| aidemia--modules-homework_type | Create a homework in a form of a quiz |
| Which subject | Mathematics |
| What age group | Year or Grade 11 |
| What topic | |
| Question types | Open-ended |
| Number of questions | 20 |
| Number of answers | 1 |
| Correct answers | Exactly 1 |
| Show correct answers | |
| Use images (descriptions) | |
| Any other preferences |
Answer each question below. Ensure you show all your workings for full credit.
Algebra: Solve the equation (3x - 7 = 11). What is the value of (x)?
Geometry: A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? Justify your answer.
Trigonometry: Calculate ( \sin(30^\circ) + \cos(60^\circ) ). What is the result?
Statistics: The following data set represents the ages of students in a class: 15, 16, 16, 17, 18, 18, 19, 20. What is the median age?
Functions: Given the function (f(x) = 2x^2 - 3x + 1), find the value of (f(4)).
Probability: A bag contains 3 red, 2 blue, and 5 green balls. If one ball is drawn at random, what is the probability that it is blue?
Linear Equations: Find the slope of the line given by the equation (y = 4x - 12).
Quadratic Equations: Solve the quadratic equation (x^2 - 5x + 6 = 0). What are the roots?
Sequences: Determine the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3.
Complex Numbers: Simplify the expression ( (3 + 4i) + (2 - 3i) ). What is the result?
Graphs: What is the x-intercept of the linear equation ( y = -2x + 8 )?
Matrices: Given the matrix ( A = \begin{pmatrix} 2 & 4 \ 1 & 3 \end{pmatrix} ), calculate the determinant of matrix (A).
Inequalities: Solve the inequality ( -2x + 3 < 7 ) and represent the solution on a number line.
Circles: Find the circumference of a circle with a radius of 7 cm. Use (\pi \approx 3.14).
Exponents and Logarithms: Simplify the expression ( \log_10(1000) ).
Statistics: Calculate the range of the data set: 22, 29, 15, 41, 31.
Area: Calculate the area of a triangle with a base of 10 cm and a height of 5 cm.
Functions: If (g(x) = x^3 - 2x), calculate (g(-2)).
Transformation of Functions: Describe how the graph of (y = f(x) + 3) differs from the graph of (y = f(x)).
Integration: What is the integral of the function (f(x) = 3x^2) with respect to (x)?
Please ensure all your answers are complete and neatly presented. Good luck!