H
CfE New Higher
4. Find the points of intersection of the line 𝑦 = 3𝑥 + 2 and the circle
with equation 𝑥 2 + 𝑦 2 + 4𝑥 − 6𝑦 − 28 = 0.
Homework Sheet 13
1. A(4, 5), B(0, 7) and C(-2, 2) are vertices of triangle ABC.
1
1
5. Evaluate 3 𝑙𝑜𝑔10 64 + 2 𝑙𝑜𝑔10 100 + 2𝑙𝑜𝑔10 5
a. Find the coordinates of D, the midpoint of AB.
b. Find the coordinates of E, the points that divides AC in the ratio
1:2
c. Find the coordinates of F, the point of intersection between BC
and DE.
6. A radio-isotope decays according to the formula 𝑚𝑡 = 𝑚0 𝑒 𝑘𝑡 ,
where 𝑚0 is the initial mass and 𝑚𝑡 the mass left after 𝑡 hours.
a. The half life of the radio-isotope is 60 years, find 𝑘.
b. How long will it take for the isotope to decay by 95%.
d. Find the ratio in which D divides EF.
2. 𝑓(𝑥) = 3𝑥, 𝑔(𝑥) = 𝑥 + 1 and ℎ(𝑥) = 𝑥 3
a. Find a formula for 𝑘(𝑥) where 𝑘(𝑥) = 𝑓(𝑔(𝑥)).
b. Find a formula for 𝑘 −1 (𝑥).
c. Find a formula for 𝑓(𝑔(ℎ(𝑥)))
3. If 𝑡𝑎𝑛𝐴 = 2 and 𝑡𝑎𝑛𝐵 = 3 find the value of cos⁡(𝐵 − 𝐴)
7. a) If 𝒂 = 𝒊 − 2𝒋 + 𝒌 and 𝒃 = −2𝒊 − 3𝒋 − 𝑐𝒌 are perpendicular,
find the value of 𝑐.
b) 𝒂 = −𝒊 − 2𝒋 − 𝒌 and 𝒃 = 𝒊 + 2𝒋 + 𝑐𝒌 make an angle of π
radians with each other. Find the value of 𝑐.