Test exercise 1a
1 Simplify the following algebraic expressions:
(a)3x4x22 5x8x2[2]
(b)x(3×2) 3x(x5)[2]
(c)2
4 2x
x y y
[2]
2 A consumption function is given byC aY b.
It is known that when Y= 10, the value of Cis 28, and that when Y= 30, the value
of Cis 44.
By solving a pair of simultaneous equations, find the values of aand b, and deduce
that the corresponding savings function is given by
S0.2Y20[6]
Determine the equilibrium level of income when planned investment I= 13. [4]
3 A demand equation of a certain good is given by
20 0.04 4 3rQ P Y T P
where Qand Pdenote the quantity and price of the good, Yis income, Tis taste,
andrPis the price of a related good.
(a) Calculate Qwhen P= 8, Y =1000, T= 15 and30rP. [2]
(b) Is the related good, substitutable or complementary? Give a reason for
your answer. [2]
(c) Find the value of Pwhen Q =235, Y= 8000, T= 30 andrP= 25. [3]
(d) The exogenous variables are now fixed at Y= 2000, T= 10 and5rP. State
the values of the slope and vertical intercept when the demand equation is
sketched with
(i) Pon the horizontal axis and Qon the vertical axis [2]
(ii) Qon the horizontal axis and Pon the vertical axis. [4]
Jacques: Mathematics for Business and Economics, 5th edition, Instructors Manual
10
© Pearson Education Limited 2006
4 (a) Solve the equation
6(2 x) 5(1 4x)[3]
(b) Solve the inequality
3×6 5×14[3]
(c) Make xthe subject of the formula
y3 2
x
[3]
5 (a) Copy and complete the following table of values for the supply function
1 20
2
P Q[3]
Q 0 50
P 25
Hence, or otherwise, draw an accurate sketch of this function using axes with
values of Qand Pbetween 0 and 50. [2]
(b) On the same axes draw the graph of the demand function
P50 Q
and hence find the equilibrium quantity and price. [5]
(c) The good under consideration is superior. Describe the effect on the
equilibrium quantity and price when income rises. [2]
Jacques: Mathematics for Business and Economics, 5th edition, Instructors Manual