Advanced level 2025 South West Regional Mock mathematics mechanics 1

Posted on April 15, 2025April 15, 2025 by T- frank

Advanced level 2025 South West Regional Mock mathematics mechanics 1

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1. $( x ^{2} + 5 ) ^{2} 7 x ^{2} + 5$ decomposed in partial fractions, where $a, b, c$ and $d$ are real constants is: A. $x ^{2} + 5 a x + b$ B. $x ^{2} + 5 a x + b + ( x ^{2} + 5 ) ^{2} c x + d$ C. $x ^{2} + 5 a x + b + x ^{2} + 5 c x + d$ D. $x ^{2} + 5 a x + b + ( x ^{2} + 5 ) ^{2} c x + d$

2. Two vectors $a ” />$ and $b ” />$ are given as $a ” /> = i + 2 j + k$ and $b ” /> = 3 i + j + 2 k$ . The vector product $a ” /> \times b ” />$ is: A. $3 i - j - 5 k$ B. $3 i + j - 5 k$ C. $3 i + j + 5 k$ D. $3 i - 5 j - 5 k$

3. Which of the following defines an equation of a curve that does NOT have a vertical asymptote? A. $y = x + 2 x ^{3} + 2 x ^{2}$ B. $y = x + 2 x ^{2} - x - 2$ C. $y = x + 2 x ^{2} + 2$ D. $y = ( x + 2 ) ^{2} x ^{2} + 2$

4. The general solution of the differential equation $sin x d x d y + y cos x = cos x$ is: A. $y = - x + k csc x$ B. $y = 1 + k csc x$ C. $y = - 1 + k cos x$ D. $y = (1 + k) sec x$

5. Given that $f (x) = ⎩ ” /> ⎨ ” /> ⎧ 2 x - 1, 1 \leq x \leq 3 7 - x, for x < 1 for x > 3$ The value of $x$ for which $f (x)$ is discontinuous is: A. 0 B. 1 C. 3 D. 2

6. Given the statements $p$ and $q$ , $\sim (p ⟹ \sim q) \equiv$ : A. $\sim p \land q$ B. $p \land \sim q$ C. $p \land q$ D. $\sim p \land \sim q$

7. Given the non-singular square matrices $N$ and $M$ , and non-zero column vectors $x$ and $y$ such that $(NM)^{-1} y = x$ , then $y =$ A. $M N^{-1} y$ B. $N^{-1} M y$ C. $M^{-1} N y$ D. $NM x$

8. $\int_{0 l n 3} e^{x} cosh x d x =$ A. $4 e ^{4} - 1$ B. $4 e ^{4} - e ^{-2}$ C. $2 e ^{2} - 1$ D. $2 e ^{2} - e ^{-2}$

9. The general solution of the differential equation $d x ^{2} d ^{2} y - 4 d x d y + 3 y = 0$ , where $P$ and $Q$ are real constants is: A. $e^{x} (P cos x + Q sin x)$ B. $e^{3 x} (P cos x + Q sin 3 x)$ C. $P e^{x} + Q e^{3 x}$ D. $(P + Q x) e^{3 x}$