**SECTION I** (50 MARKS)

** **Answer **ALL** the questions from this section.

- Use logarithms to evaluate, (4 marks)

- Make P the subject of the formula (3 marks)

- Find the circle centre and radius whose equation is

3x^{2}+ 3y^{2}+ 18x – 6y + 18 = 0 (3 marks)

- The volumes of two similar cylindrical containers are 27cm
^{3}and 64cm^{3}Given that the height of the smaller container is 12cm, find the height of the larger container. (2 marks) - 3cm
^{3}of water is added to 2cm^{3}of a certain medicine which costs sh.12 per cm^{3}. The chemist sells the diluted medicine at sh.6 per cm^{3}. Calculate the percentage profit.

(3 marks) - Given that 4y = 3 sin
^{ 2}/_{5}for 0 < θ< 360^{o}. Determine- The amplitude of the curve (1 mark)
- The period of the curve. (1 mark)

- Find the length BC of the following triangle if AC = 3.7cm, AB = 4cm and angle ABC = 63
^{o}. (3 marks)

- Solve for x in the equation

27^{x }^{-}^{ 1}3^{x + 1}= 729 (3 marks)

- In the figure below ABCD is a cyclic quadrilateral. Point O is the centre of the circle. <ABO = 30
^{o}and <BCD = 110^{o}.

Calculate the size of angle ADB. (2 marks)

- Three people Mutua, Wanza and Kiilu contributed money to start a business. Mutua contributed a quarter of the money and Wanza two fifths of the reminder. Kiilu’s contribution was one and a half times that of Mutua. They borrowed the rest of the money from a bank which was sh.60,000 less than Kiilu’s contribution. Find the total amount required to start the business. (4 marks)

- Simplify (3 marks)

- Expand (2-
^{1}/_{4}x)^{5}and use the first three terms to find the value of 1.975^{5}to four significant figures. (4 marks)

- The radius of a spherical ball is measured as 7cm correct to the nearest centimeter. Determine to 2 decimal places, the percentage error in calculating the surface area of the ball. (3 marks)

- Given that tan θ=
^{1}/_{√5 }where θ is an acute angle, find without using tables or calculator sin (90−θ) leaving your answer in the simplified surd form. (4 marks)

- Given that a = 1.2, b = 0.02 and c = 0.2, express ac b in the form where m and n are integers. (3 marks)

- The diagram below shows sector AOB of a circle centre O. <AOB = 1.5
^{C}and arc AB is of length 12cm.- Determine the radius OA of the circle. (1 mark)
- Calculate the area of the shaded region. Give your answer correct to 3 s.f. (3 marks)

**SECTION II** (50 MARKS)

* Answer any FIVE questions from this section*