- This test contains 5 multiple-choice questions
- Each question is worth 1 mark
- You have 15 minutes to complete the test
- There is negative marking (0.25 points per wrong answer)
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- After submission, you can review explanations for each question
what is the product \(A \times B\)?
Test Results
Question 1: Derivative
Your answer: Not answered
Correct answer: a) \(12x^3 – 6x^2 + 5\)
Explanation: The derivative of a polynomial is found by applying the power rule to each term. For \(3x^4\), the derivative is \(12x^3\); for \(-2x^3\), it’s \(-6x^2\); for \(5x\), it’s \(5\); and the derivative of a constant \(-7\) is \(0\).
Question 2: Matrix Multiplication
Your answer: Not answered
Correct answer: a) \(\begin{bmatrix} 8 & 11 \\ 4 & -7 \end{bmatrix}\)
Explanation: Matrix multiplication is performed by taking the dot product of rows and columns. For the first row: \(2*4 + 3*0 = 8\), \(2*(-2) + 3*5 = -4 + 15 = 11\). For the second row: \(1*4 + (-1)*0 = 4\), \(1*(-2) + (-1)*5 = -2 – 5 = -7\).
Question 3: Trigonometric Identity
Your answer: Not answered
Correct answer: b) \(1\)
Explanation: This is the Pythagorean trigonometric identity. For any angle \(x\), \(\sin^2(x) + \cos^2(x) = 1\). This is one of the most fundamental identities in trigonometry.
Question 4: Quadratic Equation
Your answer: Not answered
Correct answer: a) \(x = -1, x = 3\)
Explanation: Solve using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\). Here, \(a=2\), \(b=-4\), \(c=-6\). The discriminant is \(16 + 48 = 64\), so \(x = \frac{4 \pm 8}{4}\), which gives \(x = 3\) and \(x = -1\).
Question 5: Limit
Your answer: Not answered
Correct answer: b) \(1\)
Explanation: This is a standard limit in calculus. As \(x\) approaches 0, \(\frac{\sin(x)}{x}\) approaches 1. This can be proven using the squeeze theorem or L’Hôpital’s rule.