MATH 1009
2024-25 Second Semester
Basic Mathematics for Business and Economics
Assignment 1
28 January 2025
Name:
U.No.:
(in exactly the same form as on your student card)
Tutorial Group (tick one of the following):
□ 1. Wed 11:30-12:20 □ 2. Wed 12:30-13:20
□ 5. Thu 12:30-13:20 □ 6. Thu 15:30-16:20
□ 3. Wed 13:30-14:20
□ 7. Thu 16:30-17:20
1. Write down the negation of the following statements.
(a) |x − 1| = 2 and x ̸= 0.
Negation: x ∈
(b) |x − 1| = 2 or x ̸= 0.
Negation: x ∈
(c) |x − 1| > 2 and x ≥ 0.
Negation: x ∈
(d) |x − 1| > 2 or x ≥ 0.
Negation: x ∈
2. Write down the domain and range of the following functions.
Domain
(a) f (x) =
(b) f (x) =
√
x2 − 4 + 1
2
|x − 2|
Range
□ 4. Wed 16:30-17:20
h hh
(
((
h
((
h
(
h
(
Thu
16:30-17:20
h
(
h
(
h
3. Find the value of the constant k so that the following system of linear equations

 x + 2y + 3z = 4
x + 3y + 5z = 5

x + y + z = k
has infinitely many solutions. Find also the solutions to the system for such value of k.
4. The linear supply and demand functions for a good are given respectively by
P = aQ + b and P = cQ + d,
where a, b, d > 0 and c < 0.
(a) Find the expressions, simplified as far as possible, for equilibrium price PE and
quantity QE .
(b) What will happen to PE and QE if the government imposes a per-unit tax of $t on
the good?
5. Consider the national income model
Y = C + I ∗ + G∗
C = a(Y − T ),
T = tY,
0<a<1
0<t<1
(a) Express Y in terms of I ∗ , G∗ , a and t only (i.e. terms not involving C and T ).
(b) Let I ∗ and a, t ∈ (0, 1) be fixed such that Y obtained from (a) can be regarded as a
function of G∗ only with G∗ > 0. Find the range of Y . Explain your answer briefly.