Advanced level 2025 North West Regional Mock mathematics mechanics 3 guide

Advanced level 2025 North West Regional Mock mathematics mechanics 3 guide

Advanced level 2025 North West Regional Mock mathematics mechanics 3 guide

PURE MATHS AND MECHANICS
(PMM)-0765 P3_2025_MOCK GCE
GUIDE
1(a) 𝑡 = 2, 𝑟⃗ = 3𝑖 + 8𝑗 M1A1
(b) 𝑣⃗ = 𝑑𝑟⃗
𝑑𝑡
= 2𝑖 + 3𝑡2𝑗 M1A1

(c) 𝑣⃗𝐵 – 𝑣⃗𝐴 = 2𝑡𝑖 + 2𝑗 𝑣⃗𝐵 = (2𝑡 + 2)𝑖 + (2 + 3𝑡2)𝑗

M1

M1A1
𝑡 = 0, ⇒ 𝑣⃗𝐵 = 2𝑖 + 2𝑗

|𝑣⃗𝐵| = √22 + 22 = 2√2 (d) 𝑟⃗ = ∫ 𝑣⃗ 𝑑𝑡

M1A1

𝑟⃗ = (𝑡2 + 2𝑡)𝑖 + (2𝑡 + 𝑡3)𝑗 + 𝑐⃗ M1
𝑡 = 0, 𝑟⃗ = (𝑖 – 𝑗) ⟹ 𝑐⃗ = 𝑖 – 𝑗 M1A1
∴ 𝑟⃗ = (𝑡2 + 2𝑡 + 1)𝑖 +
(𝑡3 + 2𝑡 – 1)𝑗 A1
2. (q) 𝐼 = 𝑚𝑣 – 𝑚𝑢

⇒ -𝑚𝑢 = 𝑚𝑣 – 𝑚(3𝑢)	M1
⇒ 𝑣 = 2𝑢	A1
𝑣 = 2𝑢, 0 < 2𝑢 < 3𝑢 hence lowered
and in same direction (b) 𝐾𝐸𝑖 = 1 2 𝑚(3𝑢)2,	A1

𝐾𝐸
𝑓 =
1 2
𝑚(2𝑢)2 M1
Δ𝐾𝐸 = 𝐾𝐸𝑖 – 𝐾𝐸𝑓 = 5 2 𝑚𝑢2 M1A1
c) 𝑣 = 𝑠
𝑡
⇒ 𝑡 = 𝑠
𝑣
=
6𝑢
2𝑢
= 3𝑠 M1A1
d) 𝑉 = -𝑒𝑣 = – 1
2
(2𝑢) = -𝑢
M1A1
𝑡2 = |-6𝑢𝑢| = 6𝑠
M1
𝑇 = 𝑡 + 𝑡2 = 9𝑠 M1A