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
3x2 + 3y2 + 18x – 6y + 18 = 0 (3 marks)
- The volumes of two similar cylindrical containers are 27cm3 and 64cm3 Given that the height of the smaller container is 12cm, find the height of the larger container. (2 marks)
- 3cm3 of water is added to 2cm3 of a certain medicine which costs sh.12 per cm3. The chemist sells the diluted medicine at sh.6 per cm3. Calculate the percentage profit.
- Given that 4y = 3 sin 2/5 for 0 < θ< 360o. 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 = 63o. (3 marks)
- Solve for x in the equation
27x - 1 3x + 1 = 729 (3 marks)
- In the figure below ABCD is a cyclic quadrilateral. Point O is the centre of the circle. <ABO = 30o and <BCD = 110o.
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 (2-1/4x)5 and use the first three terms to find the value of 1.9755 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 = 1.5C 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