Algebra for Advanced Diploma in Public Services: Quizzes and Practice

Question 1

Solve the linear inequality: 2x - 5 > 7.

Accepted Answer

x > 6

Answer

x < 6

Answer

x > -6

Answer

x < -6

Question 2

Find the domain of the function: f(x) = sqrt(x - 5).

Accepted Answer

x > 5

Answer

x < 5

Answer

x ≥ 5

Answer

x ≤ 5

Question 3

Solve the quadratic equation x² - 5x + 6 = 0.

Accepted Answer

x = 2 or x = 3

Answer

x = -2 or x = -3

Answer

x = 1 or x = 6

Answer

x = -1 or x = -6

Question 4

Which of the following is the graph of the function f(x) = 2x - 1?

Accepted Answer

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

Answer

A parabola opening upwards with a vertex at (0, -1)

Answer

A circle with a radius of 2 and a center at (0, -1)

Answer

An ellipse with a major axis of length 2 and a minor axis of length 1

Question 5

Find the discriminant of the quadratic equation 2x² - 5x + 3 = 0.

Accepted Answer

25

Answer

-1

Answer

1

Answer

5

Question 6

Find the equation of the line passing through the points (2, 3) and (5, 7).

Accepted Answer

y = 2x + 1

Answer

y = x + 5

Answer

y = -x + 7

Answer

y = -2x + 9

Question 7

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

Accepted Answer

y = mx + c

Answer

Ax + By = C

Answer

ax^2 + bx + c = 0

Answer

y^2 - x^2 = 1

Question 8

Factor the quadratic expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x + 3)^2

Answer

(x - 3)^2

Question 9

Determine the 10th term of an arithmetic sequence with first term 5 and common difference 3.

Accepted Answer

44

Answer

26

Answer

35

Answer

53

Question 10

Identify the condition necessary for real roots in a quadratic equation.

Accepted Answer

The discriminant is greater than zero.

Answer

The discriminant is less than zero.

Answer

The discriminant is equal to zero.

Answer

The discriminant is undefined.

Question 11

Solve the inequality: 3x + 2 > 8

Accepted Answer

x > 6/3

Answer

x > 2

Answer

x < 2

Answer

x < 6/3

Question 12

Which of the following equations is a quadratic equation?

Accepted Answer

x^2 + 2x - 3 = 0

Answer

x + 2 = 5

Answer

x^2 + y^2 = 1

Answer

3x - 4 = 7

Question 13

Which of the following sequences is an arithmetic sequence?

Accepted Answer

2, 5, 8, 11, ...

Answer

2, 7, 14, 28, ...

Answer

2, 6, 12, 24, ...

Answer

2, 4, 8, 16, ...

Question 14

Solve the inequality: 2x - 5 > 7.  What is the solution for x?

Accepted Answer

x > 6

Answer

x > -6

Answer

x < -6

Answer

x < 6

Question 15

What is the vertex of the parabola represented by the equation y = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(-2, -1)

Answer

(4, -3)

Answer

(0, 3)

Question 16

What is the domain of the function: f(x) = sqrt(x - 2)?

Accepted Answer

x ≥ 2

Answer

x < 2

Answer

x > 2

Answer

x ≤ 2

Question 17

What is the solution to the equation 2x + 5 = 13?

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 2

Answer

x = 6

Question 18

Simplify the polynomial expression: 2x² + 3x - 5 + x² - 2x + 1

Accepted Answer

3x² + x - 4

Answer

3x² + 5x - 4

Answer

x² + 5x - 6

Answer

x² + x - 4

Question 19

Which graph represents the equation y = x²?

Accepted Answer

A parabola opening upwards

Answer

A parabola opening downwards

Answer

A circle

Answer

A straight line with a positive slope

Question 20

What is the next term in the sequence: 2, 5, 10, 17, 26, ...?

Accepted Answer

37

Answer

45

Answer

40

Answer

35

Question 21

Solve the inequality: 3x - 5 > 10

Accepted Answer

x > 5

Answer

x < 5

Answer

x > -5

Answer

x < -5

Question 22

Simplify the expression: (2x + 3)²

Accepted Answer

4x² + 12x + 9

Answer

4x² + 6x + 9

Answer

2x² + 6x + 9

Answer

2x² + 12x + 3

Question 23

Which statement is NOT a property of logarithms?

Accepted Answer

The logarithm of a negative number is positive.

Answer

The logarithm of a quotient is the difference of the logarithms.

Answer

The logarithm of 1 is 0.

Answer

The logarithm of a product is the sum of the logarithms.