 oranges?

Accepted Answer

$4.00

Answer

$4.50

Answer

$5.00

Answer

$3.50

Question 63

Which of the following is the solution to the system of equations:  x + y = 5 and 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 64

What is the value of 'y' in the equation 3y - 6 = 12?

Accepted Answer

y = 6

Answer

y = 2

Answer

y = 8

Answer

y = 4