Advanced level 2025 Littoral Regional Mock mathematics mechanics 1

Advanced level 2025 Littoral Regional Mock mathematics mechanics 1

Advanced level 2025 Littoral Regional Mock mathematics mechanics 1

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1.

Given that x2−2x+1​=x−2​A​+x+2​B​, the values of A and B are: [A] $A=1,B=-3$ [B] $A=-1,B=3$ [C] $A=1,B=3$ [D] $A=-1,B=-3$

2. The asymptotes to the curve y=(x−2)(x+3)4​ are [A] $x=-2,x=3$ and $y=4$ [B] $x=2,x=-3$ and $y=-4$ [C] $x=2,x=-3$ and $y=0$ [D] $x=-2,x=3$ and $y=0$

3. The value of b for which (x−1)2 is a factor of the polynomial f(x)=x3−b2x+2ax−b is [A] −21​ [B] 21​ [C] 23​ [D] −23​

4. If $|x-1|=-x$, then [A] $x\ge 0$ [B] $x>0$ [C] $x\le 0$ [D] $x<0$

5. The range of the function f:x↦x+2x​ is [A] $\mathbb{R}\setminus \{0\}$ [B] $\mathbb{R}\setminus \{1\}$ [C] $\mathbb{R}\setminus \{-2\}$ [D] $\mathbb{R}\setminus \{2\}$

6. ∫e2xsinxdx= [A] 51​e2x(2sinx−cosx)+c [B] 51​e2x(sinx−2cosx)+c [C] 51​e2x(2sinx+cosx)+c [D] 51​e2x(sinx+2cosx)+c

7. limx→0​4+x​−21+x​−1​= [A] 2 [B] 1 [C] 3 [D] -6

11. Given the statements p: Bamunkumblit is in the North West Region q: Bamunkumblit is English speaking It is not true that if Bamunkumblit is in the North West region then it is English speaking Can be represented by [A] $\sim (p⟹q)$ [B] $\sim p⟹q$ [C] $\sim (q⟹p)$ [D] $\sim q⟹p$

12. The equation of a plane $\pi$ is given by $2x-2y+z+12=0$. The perpendicular distance from the origin to the plane $\pi$ is [A] 3 units [B] 12 units [C] 4 units [D] 5 units

13. A relation R defined on a nonempty set A is an equivalence relation if R is [A] Reflexive, transitive, and anti-symmetric [B] Reflexive, symmetric and transitive [C] Symmetric, anti-symmetric and transitive [D] Transitive, symmetric and anti-symmetric

14. The direction ratios of the line with equation 2x−1​=3y+1​=−1z−2​ are [A] $2,3,1$ [B] $2,-3,1$ [C] $2,3,-1$ [D] $-2,3,-1$

15. The range of values of k for which a root of the equation x2+kx+1=0 exists in the interval $0<x<1$ is [A] $k<-2$ [B] $k>-2$ [C] k<−25​ [D] k>−25​