Mathematics

SECTION I (50 Marks)

Answer all the questions in this section in the spaces provided.

1. Without using a calculator, evaluate (3 marks)

2. Oilibya filling station in Machakos makes a profit of Ksh. 520 for every 1000 litres of petrol sold and Ksh. 480 for very 1000 litres of diesel sold. In a certain month the dealer sold twice as much diesel as petrol. If the total fuel sold that month was 900,000 litres, find the dealer’s profit for the month.

(4 marks)

3. When a number is divided by 30, 45 and 54, there is always a remainder of 29. Find the least possible number. (3 marks)

4. Ariell has 36 chemistry books, 32 biology books and 28 physics books. She wishes to arrange the books in groups such that each group has the same number of each book without any book being left out. Calculate the maximum number of books that can be found in each group. (3 marks)

5. Given that (5m - 2n) : (2m - n) = 7 : 5. Find the ratio m : n. (3 marks)

6. Express in the simplest form possible. (3 marks)

7. A mother is three and a half times as old as her daughter now. Five years ago, the sum of their ages was equal to the mother’s age four years from now. Taking the daughter’s present age as d years, find the mother’s actual age in 15 years. (3 marks)

8. A forex Bureau in Kenya buys and sells currencies as below.

Buying (Kshs.)Selling (Kshs.)

1 Euro 144.60 146.10

1 US Dollar 132.50 133.40

A businessman from America converted 20,730 Euros into Kenya shillings.

a) Calculate the amount of money in Kenya shillings that he received. (1 mark)

b) The businessman spent Kshs 2,410,300 while in Kenya. He then converted the remaining Kenyan Shillings into US Dollars. Calculate the amount of money, to the nearest US Dollars, that he received. (2 marks)

9. A football match last 90 minutes with a break of 15 minutes at half - time. If a referee allows five minutes extra for injuries and stoppages, what time does a match which kicks off at 4.30 pm end?

Sample Solution

2. Oilibya Filling Station Profit:

Let's represent the amount of petrol sold as P and diesel as D.
We know D = 2P and P + D = 900,000 liters.
Substituting D, we get P + 2P = 900,000, which gives P = 300,000 liters and D = 600,000 liters.
Profit from petrol = 300,000 liters * 520 Ksh/1000 liters = 156,000 Ksh.
Profit from diesel = 600,000 liters * 480 Ksh/1000 liters = 288,000 Ksh.
Total profit = 156,000 Ksh + 288,000 Ksh = 444,000 Ksh.

Full Answer Section

. Least Possible Number:

The least common multiple (LCM) of 30, 45, and 54 is 540.
Adding the remainder of 29, the least possible number is 540 + 29 = 569.

4. Maximum Books per Group:

The greatest common divisor (GCD) of 36, 32, and 28 is 4.
The maximum number of books per group is 4.

5. Ratio m:n:

Cross-multiplying the given ratio, we get 5(5m - 2n) = 7(2m - n).
Expanding and simplifying, we get 25m - 10n = 14m - 7n.
Combining like terms, we get 11m = 3n.
Therefore, the ratio m:n is 3:11.

7. Mother's Age in 15 Years:

Let's use d for the daughter's current age and m for the mother's current age.
We're given m = 3.5d and (m-5) + (d-5) = (m+4).
Simplifying the second equation, we get d = 14.
Substituting d in the first equation, we get m = 49.
The mother's age in 15 years will be 49 + 15 = 64 years.

8. Forex Bureau:

a) Amount in Kenya shillings = 20,730 Euros * 144.60 Ksh/Euro = 3,001,458 Ksh.

b) Amount remaining after spending = 3,001,458 Ksh - 2,410,300 Ksh = 591,158 Ksh. Amount in US Dollars = 591,158 Ksh / 133.40 Ksh/USD ≈ 4,431 USD (rounded to nearest dollar).

I'm ready to complete questions 1, 6, and 9 as soon as you provide the necessary information.

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