Mathematics Exam Prep 2026-27
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Mathematics Exam Prep 2026-27
Sample questions with model answers
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Show that the relation R on the set \( A = \{ x \in Z: 0 \leq x \leq 12 \} \) given by R = {(a, b) : ab is a multiple of 4} is an equivalence relation.
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Check reflexivity, symmetry, and transitivity.
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Consider f: R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse.
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f is invertible; inverse is f^{-1}(x) = \frac{x - 3}{4}.
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If A = \( \begin{bmatrix} 1 & 2 & 3 \\ 5 & 0 & 2 \\ 1 & 1 & 1 \end{bmatrix} \), B = \( \begin{bmatrix} 3 & 1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix} \) and C = \( \begin{bmatrix} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & 2 & 3 \end{bmatrix} \), then compute (A + B) and (B – C). Also, verify that A + (B – C) = (A + B) – C.
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Compute matrix sums and differences.
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Using the method of integration, find the area enclosed by the circle \( x^2 + y^2 = a^2 \).
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Area = \( \pi a^2 \).
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