Topic 6: Algebra 2 – Sample Activity

Context

Bwindi and Mgahinga are national parks found in the southwestern part of Uganda. These parks are commonly known for mountain gorillas which attract tourists from all over the world and these pay a lot of money to Uganda. In turn, the Ugandan-government, through its tourism structures, gives back to the communities living around these parks by sharing revenue with them to compensate them for the damage caused to their crops by wild animals. Unfortunately, this compensation for the damage is never in relation to the revenue from each of the two national parks.

Support Material

1. The number of tourists usually depends on the number of gorilla families available for tracking. Bwindi National Park has 12 gorilla families and Mgahinga has 4 families.
2. It was proposed that each area be given UGX 10 million as basic revenue, then the remainder be shared in relation to revenue from each of the forests.

Task

You are the regional accountant for the two great national parks in southwestern Uganda. Prepare a formula to guide in sharing a total income X available for the two areas: Mugahinga and Bwindi respectively.

Topic Summary

In this topic, you have learnt that:

1. for two factors (a+b) and (c+d), then: (a+b) (c + d) = ac + bc + ad + bd
2. a difference of two squares a2 and b2 is given by: a2-b2 = (a + b) (a + b)
3. if ab = 0, then, either a = 0 or b = 0
4. for a quadratic expression x2 + bx + c = 0 which can be factorised, b is sum of roots and c is product of roots.
5. two quadratic expressions x2 + bx + c and (x +p)(x + q) are equivalent if
   • pq = c
   • p+q=b

Revision Exercise

Factorise the following algebraic expressions.

1. (a) t2 + 6t+8

(c) t2+3t-18 2.

(b) t2 t 30

(d) 25t2-36

2. Factorise the following perfect squares.

(a) t2 + 4t+4

(c) t2-18t+81

(b) t2-14t2 +49

3. Peter is 12 years older than John. Given that the product of the ages of Peter and John is 45, find the age of each person.

4. The length of a garden is 14 metres longer than the width. Given that the area of the garden is 32 square metres, find the perimeter of the garden.