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Issue No. 0933
December 10 - 16, 2016

Society

TALKING MATHEMATICS

By Vincent Obiro Orute Obunga

Revise so as to pass mathematics exam

1. (a) Three consecutive terms of an arithmetic progression (AP) are such that their sum is 15 but their product is 45. Find the three terms of the AP, hence or otherwise, find the common difference of the AP.

(b) The first three terms of the sequence 18, x, y, 48 form an arithmetic progression (AP) but the last three form a geometric progression (GP). Find all possible values of x and y.

(c) Two police officers were together at a road junction. Each had a Walkie Talkie. The maximum distance at which one could talk with the other was 2.5 km. One of the police officers walked due East at 3.2 km/h while the other walked due North at 2.4 km/h. Given that the police officer who headed East travelled for x km while the one who headed North travelled for y km before they were unable to communicate with each other.

i. Draw a sketch to represent the relative positions of the two police officers

ii. From the above information form two simultaneous equations in x and y

iii. Find the value of x and y

iv. Calculate the time taken before the two police officers were unable to communicate with each other

2. (a) The value (V) of a piece of Blue Tanzanite is directly proportional to the square of its weight (W). It is known that a piece of  Blue Tanzanite weighing 10 grams is worth  Tshs 200,000/=

i. Write down an expression which relates V and W

ii. Find the value of a piece of  Blue Tanzanite weighing 30 grams

iii. Find the weight of a piece of  Blue Tanzanite worth Tshs 5,000,000/=

(b) A car travels 250 km in the same time that a bus takes to travel 225 km. If the speed of the car is 8 km/h faster than that of the bus, calculate:

i. The speed of the car

ii. The speed of the bus

(c) An old computer takes 12 minutes longer to print a payroll than does a new one. Working together, the two computers take 8 minutes to complete printing the same payroll. How long would it take each computer working alone to complete printing the same payroll?

(d) Working together, Odunga takes 6 hours to complete painting a room. If his son, Otunga helps him, the two take 4 hours to complete painting the same room. Determine how long it would take his son to complete painting the same room if he worked alone without his father helping him.

3. The distance between two towns P and Q is 520 km. Obuya bus left town P at       7.30 a.m in the morning and travelled towards town Q at an average speed of          70 km/h. At the same time, Agwambo bus left town Q and travelled towards town     P at an average speed of 60 km/h using the same route.

(a) At what speed were the two buses approaching each other?

(b) How far apart were the two buses after travelling for 2 hours and 30 minutes?

(c) How long did the two buses take before they met?

(d) At what time of the day did the two buses meet?

(e) How far was their meeting point from town P and from town Q?

4. A group of people in Ngorongoro decided to raise money towards the community water project that required Tshs 20 million to complete. However, 40 of the members of the group were unable to raise the required amount. As a result, each of the remaining members of the group had to contribute Tshs 25,000/= more.

Determine:

(a) The original number of members in the group

(b) The new number of members in the group after 40 members of the group were unable to raise the required amount

(c) An American tourist visited the area and saw the plight of the villagers and decided to donate 40 % of the total amount required. Calculate the amount of contribution that would now be made by each of the remaining members of the group.

(d) The members’ contributions were in terms of labour provided and money contributed. If the ratio of the value of the labour to the amount of money contributed was 6 : 19, calculate the total amount of money contributed by the members of the group.

5. On a coach outing, there are x children and y adults. The coach can seat a maximum of 50 passengers when full.

(a) Write down an expression in terms of x and y which satisfies this condition. Note that the coach need not be full in order to satisfy this condition.

(b) The number of children must be greater than or equal to twice the number of adults. Write down an expression in terms of x and y which satisfies this condition.

(c) A charge of Tshs 20,000/= is made for each child and Tshs 40,000/= for each adult. Write the total charge for x children and y  adults

(d) The total amount generated must be greater than or equal Tshs 600,000/=. Write down an expression in terms of x and y which satisfies this condition.

(e) Draw a graph to show the region that is satisfied by all these conditions together with the conditions x0 and y  0. Shade out the unwanted region and label all the lines.

(f) What is the smallest possible number of children on the outing if all these conditions are satisfied?

The table below shows the marks obtained by 80 Form Four students of Arusha Day secondary school in a mathematics test.

Marks (%)

Frequency (f)

31 – 40

4

41 – 50

9

51 – 60

16

61 – 70

26

71 – 80

15

81 – 90

7

 91 – 100

3

(a) State the modal class.

(b) Calculate an estimate of the mean mark using an assumed mean of 55.5

(c) Calculate an estimate of the median mark.

 




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