Advanced level 2024 CASPA mock mathematics with mechanics 1

Advanced level 2024 CASPA mock mathematics with mechanics 1

Advanced level 2024 CASPA mock mathematics with mechanics 1

. The value of x for which 42+𝑥 − 8(22𝑥) = 2𝑥
4
is
A) −8
B) 1
C) −5
D) 5
2. Given that log6(𝑥 + 2) − log6 𝑥 = 2, then 𝑥 =
A) − 2
35
B) 2
35
C) −6
D) 1
18
3. Given that 𝑃𝑥+9
𝑥(𝑥−3)
≡
𝑄 𝑥
+ 4
𝑥−3
, then the values of P
and Q are respectively
A) 1, 3
B) −3, 1
C) 1, −3
D) −1, −3
4. Given that f is a periodic function of period 4 and
that 𝑓(𝑥) = {𝑥𝑥+2,20, 2≤≤𝑥𝑥<<24 then 𝑓(9) =
A) 1
B) 81
C) 11
D) 7
5. (𝑥 + 1) + 𝑥−1
𝑥2+1 is the result obtained by dividing
two polynomials. The remainder is
A) 𝑥 + 1
B) 𝑥 − 1
C) 𝑥2 + 1
D) 1 − 𝑥
6. Simplifying (𝑥−2)!
(𝑥−5)!5! gives
A) (𝑥 − 3)(𝑥 − 4)
B) (𝑥−3)(𝑥−4)
120
C) 1
120(𝑥−5)(𝑥−4)(𝑥−3)
D) (𝑥−2)(𝑥−3)(𝑥−4)
120
7. The set of values of x for which |𝑥 𝑥+ −3 4| = 𝑥 𝑥+ −3 4 is
A) −3 < 𝑥 < 4
B) 𝑥 ≤ −3 ∪ 𝑥 > 4
C) 𝑥 < −3 ∪ 𝑥 ≥ 4
D) 𝑥 ≤ −3 ∪ 𝑥 ≥ 4
8. Given that the roots of the equation
−𝑥2 + 𝑘𝑥 − 2 = 0 differ by 1, then
A) 𝑘2 − 9 = 0
B) 𝑘2 − 12 = 0
C) 𝑘2 + 9 = 0
D) 𝑘2 + 12 = 0
9. The domain of definition of the function f(𝑥) =
𝑙𝑛(5𝑥 − 2), 𝑥 ∈ ℝ is
A) ℝ+
B) ℝ − {2 5}
C) {𝑥: 𝑥 > 2 5 , 𝑥 ∈ ℝ}
D) {𝑥: 𝑥 < 2 5 , 𝑥 ∈ ℝ}
10. Given that k is a constant and that (1−sin 𝑦 𝑥) 𝑑𝑦 𝑑𝑥 =
(cos 𝑦 𝑥)2, then y =
A) √2𝑥 − 2 cos 𝑥 + 𝑘
B) √𝑥 − cos 𝑥 + 𝑘
C) √2𝑥 − 2 cos 𝑥 + 𝑘
D) √2𝑥 + 2 cos 𝑥 + 𝑘
11. The number of arrangements of the letters of the
word INSECT in which the vowels are together is
A) 720
B) 240
C) 120
D) 60
12. If the matrix (6 4 2 −−𝑘𝑘3 2 3 2) is singular,
then the value of k is
A −2
B 3
C −3
D 2
13. Given the complex number z = −1 + i, then
arg(z6) =
A) − 3π
2
B) 3𝜋
2
C) − 9π
2
D) 9𝜋
2
14. The sum of the first n terms of an arithmetic
progression is 187. Given that the first term is 2 and
the 𝑛𝑡ℎ term is 32, the value of n is
A) 11
B) 6
C) 66
D) 67
15. For odd values of n, ∑n r=1(−1)r(2r + 1) is equal
to
A) 2 − n
B) n + 2n2
C) n − 2n2