Advanced level 2024 CASPA mock Further mathematics 1

Advanced level 2024 CASPA mock Further mathematics 1

Advanced level 2024 CASPA mock Further mathematics 1

Let 𝑝 be the proposition “I work hard” and 𝑞 the proposition “I

pass the G.C.E 2024 session”.
A notation for the statement “I will pass the G.C.E 2024 session if
and only if I work hard” is
A) 𝑝 ⟹ 𝑞
B) ∼ 𝑝 ⟹ ∼ 𝑞
C) 𝑝 ∧ 𝑞
D) 𝑝 ⟺ 𝑞
2. Given that f x x      is the greatest integer function, then
f x  is continuous in the interval
A) 1,0
B) 1,0
C) 1,0
D) 1,0
3. The value of x for which arcsinh 3 ln 4 x  is

4. Which one of the following series converges
A) ∑∞ 𝑟=0(−1)𝑟
B) ∑ 1
𝑟3
∞𝑟=
1
C) ∑ 1
√𝑟
∞𝑟=
1
D) ∑ 1
𝑟
∞𝑟=
1
5. Expressing 3𝑥2+1
(𝑥2−4)(𝑥−2)2 into partial fractions, where 𝐴, 𝐵, 𝐶, and
𝐷 are constants is
A) 𝐴𝑥+𝐵
𝑥2−4 + 𝑥−𝐶2 + (𝑥−𝐷2)2
B) 𝐴
𝑥+2
+ 𝐵
𝑥−2
+ 𝐶
(𝑥−2)2
C) 𝐴
𝑥+2
+ 𝐵
𝑥−2
+ 𝐶
(𝑥−2)2 + (𝑥−𝐷2)3
D) 𝐴𝑥+𝐵
𝑥2−4 + (𝐶𝑥 𝑥−+2𝐷)2
6. An equation of the tangent at the pole to the polar curve
r   4(1 cos )  is =
A) 0
B)
 2
C) 
D) 2
7. The vector product 𝒊 × (𝒊 − 𝒋) =
A) 𝒌
B) −𝒌
C) 0
D) 𝒊 − 𝒌
8. A particle P moves on the curve 𝒓 = 3𝑡𝒊 + 4𝑡2𝒋. The distance of
P from the origin when 𝑡 = 1 is
A) 3
B) 4
C) 5
D) 7
9. The binary operation ∗ is defined on the set S  0,1, 2, by
𝑎 ∗ 𝑏 = (𝑎 × 𝑏)𝑚𝑜𝑑𝑢𝑙𝑜3, the pair (𝑆,∗) does not form a group
because
A) ∗ is not associative
B) there is no identity element
C) 𝑆 is not closed under ∗
D) not all elements have inverses
10. The velocities of a smooth sphere A before and after colliding
with an identical sphere B, are (3𝒊 – 𝒋) ms1 and (3𝒊 – 2 𝒋) ms1
respectively. Their line of centres is in the direction of the vector
A) 𝒊
B) −𝒊 + 𝒋
C) 𝒊 – 𝒋
D) 𝒋
11. A component of the force (3𝒊 − 𝒋 + 𝒌) 𝑁 in the direction of
the vector (𝒊 − 𝒌) is
A) 2
B)
2
2
C) 2
D) 2√3
3
12. A particle moves round the curve r ae   , a > 0, with
constant angular velocity  . If V R and V T
are the radial and transverse components of its velocity
respectively, then
A) V V R T 
B) V V R T 
C) V V T R 
D) V V R T 
13. If X is a discrete random variable with probability function
f , then its mean, E X ( ) 
A) ( )
allx
 f x
B) 2 ( )
allx
x f x
C) ( )
allx
xf x
D) ( ) 2
allx
 f x
14. The statement “some real numbers are not integers” can be
represented symbolically as
A) ∃𝑥 𝜖 ℝ 𝑠. 𝑡 𝑥 𝜖 ℤ
B) ∃𝑥 𝜖 ℝ 𝑠. 𝑡 𝑥 ∉ ℤ
C) ∀𝑥 𝜖 ℝ , 𝑥 ∉ ℤ
D) ∃𝑥 ∉ ℝ 𝑠. 𝑡 𝑥 𝜖 ℤ
15. If the real – valued function