Cameroon GCE advanced level June 2025 further mathematics 1

Here are the extracted questions from the provided images:

Page 1

1. (1+x)2(x2−x+1)−1, expressed in partial fractions where A,B and C are real constants is

   A x+1A​+x2−x+1Bx+C​

   B x+1A​+x2−x+1B​

   C x+1A​+x2−x+1Bx​

   D x+1A​+x2−x+1B​+x2−x+1C​

2. The integrating factor for the differential equation xdxdy​+4xy=ex is

   A 4x

   B e4x

   C x4

   D ex4​

3. If f(x)=3cosh3x−2, then the minimum value of f(x) is

   A −2

   B −1

   C 1

   D 2

4. Given that y=∣x2+x−x∣, if x<0, then $y = $

   A x2

   B −x2

   C 2x+x2

   D 2x−x2

5. The range of values of x for which the Taylor’s expansion about x=0 of ln((1+2x)21−2x​) is valid is

   A −21​<x<21​

   B $ -\frac{1}{2} \le x \le \frac{1}{2}$

   C 21​≤x<21​

   D −21​≤x<21​

6. The conjugate of the complex number 1+eiθ is

   A 1+eiθ

   B 1−eiθ

   C 1+e−iθ

   D 1−e−iθ

7. Given the truth table below

   | p | q | p ∨ q | (p ∨ q) ⇒ q |

   |—|—|—|—|

   | T | T | T | T |

   | T | F | T | F |

   | F | T | a | T |

   | F | F | b | F |

   The truth values of a and b are respectively

   A T,T

   B T,F

   C F,T

   D F,F

8. To establish a reduction formula for the integration of tannθ, it can be expressed as:

   A ∫secθtannθdθ

   B ∫tannθtann−1θdθ

   C ∫tannθtann−2θdθ

   D ∫secθtann−2θdθ

9. The root mean square value of x1​ in the interval 1≤x≤4 is

   A 3ln4​​

   B 31​

   C 41+ln3​​

   D 41​

10. The polar equation of the curve x2+y2=2x is

    A r2=2cosθ

    B r=2sinθ

    C r2=2sinθ

    D r=2cosθ

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11. The coordinates of the focus of the parabola x2=16(y+1) is

    A (4,0)

    B (0,4)

    C (0,3)

    D (3,0)

12. Given that (λi−4k)×(2i−j−k)=−4i+8j−16k, the value of λ is

    A 0

    B 4

    C 8

    D 16

13. Given that 3​131​λ52​​=3, then $\begin{pmatrix} 1 & \lambda \ 3 & 5 \ 1 & 2 \end{pmatrix} \begin{pmatrix} 3 & 5 & 1 \ 1 & 2 & 0 \end{pmatrix} = $

    A −3

    B 3

    C 6

    D 9

14. Given that ({x,x2,x3,x4},⋅) in the table below, is a group, then the identity element is

    | * | x | x2 | x3 | x4 |

    |—|—|—|—|—|

    | x | x2 | x3 | x4 | x |

    | x2 | x3 | x4 | x | x2 |

    | x3 | x4 | x | x2 | x3 |

    | x4 | x | x2 | x3 | x4 |

    A x

    B x2

    C x3

    D x4

15. Which one of the following linear congruencies has no solution?

    A 15z≡6(mod21)

    B 15z≡6(mod40)

    C 15z≡6(mod36)

    D 15z≡6(mod81)

16. All the asymptotes to the curve y=f(x), where f(x)=x+1+ln​x−1x+2​​ are .

    A x=−1,x=2

    B y=x+1,x=−2

    C y=x+1,x=−2,x=1

    D y=x+1,x=−2,x=1

17. If P and Q are statements, then ∼(P⇒Q)≡

    A P∨Q

    B P∧∼Q

    C ∼P∧Q

    D ∼P∧∼Q

18. A function f is defined by

    f(x)={x2,cx+3,​0≤x<22≤x≤5​.

    The value of c for which f is continuous in 0≤x≤5, is

    A 0

    B 21​

    C −21​

    D −23​

19. The value of x for which cosh−1(2x)=ln4 is:

    A 1617​

    B 815​

    C 1615​

    D 817​

20. A similarity transformation (similitude) f, on a complex plane is defined by z′=(1+i)z+3−4i. Its scale factor is

    A 1

    B 2​

    C 2

    D 5

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A LEVEL 2025 Further mathematics 1