Learning, Teaching and Applying Number and Algebra Past Question (Theory) for Level 100 Students

General Instructions:

This paper is made up of four essay-type questions
Answer Two questions in your answer booklet
Each question carries equal marks. You are expected to start each question from a new page
You are expected to handover your answer booklet to the invigilator before you leave the examination Hall

The Questions

1. The Function f and g are defined on the set of real numbers by f:x→2x+3 and  g:x→3x-1.
A teacher made a claim that fog(x)≠gof(x). As a student teacher, explain whether or not this claim is correct.
A number was expressed in base five as 3123five. What is the same number given in mod 5?
Given that x is areal number, solve for the value of x and represent your answer on the number line from the inequality 2/3 x-x/3+x/2 < 5


2. If n(AnB)=2,n(AnB^' )=14 and n(A^' nB)=12.

a, Find n(B)
b, the Sum of the ages of a mother and her son is 46years. In four years’, time, the ratio of their ages will be 7:2. Find their present ages.
c, Write the rational number 0.5 in the form x/y where x and y are real number such that y≠0

3. In his will, a father left an estate worth GH¢76,000,000.00. Out of this, GH¢ 16,000,000.00 was reserved for various purposes. The rest of the amount was shared among his three children. The oldest son received 20% of the amount. The remaining amount was shared between the son and the daughter in the ratio 3:2 respectively. Calculate, the
a, amount that the oldest son received;
b, the amount that the daughter received;
c, the difference between the amounts the two sons received.

4. a. in about three sentences, describe the closure property of sets, with an example

b. Identify the operations which would make the set of integers closed.
c. Two student teacher in a discussion, argued that a counting numbers are rational numbers but not all rational numbers are counting numbers. Using the theory of sets, illustrate the relationship between the two sets of numbers.