Algebraic Expressions and Equations: Master the Basics of Algebra

Question 1

Which shape is three-dimensional and has no flat surfaces?

Accepted Answer

Sphere

Answer

Square

Answer

Triangle

Answer

Circle

Question 2

Which property is NOT a characteristic of parallelograms?

Accepted Answer

Adjacent sides are perpendicular.

Answer

Opposite sides are parallel.

Answer

Diagonals bisect each other.

Answer

Opposite angles are congruent.

Question 3

In geometry, what are the key differences between points, lines, and planes?

Accepted Answer

A point has no dimensions, a line has one dimension, and a plane has two dimensions.

Answer

A point is a one-dimensional object, a line is a three-dimensional object, and a plane has two dimensions.

Answer

A point has two dimensions, a line has three dimensions, and a plane has one dimension.

Answer

A point has three dimensions, a line has zero dimensions, and a plane has one dimension.

Question 4

Which property does NOT apply to parallelograms?

Accepted Answer

Diagonals are perpendicular.

Answer

Opposite sides are parallel.

Answer

Opposite sides are congruent.

Answer

Diagonals bisect each other.

Question 5

Which characteristic is NOT true for trapezoids?

Accepted Answer

Diagonals that bisect each other

Answer

Two parallel sides

Answer

Opposite angles that add up to 180 degrees

Question 6

In a coordinate plane, point A is at (-3, 2) and point B is at (5, 6). Find the distance between point A and point B.

Accepted Answer

√34

Answer

3

Answer

5

Answer

2√17

Question 7

Which of these statements is NOT true for ALL regular polygons?

Accepted Answer

Diagonals always bisect each other at right angles.

Answer

All sides are the same length.

Answer

All interior angles are equal.

Question 8

Calculate the slope of the line passing through points A(2, 3) and B(8, 15).

Accepted Answer

2

Answer

3

Answer

-2

Question 9

A quadrilateral is translated 5 units to the right and 3 units down. How does the image compare to the original quadrilateral?

Accepted Answer

The image is congruent to the original and 5 units to the right and 3 units down.

Answer

The image is congruent to the original and 5 units to the right and 3 units above.

Answer

The image is congruent to the original and 5 units to the left and 3 units above.

Answer

The image is similar to the original but not congruent.

Question 10

In the diagram, line XY is parallel to line ZW. If angle WZY measures 125 degrees, what is the measure of angle YXZ?

Accepted Answer

125 degrees

Answer

45 degrees

Answer

65 degrees

Question 11

Which property applies exclusively to circles and not to ellipses?

Accepted Answer

All points are equidistant from a central point.

Answer

Enclosed, two-dimensional shape.

Answer

Symmetrical about two perpendicular axes.

Answer

Constant ratio of distances from any point to two fixed points.

Question 12

What is the definition of a polynomial?

Accepted Answer

An expression with the form y = a_0 + a_1x + a_2x^2 + ... + a_nx^n, where the coefficients a_0, a_1, ..., a_n are constants

Answer

An expression with the form ax + b, where a and b are constants

Answer

An expression with a fraction that has a polynomial in the numerator and a polynomial in the denominator

Answer

An expression with a variable raised to a constant power

Question 13

Factor the expression: x^2 + 6x + 8

Accepted Answer

(x + 2)(x + 4)

Answer

(x - 2)(x - 4)

Answer

(x + 8)(x - 1)

Answer

Prime

Question 14

Which of the following is a polynomial of degree 3?

Accepted Answer

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

Answer

x + 2

Answer

x^2 + 3x - 1

Answer

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

Question 15

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 1 and a y-intercept of 2

Answer

A line with a slope of 2 and a y-intercept of 0

Answer

A line with a slope of 1 and a y-intercept of 0

Question 16

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

Accepted Answer

x^2 + 2x + 1 = 0

Answer

2x + 1 = 0

Answer

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

Answer

x - 1 = 0

Question 17

Factor the following quadratic expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Question 18

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

Accepted Answer

8x^6y^3

Answer

6x^6y^3

Answer

8x^5y^3

Answer

16x^5y^3

Question 19

Find the algebraic expression for the area of a rectangle with a length of (x+2) units and a width of (x-1) units.

Accepted Answer

(x+2)(x-1)

Answer

x^2 - 1

Answer

x^2 + x - 2

Answer

2x - 1

Question 20

Which of the following is an algebraic expression that represents the sum of 2x and 5?

Accepted Answer

2x + 5

Answer

x = 5

Answer

y > 10

Answer

The sum of two numbers is 10

Question 21

Solve the equation: 3x - 7 = 16

Accepted Answer

8

Answer

3

Answer

7

Answer

16

Question 22

Which of the following is a monomial?

Accepted Answer

3x^2y

Answer

2x + 3

Answer

x^2 - 2x + 1

Answer

1 / x

Question 23

How does linear algebra aid in solving systems of equations effectively?

Accepted Answer

Linear algebra enables the representation of systems of equations as matrices, facilitating their solution using linear algebra techniques.

Answer

Linear algebra simplifies equations, making manual solving easier.

Answer

Linear algebra is primarily used to solve quadratic equations.

Question 24

Which of the following is NOT an algebraic expression?

Accepted Answer

6

Answer

2x + 3

Answer

x - 5

Answer

(y + 3) * 2

Question 25

Which inequality represents the statement: 'The sum of x and 5 is greater than or equal to 10'?

Accepted Answer

x + 5 ≥ 10

Answer

x + 5 < 10

Answer

x + 5 > 10

Answer

x + 5 ≤ 10

Question 26

Solve the inequality: |x - 2| > 5

Accepted Answer

x < -3 or x > 7

Answer

x > -3 and x < 7

Answer

x < 7

Answer

x > 7

Question 27

Which one of the following represents an algebraic expression?

Accepted Answer

3 + x

Answer

y = 2x + 1

Answer

The sum of two numbers

Answer

The area of a circle

Question 28

Graph 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 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 29

Which of the following is the standard form of a linear equation?

Accepted Answer

Ax + By = C

Answer

y = mx + b

Answer

x = y

Answer

y = x^2

Question 30

In solving the equation **2x - 5 = 11**, which property allows us to add 5 to both sides?

Accepted Answer

Addition Property of Equality

Answer

Subtraction Property of Equality

Answer

Multiplication Property of Equality

Answer

Division Property of Equality

Question 31

You have $5 and you want to buy a sandwich that costs $3. Which equation represents how much more money you need to buy the sandwich?

Accepted Answer

x - 5 = 3

Answer

x + 5 = 3

Answer

5 - x = 3

Question 32

Identify the linear inequality:

Accepted Answer

x + y > 5

Accepted Answer

x - 2y > 5

Answer

x^2 + y < 5

Answer

x + y^3 > 5

Question 33

Solve the inequality: 2x - 5 > 11

Accepted Answer

x > 8

Answer

x < 8

Answer

x > -8

Answer

x < -8

Question 34

Factor the expression: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)^2

Answer

(x - 2)^2

Answer

x(x - 4)

Question 35

Solve for x: |x - 1| = 5

Accepted Answer

x = 6 or x = -4

Answer

x = 6

Answer

x = -4

Answer

x = 4 or x = -6

Question 36

Which of the following represents the equation of a line with a slope of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

x = 2y - 3

Answer

y = 3x - 2

Question 37

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

Cannot be factored

Question 38

Expand the expression: (2x + 3)^2

Accepted Answer

4x^2 + 12x + 9

Answer

2x^2 + 9

Answer

2x^2 + 6x + 9

Answer

4x^2 - 12x + 9

Question 39

Which of the following is an algebraic expression containing a single variable?

Accepted Answer

2x + 5

Answer

5

Answer

x + y = 5

Answer

5x^2 + 2x - 1

Question 40

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

Accepted Answer

5x + 4

Answer

5x - 4

Answer

x + 4

Question 41

Solve the equation: 2x + 5 = 11

Accepted Answer

3

Answer

2

Answer

5

Answer

4

Question 42

Solve the inequality: x - 3 is less than 5

Accepted Answer

x < 8

Answer

x > 8

Answer

x < 5

Question 43

Which of the following is a quadratic equation?

Accepted Answer

x^2 + 2x - 3 = 0

Answer

2x + 3 = 5

Answer

x + 2 = 3

Question 44

Factor the quadratic expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

Cannot be factored

Answer

(x - 2)(x - 2)

Answer

(x + 4)(x - 4)

Question 45

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = -3, y = 2

Answer

x = 3, y = -2

Question 46

Which of the following is equivalent to the inequality x > 2?

Accepted Answer

2 < x

Answer

-2 < x

Answer

x < 2

Answer

-x < 2

Question 47

Find the value of x that makes the following equation true: x^2 - 4 = 0

Accepted Answer

x = -2 or x = 2

Answer

x = -4

Answer

x = 0

Answer

x = 4

Question 48

Solve the inequality: |x - 2| < 5

Accepted Answer

-3 < x < 7

Answer

x < -3 or x > 7

Answer

x > 2 or x < 7

Answer

x < 2 or x > 7

Question 49

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

Accepted Answer

x = 3, y = 2

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Answer

x = 2, y = 3

Question 50

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

Accepted Answer

3x^2 + 10x - 8

Answer

12x - 8

Answer

x^2 + 10x - 6

Answer

3x^2 - 10x + 8

Question 51

Solve the inequality x + 3 < 7. Express your answer using set notation:

Accepted Answer

{x | x < 4}

Answer

{x | x ≤ 4}

Answer

{x | x ≥ 4}

Answer

{x | x > 4}

Question 52

Factor the expression x^2 - 49:

Accepted Answer

(x + 7)(x - 7)

Answer

Cannot be factored

Answer

(x + 7)^2

Answer

(x - 7)^2

Question 53

Identify the linear equation in one variable:

Accepted Answer

y = 2x + 5

Answer

y = √x + 2

Answer

y = sin(x) + 1

Answer

y = x^2 + 3x - 1

Question 54

Solve for x in the equation |x - 3| = 5:

Accepted Answer

x = 8 or x = -2

Answer

x = 15

Answer

x = 10

Answer

x = 5

Question 55

Describe the graph of the linear equation y = 2x - 1:

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 1.

Question 56

Evaluate the expression 2x + 3 when x = 5.

Accepted Answer

13

Answer

15

Answer

10

Answer

8

Question 57

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

Accepted Answer

2x + 7

Answer

4x + 3

Answer

x + 7

Answer

2x - 3

Question 58

Solve for x: 2x - 5 = 11

Accepted Answer

8

Answer

10

Answer

4

Answer

6

Question 59

Find the value of y that makes the equation true: y + 7 = 15

Accepted Answer

8

Answer

10

Answer

7

Answer

9

Question 60

Graph the equation y = 2x + 1.

Accepted Answer

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

Answer

A circle with a radius of 1

Answer

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

Answer

A parabola with a vertex at (0, 1)

Question 61

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

Accepted Answer

x^2 + 5x - 6

Answer

5

Answer

2x^(1/2) + 1

Answer

3x + 4

Question 62

Factor the expression x^2 - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

Cannot be factored

Answer

(x - 3)^2

Answer

(x + 9)(x - 9)

Question 63

Solve the inequality 2x + 5 > 15.

Accepted Answer

x > 5

Answer

x < -5

Answer

x < 5

Answer

x > -5

Question 64

Which of the following is equivalent to the expression (2x - 3y)^2?

Accepted Answer

4x^2 - 12xy + 9y^2

Answer

2x^2 + 3xy + 9y^2

Answer

4x^2 + 12xy + 9y^2