Advanced level 2025 Littoral Regional Mock further mathematics 1

Advanced level 2025 Littoral Regional Mock further mathematics 1

Advanced level 2025 Littoral Regional Mock further mathematics 1

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1. f(x)=(x−1)2x​ in partial fractions is A. x−11​+(x−1)21​ B. x−11​−(x−1)21​ C. x+11​+(x−1)21​ D. x+11​−(x−1)21​

2. The nth term of an infinite series is n2(x−2)n​. Which of the following statements is correct? A. The series converges for all real values of x. B. When $x=1$, the series converges to $\ln 2$. C. The series diverges when $x<0$. D. When $x=3$, the series is a term of the series.

3. Given that z=1+i3​, then the maximum value of $|z+2-3i|$ is A. 4 B. 6 C. 13​ D. 8

4. The number of asymptotes of the curve y=(x−2)x2​ is A. 1 B. 2 C. 3 D. 0

5. The relation R on $\mathbb{Z}$, where $\mathbb{Z}$ is the set of integers, is defined by $(x,y)\in R$ if x2+y2=25. Which of the following describes the relation R? A. $R=\{(3,4),(4,3),(-3,4),(-4,3)\}$ B. $R=\{(3,4),(4,3),(-3,-4),(-4,-3)\}$ C. $R=\{(3,4),(4,3),(-3,4),(-4,3),(3,-4),(4,-3),(-3,-4),(-4,-3),(5,0),(-5,0),(0,5),(0,-5)\}$ D. $R=\{(3,\pm 4),(4,\pm 3),(\pm 3,4),(\pm 4,3)\}$

6. $\int \cos (4x)\cos (2x)dx$ is equal to A. 21​sin(6x)+21​sin(2x)+c B. 121​sin(6x)+41​sin(2x)+c C. 61​sin(6x)+21​sin(2x)+c D. 61​sin(3x)+21​sin(x)+c

7. A system of forces acting through a point is in equilibrium when A. the vector sum of the forces is a non-zero vector. B. the vector sum of the forces reduces to a couple. C. the vector sum of the forces is a zero vector. D. the algebraic sum of the forces is zero.

8. A particular integral of the differential equation dx2d2y​−5dxdy​+6y=e2x is A. −xe2x B. xe2x C. 21​xe2x D. −2xe2x

9. The binary operation $\ast$ is defined by $a\ast b=a+b-2$. The identity element is A. 2 B. 0 C. 1 D. -2

10. The function f(x)=x2−1x2+x​ in partial fractions is A. x−11​ B. x+11​ C. 1+x−11​ D. 1−x+11​

11. Which of the following is not a solution to the congruence equation x2≡2(mod7)? A. 3 B. 5 C. 9 D. 11

12. A plot of land lies between a straight fence and a stream. At various distances, in meters, from the end of the fence, the width of the plot, in meters, was measured as follows:

Using Simpson’s rule, the area of the plot is A. 1580m2 B. 10560m2 C. 5280m2 D. 3360m2

13. The mean value of the function f(x)=x23​ over the interval $[1,3]$ is A. $2\ln 3$ B. $\ln 3$ C. 32​ D. 323​​

14. A thin circular disc of mass m and radius r rotates about its diameter with angular velocity $\omega$. The speed of the centre of the disc is … the kinetic energy of the disc. A. proportional to B. directly equal to C. inversely proportional to D. independent of

15. limx→0​sinh2xsin3x​ is A. 0 B. 23​ C. 32​ D. $\infty$

16. A particle of mass falls from rest through a medium whose resistance is proportional to the square of its velocity. The velocity of the particle after a long time is A. kmg​​, where k is a constant B. kmg​, where k is a constant C. mgk​​, where k is a constant D. mgk​, where k is a constant

17. Which of the following spans R3? A. $\{(1,0,0),(0,1,1)\}$ B. $\{(1,0,1),(1,1,0),(0,1,1)\}$ C. $\{(1,2,3),(1,1,2)\}$ D. $\{(1,0,0),(0,1,0),(0,0,1),(1,1,1)\}$