Engineering Mathematics Practice Test
Ten questions on calculus, matrices and probability, the first-year mathematics that later engineering subjects rely on.
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Question 1 of 10
What is the derivative of sin x?
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Answer: cos x. The derivative of sin x is cos x. The derivative of cos x is −sin x.
Question 2 of 10
What is the derivative of x³?
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Answer: 3x². By the power rule, d/dx (xⁿ) = n xⁿ⁻¹, so the answer is 3x².
Question 3 of 10
What is the integral of 2x with respect to x?
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Answer: x² + C. Integrating raises the power by one and divides by it: 2 · x²/2 + C = x² + C.
Question 4 of 10
What is the limit of (sin x) / x as x approaches 0?
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Answer: 1. This is a standard limit, and its value is 1. L'Hôpital's rule also gives cos 0 = 1.
Question 5 of 10
What is the determinant of the matrix [[1, 2], [3, 4]]?
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Answer: −2. For a 2×2 matrix, det = ad − bc = (1)(4) − (2)(3) = −2.
Question 6 of 10
What is the rank of a 3×3 identity matrix?
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Answer: 3. All three of its rows are linearly independent, so the rank is 3.
Question 7 of 10
The product AB of two matrices is defined only when:
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Answer: Columns of A equal rows of B. An m×n matrix can multiply an n×p matrix, so the number of columns of A must equal the rows of B.
Question 8 of 10
What are the eigenvalues of a triangular matrix?
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Answer: Its diagonal entries. The determinant of a triangular matrix is the product of its diagonal, so the eigenvalues are the diagonal entries.
Question 9 of 10
What is the dot product of two perpendicular non-zero vectors?
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Answer: 0. a · b = |a||b| cos θ, and cos 90° = 0.
Question 10 of 10
A fair coin is tossed twice. What is the probability of getting two heads?
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Answer: 1/4. The tosses are independent, so P = 1/2 × 1/2 = 1/4.
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Written by StudyZone for revision. This is not an official exam paper. Always check the latest syllabus from the official exam body.