Algebraic Reasoning: Master Equations, Inequalities, and Polynomials

Question 1

Solve the equation: 2(x - 3) + 5 = 15

Accepted Answer

x = 7

Answer

x = 2

Answer

x = 9

Question 2

Which of these is a polynomial?

Accepted Answer

2x + 5

Accepted Answer

(x + 2)^2

Answer

x / 2

Answer

sin(x)

Question 3

Which equation type graphs as a straight line?

Accepted Answer

Linear equation

Answer

Quadratic equation

Answer

Polynomial equation

Answer

Inequality

Question 4

Find the solution to the inequality: 2x + 5 is greater than 15

Accepted Answer

x is greater than 5

Answer

x is less than 5

Answer

x is greater than 10

Answer

x is less than 10

Question 5

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 6

Answer

x = 8

Answer

x = 10

Question 6

Which step is NOT used to solve a linear equation with one variable?

Accepted Answer

Setting the variable equal to zero

Answer

Isolating the variable term on one side of the equation

Answer

Combining like terms on both sides of the equation

Answer

Solving for the variable by dividing or multiplying by the constant term

Question 7

Which expression is a factor of x^2 - 4?

Accepted Answer

(x - 2)(x + 2)

Answer

x - 2

Answer

x + 2

Answer

x^2 + 4

Question 8

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 9

Which equation represents the expression 2y = 6?

Accepted Answer

y = 3

Answer

y = 6

Answer

y = 12

Answer

y = 18

Question 10

Which expression is a polynomial?

Accepted Answer

x^2 - 4

Answer

2x + 3

Answer

1/x

Answer

sin(x)

Question 11

Solve the system of equations: {y = 2x + 1, x + y = 7}

Accepted Answer

x = 3, y = 4

Answer

x = 2, y = 5

Answer

x = 4, y = 3

Answer

x = 5, y = 2

Question 12

Convert the quadratic equation y = -x^2 + 4x - 5 to standard form.

Accepted Answer

y = -x^2 + 4x - 5

Answer

y = x^2 + 4x - 5

Answer

y = -x^2 - 4x - 5

Answer

y = x^2 - 4x + 5

Question 13

Find the value of y when x = 2 in the equation y = 2x - 5. What is the value of y?

Accepted Answer

y = 1

Answer

y = -1

Answer

y = 3

Answer

y = 5

Question 14

Identify the slope and y-intercept of the equation: y = -2x + 5. What are the slope and y-intercept of the equation?

Accepted Answer

Slope: -2, y-intercept: 5

Answer

Slope: 2, y-intercept: -5

Answer

Slope: -5, y-intercept: 2

Answer

Slope: 5, y-intercept: -2

Question 15

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

Accepted Answer

2x^2 - 5x + 3

Answer

2x^2 + 5x - 3

Answer

x^2 - 5x + 3

Answer

x^2 + 5x + 3

Question 16

Solve the absolute value equation: |x - 3| = 5

Accepted Answer

x = 8 or x = -2

Answer

x = 5 or x = -5

Answer

x = 3 or x = -3

Answer

x = 8 or x = 2

Question 17

Identify the equation from the provided options.

Accepted Answer

A statement with two expressions set equal to each other

Answer

An expression with a variable and a number

Answer

A set of possible values for a variable

Answer

A graph showing the relationship between two variables

Question 18

Factor the polynomial: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)(x + 2)

Answer

(x - 2)(x - 2)

Answer

Cannot be factored

Question 19

What is the vertex form of a quadratic equation?

Accepted Answer

y = a(x - h)^2 + k

Answer

y = ax^2 + bx + c

Answer

y = mx + b

Answer

y = ax^3 + bx^2 + cx + d

Question 20

To solve for y in the equation 2x + 3y = 12, which operation should you perform first?

Accepted Answer

Subtract 2x from both sides

Answer

Add 2x to both sides

Answer

Multiply both sides by 3

Answer

Divide both sides by 3

Question 21

To find the roots of a quadratic equation in the form ax^2 + bx + c using the quadratic formula, what steps should you take?

Accepted Answer

Substitute the values of a, b, and c into the quadratic formula and solve for x.

Answer

Factor the trinomial and set each factor equal to zero.

Answer

Graph the trinomial and estimate the roots from the x-intercepts.

Answer

The quadratic formula cannot be used to find the roots of a trinomial.

Question 22

To solve for 'x' in the equation 'ax + 5 = 13' and get 'x = 2', what value should 'a' be?

Accepted Answer

a = 3

Answer

a = 4

Answer

a = 5

Answer

a = 6

Question 23

Find the value of x in the equation: 2x + 5 equals 13

Accepted Answer

x = 4

Answer

x = 9

Answer

x = 18

Question 24

To solve the equation 2x + 5 = 11, subtract 5 from both sides first. What do you do next?

Accepted Answer

Divide both sides by 2

Answer

Add 5 to both sides

Answer

Subtract 2 from both sides

Answer

Multiply both sides by 2

Question 25

Simplify the expression 3(x - 2) + 4x. Which step should you do first?

Accepted Answer

Distribute the 3 to x and -2

Answer

Combine like terms

Answer

Factor out a common factor

Answer

Divide by x

Question 26

Solve the inequality x - 5 > 2. What is the first step?

Accepted Answer

Add 5 to both sides

Answer

Subtract 2 from both sides

Answer

Multiply both sides by -1

Answer

Divide both sides by 5

Question 27

Which of the following expressions is a polynomial?

Accepted Answer

x^2 + 2x - 3

Answer

x^2 - 2x + 3 + 1/x

Answer

1/x + 2

Answer

√x + 3

Question 28

Which graph represents the equation y = x^2?

Accepted Answer

[Image of a parabola opening upwards]

Answer

[Image of a parabola opening downwards]

Answer

[Image of a straight line]

Answer

[Image of a circle]

Question 29

Which of the following is a rational number?

Accepted Answer

3/4

Answer

√2

Answer

π

Answer

e

Question 30

Factor 2x^2 - 8x + 6:

Accepted Answer

2(x - 1)(x - 3)

Answer

2(x + 1)(x + 3)

Answer

2(x - 2)(x - 3)

Answer

It cannot be factored

Question 31

Select the inequality that represents the solution set x < 5.

Accepted Answer

x - 5 < 0

Answer

5 - x > 0

Answer

5 - x < 0

Answer

x + 5 > 0

Question 32

Define the domain of the function y = 1 / (x - 2).

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

x > 2

Answer

x < 2

Question 33

Which expression is equivalent to 2x + 5?

Accepted Answer

5 + 2x

Answer

2x - 5

Answer

10x + 2

Answer

x + 10

Question 34

Select the inequality that represents 'the number x is no less than 5'.

Accepted Answer

x ≥ 5

Answer

x > 5

Answer

x < 5

Answer

x ≤ 5

Question 35

What is the degree of the polynomial: 3x³ + 2x² - 5x + 1?

Accepted Answer

3

Answer

5

Answer

2

Answer

4

Question 36

Identify the constant term of the polynomial: 2x³ - 3x² + 5x - 7

Accepted Answer

-7

Answer

2

Answer

-3

Answer

5

Question 37

Which expression is equivalent to 2x + 5?

Accepted Answer

5 + 2x

Answer

2 + 5x

Answer

5 - 2x

Answer

x - 2 + 5

Question 38

Which of these equations represents a line?

Accepted Answer

y = 2x + 3

Answer

y = x^2 + 2

Answer

y = 1/x

Answer

y = |x|

Question 39

Which system of equations has no solution?

Accepted Answer

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

Answer

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

Answer

y = -2x + 5, y = x - 1

Answer

y = x + 2, y = 2x + 4

Question 40

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

Accepted Answer

Image of a line sloping down from left to right, passing through (0, 2) and (-2, 4).

Answer

Image of a line sloping up from left to right, passing through (0, 2) and (2, 4).

Answer

Image of a parabola opening upwards, with vertex at (0, 2).

Question 41

Solve the following one-step linear equation: 2x - 5 = 11

Accepted Answer

8

Answer

6

Answer

10

Answer

12

Question 42

Multiply the following binomials: (x + 2)(x - 3)

Accepted Answer

x^2 - x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + x - 6

Answer

2x^2 - 5x - 6

Question 43

Simplify the following inequality: 3x + 5 > 14

Accepted Answer

x > 3

Answer

x < 5

Answer

x > 5

Answer

x < 3

Question 44

Find the solution to the system of linear equations: y = 2x + 1 and y = x - 3

Accepted Answer

(-2, -3)

Answer

(0, -3)

Answer

(-4, 5)

Answer

(2, 1)

Question 45

Expand and simplify the following expression: (2x - 3) ^ 2

Accepted Answer

4x^2 - 12x + 9

Answer

x^2 - 6x + 9

Answer

4x^2 - 6x + 9

Answer

2x^2 + 6x + 9

Question 46

Factor the following quadratic polynomial: x ^ 2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 3)^2

Answer

x(x - 9)

Answer

(x - 3)^2

Question 47

Which of the following functions is linear?

Accepted Answer

y = 3x - 2

Answer

y = x^2 + 2x

Answer

y = 1/x

Answer

y = sin(x)

Question 48

Find the slope of the line represented by the equation 2y = 6x + 4

Accepted Answer

3

Answer

2

Answer

-3

Question 49

Solve the following absolute value equation: |2x - 5| = 9

Accepted Answer

x = 2 or x = 7

Answer

x = -2 or x = -7

Answer

x = 4 or x = 8

Answer

x = 6 or x = 10

Question 50

Which of the following equations is a quadratic equation?

Accepted Answer

x ^ 2 - 4x + 3 = 0

Answer

y = x ^ 3 + 2x

Answer

y = sin(x) + cos(x)

Answer

y = 3x

Question 51

Solve the equation: 3x + 5 = 14

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 2

Answer

x = 5

Question 52

Which inequality is represented by the graph shown?

Accepted Answer

x > 2

Answer

x < 2

Answer

x ≤ 2

Answer

x ≥ 2

Question 53

If the equation is y = 2x + 1, find the value of y when x = 3.

Accepted Answer

y = 7

Answer

y = 6

Answer

y = 5

Answer

y = 9

Question 54

Solve the system of equations: 2x + y = 5, x - y = 1

Accepted Answer

x = 2, y = 1

Answer

x = -3, y = 1

Answer

x = 1, y = 3

Answer

x = 3, y = -1

Question 55

Simplify the expression: 4(2x - 3)

Accepted Answer

8x - 12

Answer

6x - 7

Answer

6x - 12

Answer

8x - 3

Question 56

Simplify the expression: 3x² + 5x - 2x² + 7x

Accepted Answer

x² + 12x

Answer

x² + 2x

Answer

5x² + 12x

Answer

5x² + 2x

Question 57

The length of a rectangle is 3 more than twice its width. If the width is 'w', find the perimeter of the rectangle.

Accepted Answer

6w + 6

Answer

4w + 6

Answer

2w + 3

Answer

5w + 3

Question 58

Which is NOT a solution to the inequality 2x - 4 < 6?

Accepted Answer

x = 6

Answer

x = 4

Answer

x = 0

Answer

x = 2

Question 59

The sum of two consecutive even numbers is 54. What is the smaller number?

Accepted Answer

26

Answer

27

Answer

25

Answer

28

Question 60

Evaluate the expression 5x² - 2x + 1 when x = -2.

Accepted Answer

25

Answer

21

Answer

19

Answer

29