Advanced level 2025 South West Regional Mock mathematics mechanics 1

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1. (x2+5)27x2+5​ decomposed in partial fractions, where $a,b,c$ and $d$ are real constants is: A. x2+5ax+b​ B. x2+5ax+b​+(x2+5)2cx+d​ C. x2+5ax+b​+x2+5cx+d​ D. x2+5ax+b​+(x2+5)2cx+d​

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

3. Which of the following defines an equation of a curve that does NOT have a vertical asymptote? A. y=x+2x3+2x2​ B. y=x+2x2−x−2​ C. y=x+2x2+2​ D. y=(x+2)2x2+2​

4. The general solution of the differential equation sinxdxdy​+ycosx=cosx 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)=⎩” />⎨” />⎧​2x−1,1≤x≤37−x,​for x<1for 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. $\sim p\wedge q$ B. $p\wedge \sim q$ C. $p\wedge q$ D. $\sim p\wedge \sim q$

7. Given the non-singular square matrices $N$ and $M$, and non-zero column vectors $x$ and $y$ such that (NM)−1y=x, then $y=$ A. MN−1y B. N−1My C. M−1Ny D. $NMx$

8. ∫0ln3​excoshxdx= A. 4e4−1​ B. 4e4−e−2​ C. 2e2−1​ D. 2e2−e−2​

9. The general solution of the differential equation dx2d2y​−4dxdy​+3y=0, where $P$ and $Q$ are real constants is: A. ex(Pcosx+Qsinx) B. e3x(Pcosx+Qsin3x) C. Pex+Qe3x D. (P+Qx)e3x