(a) Explain the circumstances which made the early Christians to put into writing the oral traditions about the life and teachings of Jesus a few years after his ascension. (7marks)

(b) Outline seven teachings about marriage from the creation accounts in Genesis chapter 1 and 2 (7marks)

(c) Give six reasons why Christians use songs as a way of spreading the word of God today. (6marks)

The vertices of a triangle PQR are P(1,1), Q (4,1) and R(5,4).

a) On the graph provided, plot the triangle PQR.           (1mk)

b) A transformation represented by a matrix T = maps triangle PQR onto P^IQ^IR^I . Draw and state the coordinates of P^IQ^IR^I.           (3mks)

c) Another transformation U = maps P^IQ^IR^I onto P^IIQ^IIR^II. Draw and state the coordinates of PIIQ IIR II . (3mks)

d) Describe a single transformation that maps PQR onto P^IIQ^IIR^II and find its matrix. (3mks)

Using the equation of the curve y = ¹/₂ x² - 2 for 0 x  8

a) Complete the table below.        (1mks)

b) Using trapezium rule with 8 strips, determine the area bounded by the curve, the lines x = 0, x = 8 and the x - axis. (2mks)

c) Find the area in (b) above using the mid-ordinate rule with 4 strips (2mks)

d) Find the exact area by integration (3mks)

e) What is the percentage error in using the mid-ordinate rules? (2mks)

Triangle OPQ is such that OP = p and OQ = q. Point R divides OP in the ratio 1: 3 and point S divides PQ in the ratio 5: 2. OS and RQ meet at T.

(a) Express OS and QR in terms of p and q.    (3 mks)

(b) Given that OT = kOS, express OT in terms of k, p and q.    (1mk)

(c) (i) Given also that RT = hRQ, express OT in terms of h, p and q.   (2mks)

(ii) Find the values of h and k.      (3mks)

(iii) In what ratio does O divide TS?   (1mk)

(a) Complete the table below to 2 dp. (2mks)

(b) On the same axes, draw the graphs of y = sin(x + 30°) and y = 2 cos(x + 30°). (5mks)

(c) State the amplitude and period of each wave. (2mks)

(d) Use the graph to solve the equation 2 cos(x + 30°) = sin(x + 30°). (1mk)

A plane leaves an airport X (41.5° N, 36.4° W) at 9.00 a.m. and flies due North to airport Y on latitude 53.2° N.

(a) Calculate the distance covered by the plane in km.       (3mks)

(b) After stopping for 30 minutes to refuel at Y, the plane then flies due East to airport Z, 2500 km from Y. Find the:

 i. Position of Z                            (3mks)

ii. Time the plane lands at Z, if its speed is 500km/h. (4mks) (take = 22/7 and the radius of the earth R = 6370 km)

The marks scored by 40 students in a mathematics class were shown in the table below:

(a) State the upper class limit of the modal class     (1mks)

(b) Estimate the mean mark    (3mks)

(c) If the pass mark is 55%, how many students passed?    (3mks)

(d) Find the range of marks scored by the middle 50% of the students.    (3mks)

(a) Using a ruler and a pair of compasses only, construct a parallelogram ABCD such that AB = 7cm, BC = 5cm and <ABC = 120°.     (3mks)

(b) Construct the following loci on the same diagram above

i. P is such that AP = BP.           (1mk)

ii. R is such that it is equidistant from DA and BA.          (1mk)

iii. Q is such that AQ = 3.5 cm.              (1mk)

(c) A region T is such that ATBT, <DAT  <BAT and AT  3.5 cm. By shading, show the region T.          (1mks)

(d) Locate point S such that <ASB = 60° and the area of triangle ASB is 11.2 cm² . Hence measure the shortest distance from S to C         (3mks)

The table below shows monthly income tax rates for a certain year

Mr Tundu earned a salary of Ksh 58 000, a house allowance of Ksh. 8 200 and a commuter allowance of Ksh. 6 000. He gets a monthly personal relief of Ksh. 1280.

a. Calculate

i. Mr Tundu’s monthly taxable income in Ksh.               (2mks)

ii. The tax payable by Mr Tundu in that month.            (5mks)

b. The following month that year, Tundu’s basic salary was raised by 5%. Determine his net salary for that month. (3mks)

Using the diagram below, find the angle;

(a) Plane BFC makes with ABCD                        (2mks)

(b) Plane ABFE makes with ABCD                     (2mks)