Using a ruler and a pair of compasses only, draw a parallelogram ABCD, such that angle DAB = 75⁰. Length AB = 6.0cm and BC = 4.0cm.From point D, drop a perpendicular to meet line AB at N.                                                   (7 Marks)

(i) Measure length DN                                                                                                            (1 Mark)

(ii) Find the area of the parallelogram.                                                                                  (2 Marks)

A number of people agreed to contribute equally to buy books worth KSh. 1200 for a school library. Five people pulled out and so the others agreed to contribute an extra Shs. 10 each. Their contributions enabled them to buy books worth Shs. 200 more than they originally expected.

(a) If the original numbers of people was x, write an expression of how much each was originally to contribute.                                                                             (1 Mark)

(b) Write down two expressions of how much each contributed after the five people pulled out.   (2 Marks)

(c) Calculate the number of people who made the contribution.                           (5 Marks)

(d) Calculate how much each contributed.                                                      (2 Marks)

A ship leaves port M and sails on a bearing of 050⁰ heading towards island L. Two Navy destroyers sail from a naval base N to intercept the ship. Destroyer A sails such that it covers the shortest distance possible. Destroyer B sails on a bearing of 20⁰ to L. The bearing of N from M is 100⁰ and distance

NM = 300KM. Using a scale of 1cm to represent 50km, determine:-

(i) the positions of M, N and L.                                                                 (3 Marks)

(ii) the distance travelled by destroyer A                                                                               (3 Marks)

(iii) the distance travelled by destroyer B.                                                                             (2 Marks)

(iv) the bearing of N from L.                                                           (2 Marks)

Karis owns a farm that is triangular in shape as shown below.

(a) Calculate the size of angle BAC                                 (2 Marks)

(b) Find the area of the farm in hectares                                                (3 Marks)

(c) Karis wishes to irrigate his farm using a sprinkler machine situated in the farm such that it is equidistant from points A, B and C.

i) Calculate the distance of the sprinkler from point C.            (2 Marks)

ii) The sprinkler rotates in a circular motion so that the maximum point reached by the water jets is the vertices A, B and C. Calculate the area outside his farm that will be irrigated.                     (3 Marks)

The distance between towns A and B is 360km. A minibus left town A at 8.15 a.m. and traveled towards town B at an average speed of 90km/hr. A matatu left town B two and a third hours later on the same day and travelled towards A at average speed of 110km/hr.

a) (i) At what time did the two vehicles meet?                                        (4 Marks)

(ii) How far from A did the two vehicles meet?                                        (2 Marks)

b) A motorist started from his home at 10.30 a.m. on the same day as the matatu and travelled at an average speed of 100km/h. He arrive at B at the same time as the minibus. Calculate the distance from A to his house.                               (4 Marks)

Oketch sells his car to Jane and makes a profit of 20%. Jane sells the same to Issa at Sh.180, 000, making a loss of 10%. Determine the price at which Oketch bought the car.                        (3 Marks)

Solve for x in  2^2x  -  18  x  2^x = 40                                                     (3 Marks)

Town X is 20km in a bearing of 060⁰ from Y, and Z is 30km in the direction 150⁰ from Y. Using the scale 1cm represents 5km, find by scale drawing:

(a) the bearing of Y from Z.                                        (2 Marks)

(b) the distance of X from Z.                                      (2 Marks )

Draw the net of the solid below and calculate the total surface area of its faces.                    (3 Marks)

In a book store, books packed in cartons are arranged in rows such that there are 50 cartons in the first row, 48 cartons in the next row, 46 in the next and so on.

(a) How many cartons will there be in the 8^th row?                                   (2 Marks)

(b) If there are 20 rows in total, find the total number of cartons in the book store.              (2 Marks)