Use logarithms to evaluate the value of

Give your answer correct to 4 significant figures

Pipes S and T can fill a tank in 2 hours and 3 hours respectively. Pipe U can empty the full tank in 4 hours.

How long will it take to fill the tank with all the pipes running?

Make d the subject in the given formula.

In the figure below, the tangents DC and BC meet at point C, angle BCD=50⁰ while angle ABE=70⁰

Calculate the sizes of angles

i) <CBD

ii) <CDE

Solve for x in the equation below.

Solve the equation 3 Sin

In the diagram below, CD is a tangent to the circle at point D. If BC=7cm and CD=9cm, calculate the length of the chord AB.

Calculate the relative error

Determine the semi-interquartile range for the given set of data. 40,20,30,42,10,18,26,32

a) Expand up to a term in x³

b) Use the expansion in(a)above to find the value of (0.9)⁸

Mrs. Ondiek invested Ksh63560 in a bank where the interest was compounded quarterly at the rate of 12% per month. Determine the amount of money she had after 2 ½ years.

. Simplify without using mathematical tables or calculator.

The figure below is a square –based pyramid with vertex V. Point O is the intersection of diagonals AC and BC. VA=VB=VC=VD=12cm and AB=BC=4cm.

a) Name the projection of line VA on plane ABCD.

b) Find the angle between line VB and the plane ABCD.

An equation of a curve is given as

Find the equation of the tangent to the curve at x=1

Find the equation of a circle whose diameter has the end points (-2,6) and 6,2)

The distance between two places
on the earth via
South Pole is 3240nm. Find

a) the value of θ^0.

b) the distance between P and Q along the parallel of latitude in nautical miles

The table below shows income tax rates.

Income p.a in K₤ .................................................Rate %

1 - 3000....................................................................10

3001 – 5400 ............................................................15

5401 -9,000.............................................................. 20

9001 -13,500 ............................................................25

13,501 and above ....................................................30

Agnes earns a monthly salary of Ksh. 20,000 per month, Her house allowance is Ksh. 15000P.M. She is entitled to a personal relief of Ksh. 1260P.M. Her deductions are NHIF sh.960, cooperative loan sh. 3500 and service charge of Ksh.400 per month. Calculate

a) the taxable income.

b) the tax charged on Agnes earning.

c) the tax paid.

d) the net salary.

In the figure below, E is the midpoint of BC,AD:DC=3:2 and AE intersect with BD at

c) What is the ratio in which F divides . AE

Using a ruler and a pair of compasses only. a) Construct

a ∆ABC in which AB =7.4cm, AC=8.2cm and <BAC=45^0.

b) On the same diagram, construct ∆ACD such that D, and B are on the opposite sides of line AC, D is equidistant from A and C and BD=8.5cm. Measure AD.

c) Draw locus of Q which passes through C and is parallel to BD.

d) The normal from C meets BD at N. Mark the points M1 and M2 on the locus of Q such that M₁N=M₂N=4.1cm.

Measure the lengths M₁M₂ and CN.

. a) i) On the grid (graph paper) plot and draw triangle ABC where A(4,3),B(4,6) and C(7,6) .

GRID

ii) Triangle ABC is given a rotation of +900 about (0,0) to map onto A^IB^IC^1.Plot A^IB^IC^I and state its co-ordinates.

iii) Triangle A^IB^IC^Iis transformed by the matrix
to map onto A¹¹B¹¹C¹¹
Plot A¹¹B¹¹C¹¹ and state its co-ordinates.

b) AIIBIICII is further transformed by a reflection on the line x=0 to map onto A^IIIB^IIIC^III. Plot A^IIIB^IIIC^III

What single transformation will map A¹¹¹B¹¹¹C¹¹¹ onto triangle ABC?

. A particle P moves in a straight line so that its velocity Vm/s at time t seconds where 0

Find

a) The time when P is instantaneously at rest.

b) The speed of P at the instant when the acceleration of P is zero.

c) Given that P passes through point O of the line when t=0

i) Find the distance of P from O when P is instantaneously at rest.

ii) Find the distance covered by the particle during the 3rd second.

. The table below shows the masses in kg of some form three students in a school.

a) i) State the median class.

ii) Using an assumed mean of 54.5, calculate the mean mass

b) Calculate the standard deviation of the data, give your answer correct to 2 decimal places

The probability that it will rain on a certain morning is1/3 . If it rains, the probability
that Sagero misses the bus is 3/4 . If it does not rain, the probability that he catches
the bus is
5/6 .

a) Represent the above information in a tree diagram.

b) Calculate the probability that on a given morning

i) it rains and he catches the bus.

ii) it rains and he misses the bus.

iii) he misses the bus.

iv) it does not rain and he misses the bus.

. A small scale farmer wishes to buy some sheep and goats for rearing. A sheep costs sh.400 and a goat costs sh.300. The farmer has enough space for only 20 animals and may spend at most sh.6800. The number of goats should not exceed twice the number of sheep.

a) By letting x and y to represent the number of sheep and goats he can buy respectively, write down all inequalities from the above information.

b) Represent the inequalities on the grid provided.