A Kenyan bank buys and sells foreign currency as shown below.

A tourist arrived in Kenya with £9600 which he converted into Kshs at a commission of 5%. He later used ¾ of the money before changing the balance of dollars at no commission calculate; to the nearest dollar, the amount he received. (3marks)

Solve the equation 2x² + 3x = 5 by completing the square method                    (3mks)

   Solve for x in the equation                              (3mks)

Annette has some money in two denominations only. Fifty shillings notes and twenty shilling coins. She has three times as many fifty shilling notes as twenty shilling coins. If altogether she has sh. 3,400, find the number of fifty shilling notes and 20 shilling coin.   (3mks)

Solve the simultaneous equalities and state the integral values of :           (3mks)

The cost price of 31 inch flat LG TV screen is Ksh 36,500. Mary bought a screen on hire purchase price by paying a deposit of Ksh 12,000 and 15 monthly installments of Ksh 2050 each. Calculate the monthly rate of interest she was charged. Give your answer to 2 decimal places.    (4mks)

The position vectors of points A and B are 2i-3j+9k  and -5i+k  respectively. Calculate \AB\ , leaving your answer in surd form.              (4 marks)

Complete the figure below to show a rotational symmetry of order 6 about O.        (3 marks)

       Evaluate             

                                                     (4mks)               

   (a) find the inverse of the matrix                                  (1mk)

   (b) Hence solve the simultaneous equation using the matrix method                      (2mks)

A farmer has a piece of land measuring 840m by 396m. He divides it into square plots of equal size. Find the maximum area of one plot.                                                 (3mks)

Solve  the equation 8x² + 2x – 3 =0 hence solve the equation 8Cos²y + 2Cosy – 3 = 0 For the range 0⁰< y <180⁰                    (4mks)

Solve for x in the equation.                          (3mks)

Express the following in surd form and simplify by rationalizing the denominator.      (3mks)

The figure below shows a circle with segments cut off by a triangle whose longest side XY is the largest possible chord of the circle. XY = 14 cm and XZ = YZ

Calculate the area of the shaded part, correct to 2 decimal places. Use                    (3 marks)

Given that  sin ⁽²/₃x+20⁰) - cos (⁵/₆x+10⁰) = 0. Without using a mathematical table or a calculator, determine tan (x+ 20⁰).      (3 mks)

  On the graph paper provided plot the points P(2,2) Q(2,5) and R(4,4)

a.     Join them to form a triangle PQR   (1mk)

b.     Reflect the triangle PQR in the line x=0 and label the image s P₁Q₁R₁. (2mks)

c.      Triangle PQR is given translation by vector T (1,2) to P₁₁Q₁₁R₁₁.plot the triangle P₁Q₁R₁.       (3mks)

d.     Rotate triangle P₁₁Q₁₁R₁₁ about the origin through -90⁰.state the coordinates of P₁₁₁Q₁₁₁R₁₁₁.    (3mks)

e.     Identify two pairs of triangle that are direct congruence (1mk)

1. Without using a protractor, construct triangle ABC, such that BC = 10cm, angle ABC = 60⁰ and angle BCA = 45⁰ (let BC be the base)             (4mks)

2. Construct the perpendicular bisector of lines BC on the above diagram. Draw the circumference of triangle ABC.                (3mks)

3. Find the radius of the circumference hence determine the area of the circle drawn.                 (3mks)

Mesurements of a maize field using a base line XY were recorded as shown below in a field book as follows: (take XY = 400cm)

(a) Use a scale of 1cm to 40m to draw the map of the maize field. (5mks)

(b) Find the area of the maize field in hectares. (5mks)

The diagram below shows a frustum made by cutting off a small cone on a plane parallel to the base of the original one. The frustum represent a bucket with the open end diameter of 36cm and diameter of the bottom 24cm. the bucket is 18cm deep as shown (Take Õ = 22/7)

Calculate the:

(a) Volume of the small cone cut off.                (3mks)

(b) Volume of the original cone                             (2mks)

(c) The capacity of the bucket in liters                    (2mks)

A cylindrical milk urn has diameter 40 cm and height 1.4 metres.

(a) Calculate the capacity of milk in litres in the urn when it is full, to the nearest litre. Use  .            (2 marks)

(b) The milk is packed into tetrahedron packets of capacity 200 ml. Calculate the number of packets used.    (2 marks)

(c) The packets are packed into boxes that contain 24 packets each. How many complete boxes are used to package the milk?                                 (2 marks)

(d) Each box is sold at Kshs. 840, a profit of 12%. Calculate the buying price of each packet.            (4 marks)

In the figure below, ABC is a tangent to the circle at B.

(a) Given that ÐABG=42⁰ , ÐEBD=27⁰  and ÐBGD=49⁰ , calculate the sizes of the following angles. Give reasons in each case

 (i) ÐDGE                                                             (2 marks)

 (ii) ÐGFE                                                              (3 marks)

 (iii) Ð DBC                                                            (2 marks)

(b) Given that BC=10  cm and CD=7  cm, calculate TS          (3 marks)

Awuor was paid an initial salary of Kshs. 180,000 per annum with a fixed annual increment. Wasonga was paid and initial salary of Kshs. 150,000 per annum with a 10% increment compounded annually.

(a) Given that Awuor’s annual salary in the 11th year was Kshs. 288,000, determine:

 i) Her annual increment                        (3 marks)

ii) The total amount of money Awuor earned during the 11 years             (3 marks)

(b) Determine Wasonga’s monthly earning, correct to the nearest 10 shillings during the 11th year.        (4 marks)

A trailer 30m long moving at an average speed of 60km/h started from station A towards station B at 4.00am ,a bus moving at an average speed of 90km/h and 20m long started also travelling from A towards B at 4.30am .

find:

a) The time the bus caught up with the trailer                 (4mks)

b) The time in seconds the bus took to pass the trailer completely          (3mks)

c) How far from A did the bus completely overtake the trailer            (3mks)