Cameroon GCE advanced level June 2025 mathematics with mechanics 1

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From the first image (image_4714c8.jpg):

SECTION A: PURE MATHEMATICS

1. Given that f:R→R, where f(x)=x+1x+2​, the range of f is

   A {x∈R,x=1}

   B {x∈R,x=−2}

   C {x∈R,x=−1}

   D {x∈R,x=0}

2. If functions g:R→R and function h:R→R are such that f(x)=3x−2 and h(x)=x2+2, then (g∘h)(x)=

   A 3x+3

   B 3x−3

   C 3x−5

   D 3x+5

3. If A=​147​258​369​​, then the cofactor of the element 6 is

   A ​17​28​​

   B −​17​28​​

   C +​17​28​​

   D −​17​28​​

4. If (1−x)(2x+x)2x+1​=1−xA​+2+xB​, then

   A A=1,B=1

   B A=1,B=−1

   C A=−1,B=1

   D A=−1,B=−1

5. The normal vector to the plane 6x+2y−7z−12=0 is

   A 6i−2j+7k

   B 6i+2j−12k

   C 6i−2j−7k

   D 6i+2j−7k

6. If α and β are roots of a quadratic equation such that α+β=3 and αβ=23​.

   The value of α2+β2=

   A 12.

   B 5

   C 6

   D 9

7. When f(x)=2×3+x2−13x+6 is divided by x+1 the remainder is

   A 20

   B −4

   C 18

   D −6

8. The range of values of x for which ∣x+4∣≤2 is:

   A x≤−6

   B x≤−6 or x≥−2

   C x≥−2

   D −6≤x≤−2

9. If sinθ=54​ and θ is an acute angle, then the exact value of 2sinθcosθ is

   A 24

   B 1625​

   C 925​

   D 2512​

10. The values of x that satisfy the equation 32x+1−10(3x)+9=0 are

    A x=1,x=2

    B x=−2,x=0

    C x=−1,x=9

    D x=0,x=2

11. If y=0 when x=2, then the solution of the differential equation dxdy​=x is

    A y2=x2+2

    B y2=x2−4

    C y2=x2−2

    D y2=x2+4

12. On the set A={2,4,8,16}, a relation R is defined by xRy if and only if y is a multiple of x. R is

    A an equivalence relation

    B symmetric

    C transitive

    D Not reffective

13. The line segment AB, where A(5,5) and B(3,−2), is the diameter of a circle. The equation of the circle is

    A (x−5)(x−3)+(y−5)(y−2)=0

    B (x−5)(x+3)+(y−5)(y+2)=0

    C (x−5)(x−3)+(y+5)(y+2)=0

    D (x−5)(x−3)+(y−5)(y−2)=0

From the second image (image_4714e3.jpg):

14. Two vectors a and b are given as a=i+3j+2k and b=2i−j+2k. The vector product a×b is

    A 8i+2j−7k

    B 8i−2j−7k

    C 8i−2j+7k

    D 8i−6j−7k

15. The volume generated when the area of the finite region enclosed by the x-axis and the curve y=2×2−4x is rotated completely about the x-axis is

    A π∫02​(2×2−4x)2dx

    B π∫02​(2×2−4x)2dx (Note: This is identical to option A in the image)

    C 2π∫02​(2×2−4x)2dx

    D π∫−20​(2×2−4x)2dx

16. A root of the equation x3+x−26=0, lies between

    A 1 and 2

    B 3 and 4

    C 4 and 5

    D 2 and 3

17. The sum of the first n terms of a sequence is given by Sn​=2n2+n. The nth term of this sequence is

    A 4n+1

    B 4n−3

    C 4n−1

    D 4n+3

18. The first three terms in the binomial expansion of (1+3x)−1 are

    A 1−3x+9×2

    B 1+3x−9×2

    C 1−3x−9×2

    D 1−3x+9×2

19. The value of x for which log2+log(2x+5)=1 is

    A 2

    B −21​

    C 1

    D 23​

20. limx→2​x2−5x+6x−2​=

    A 0

    B −1

    C ∞

    D 1

21. ∫1e​x1​dx=

    A ln2

    B ln4

    C 21​ln2

    D 21​ln4

22. If y3=12x−x3 then dxdy​=

    A y2x2−4​

    B y2x2+4​

    C y24+x2​

    D y24−x2​

23. The complex number 3−4i1+2i​ can be expressed in the form a+bi as

    A 2511+5i​

    B 25−11−5i​

    C 251−5i​

    D 5−1​−5i​

24. The argument of the complex number z=1+i1+i3​​ is

    A 4π​

    B 12π​

    C 127π​

    D −12π​