# What are the projected total costs if the car is driven 50,000 kilometers during its lifetime?

1. Kenya Securicor is contemplating the purchase of an additional patrol car. Company analysists estimate the purchase cost of fully equipped car to be \$18,000. They also have estimated an average operating cost of \$0.40 per kilometer.

i) Determine the mathematical function which represents the total cost C of owning and operating the car in terms of the number of kilometers x it is driven.

(3marks)

ii) What are the projected total costs if the car is driven 50,000 kilometers during its lifetime? (2marks) iii)If it is driven 100,000 kilometers? (2marks)

2. A sum of money invested at compound interest amounts to \$2,200 at the end of one year and to \$2,662 at the end of three years. Find the principal and the rate of interest. (4marks)

3. How long will it to take for principal to double if money is worth 7% per annum compounded continuously/ give your answer to the nearest year. (5marks)

4. A machine costs \$98,000 and its effective life is estimated to be 12 years. If scrap value of the machine is \$3,000 only, what should be retained out of profits at each of the year to accumulate at compound interest at 5% per annum so that a new machine can be purchased at the same price after 12 years? (Given; log 1.05 = 0.0212 and log 1.797 = 0.2544). (6marks)

5. In a survey of Kimathi University College students, 64% of the students take Economics and 56% take Accounting. How many students take both subjects? (4marks)

6. Solve the following quadratic equations

i) X2 – 9x + 14 = 0

ii) 3×2 + 6x – 45 = 0 (4marks)

Question two

1. A firm has the capacity to produce three types of cakes X, Y and Z using ingredients A, B and C.

the recipe for each unit of cake is given as follows:

X – 20, 15 and 40 grams of A, B and C respectively

Y – 12, 36 and 16 grams of A, B and C respectively

Z – 30, 15 and 40 grams of A, B and C respectively

If 130, 225 and 200 units of A, B and C respectively must be used. Formulate a set of simultaneous equations and solve them such that they would indicate the number of units of each cake to produce in order to utilize completely the available ingredients. (10marks)

2. Calculate the future amount of annuity immediate of \$2,000 per annum for 20 years, the rate of interest being 13.5% per annum. (6marks)

3. In the first month of production 1000 items were made. If the rise in monthly production is 5% per month, how many months are necessary to produce a total of 15,000 items?(4marks)

Question three

1. A machine is depreciated in such a way that the value of the machine at the end of any year is 90% of its value at the beginning of the year. The cost of the machine was \$12,000 and it was sold eventually as waste metal for \$200. Find the number of years during which the machine

was in use. (5marks)

2. Using relevant examples differentiate between the following terms as used in management mathematics:

i)Independent variable ii)Criterion variables iii)Discrete variables iv)Concomitant variables

v) Continuous variables (5marks)

3. The population of a country was 100 million in 1980. It has been growing since that time exponentially at a constant rate of four percent per year, p= f (t). What would be the projected

population of the country after twenty five years? (5marks)

4. Find the present value of an annuity of \$800 payable at the end of each 6 months for five years, if money is worth 6% per annum converted semi-annually? (5marks)

Question four

1. Graph the following inequalities simultaneously and show the wanted region.

X + 2y = 12

2x + y = 10

X + y =8

Y = 1

X = 2 (8marks)

2. An investor wanted to invest in two bonds. Which is a better bond, 8% per annum compounded half-yearly or 7.5% per annum compounded continuously? (4marks)

3. Solve the equations y + 2x = 3 and x2+ y2 = 2 (5marks)

4. If y = g(u) = 2u3and u = h(x) = x2– 2x + 5, determine

a) g(h(x)) (1mark)

b) g(h(2)) (1mark)

c) g(h(-3)) (1mark)

Question five

1. Magnet Publishers Limited is planning to produce a new novel. The fixed costs are Sh. 320,000 and the variable costs are Sh. 312.50 per novel. The wholesale price will be Sh. 437.50 per book.

How many books must the publisher sell to break-even? (4marks)

2. Consumer Link researchers surveyed 5200 people on how the get news. They found out that 3400 read news papers for their news, 1800 listen to radio and 1500 watch the Television. 800 read the newspapers and listen to radio, 850 read news papers and watch television and 350 listen to radio and watch television. If 250 utilize none of the three media, determine the number that used utmost two sources of news. (7marks)

3. Differentiate between the following terms as used in management mathematics:-

i.Annuity and Perpetuity (2 Marks) ii.Geometric Progression and Arithmetic Progression (2 Marks)

4. The bookstore had a sale on records, books and T-shirts. A cashier observed the purchase of 38 people and found that:

16 bought records

15 bought books

19 bought T-shirts

5 bought books and records

7 bought books and T-shirts

6 bought records and T-shirts

3 bought all three

i) How many bought records and T-shirts, but not books (2marks) ii) How many bought records, but no books (1mark) iii) How many bought T-shirts but no books and no records (1mark) iv) How many bought none of the three (1mark)

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