SECTION I (50 marks)
Answer all questions from this section in the spaces provided.
 The roots of the quadratic equation x^{2}+px=q are x= ^{−3}/_{7} and x=2. Find the values of p and q. (3mks)
 Without using a mathematical table or a calculator, evaluate leaving your answer in the form. a√b+c., where a, b and c are constants. (3mks)
 Two matrices P and Q are such that . Given that the determinant of QP is 44, find the value of k. (3mks)
 Find the value of x given that log(x−1)+2= log(3x+2)+ log25. (3mks)
 The equation of a circle is given as x^{2}+ y^{2}+4x−2y−4=0. Determine the centre and the diameter of the circle. (3mks)
 Using logarithms, evaluate (4mks)
 If . P divides AB externally in the ratio 2:1. Find the coordinates of P. (3mks)
 Kapsabet Boys’ handball team scored the following goals in 6 matches; 10, 8, 14, 16, 6 and 18. Using assumed mean of 12, determine the standard deviation leaving your answer to 2 d.p. (3mks)
 The gradient of a curve at point (x,y) is 4x−6. The curve has a minimum value at 5^{1}/_{2}. Find the equation of the curve. (3mks)
 The nth term of G.P is given by 5 x 2^{n2}
 Write down the first 4 terms of the G.P (1mark)
 Calculate the sum of the first 6 terms. (2marks)

 Expand (1− ^{1}/_{2}x)^{5} in ascending powers of x leaving the coefficients as fractions in their simplest form. (2mks)
 Using the first three terms in the expansion in (a) above, estimate the value of (^{19}/_{20})^{5} (2mks)
 A 2– digit number is made by combining any two of the digits 1, 3, 5, 7, 9 at random
 Write down all the possible outcomes. (1mk)
 Find the probability that the number is prime. (1mk)
 Find the percentage error in evaluating (a+b)−c, if a=3.2 cm,b=5cm and c=2.0cm, leaving your answer to the nearest 4 s.f (3mks)
 Three quantities A, B and C are such that A varies directly as B and inversely as the square root of C. Find the percentage decrease in A if B decreases by 5.2% and C increases by 44%. (3mks)
 Write r in terms of u, y, p and t (3mks)
 Using the diagram below, find the angle;
 Plane BFC makes with ABCD (2mks)
 Plane ABFE makes with ABCD (2mks)
SECTION II (50 marks)
Answer only five questions from the section in the spaces provided.
 The table below shows monthly income tax rates for a certain year.
Monthly taxable income in Ksh. Tax rate (%) in each shilling 0 – 11180 10 11181 – 21714 15 21715 – 32248 20 32249 – 42782 25 Above 42782 30
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. Calculate
 Mr Tundu’s monthly taxable income in Ksh. (2mks)
 The tax payable by Mr Tundu in that month. (5mks)
 The following month that year, Tundu’s basic salary was raised by 5%. Determine his net salary for that month. (3mks)
 Calculate

 Using a ruler and a pair of compasses only, construct a parallelogram ABCD such that AB=7cm,BC=5cm and ∠ABC=120°. (3mks)
 Construct the following loci on the same diagram above
 P is such that AB=BP. (1mk)
 R is such that it is equidistant from DA and BA. (1mk)
 Q is such that AQ=3.5 cm. (1mk)
 A region T is such that AT ≤BT,∠DAT ≤ ∠BAT and AT ≥3.5 ??. By shading, show the region T. (1mks)
 Locate point S such that ∠ASB=60° and the area of triangle ASB is 11.2 cm^{2}. Hence measure the shortest distance from S to C (3mks)
 The marks scored by 40 students in a mathematics class were shown in the table below:
Marks 42  46 47  51 52  56 57  61 62  66 67  71 Number of students 3 4 10 12 8 3  State the upper class limit of the modal class (1mks)
 Estimate the mean mark (3mks)
 If the pass mark is 55%, how many students passed? (3mks)
 Find the range of marks scored by the middle 50% of the students. (3mks)
 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.
 Calculate the distance covered by the plane in km. (3mks)
 After stopping for 30 minutes to refuel at Y, the plane then flies due East to airport Z, 2500 km from Y. Find the:
 Position of Z (3mks)
 Time the plane lands at Z, if its speed is 500km/h. (4mks)
(take Π= ^{22}/_{7} and the radius of the earth R=6370 km)

 Complete the table below to 2 dp. (2mks)
?° 0 30 60 90 120 150 180 210 240 270 sin(?+30°) 0.50 0 0.50 0.87 2cos(?+30°) 1.73 0 1.73  On the same axes, draw the graphs of y= sin(x+30°) and y=2cos(x+30°). (5mks)
 State the amplitude and period of each wave. (2mks)
 Use the graph to solve the equation 2cos(x+30°)= sin(x+30°). (1mk)
 Complete the table below to 2 dp. (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.
 Express OS and QR in terms of p and q. (3 mks)
 Given that OT=kOS, express OT in terms of k, p and q. (1mk)

 Given also that RT=hRQ, express OT in terms of h, p and q. (2mks)
 Find the values of h and k. (3mks)
 In what ratio does O divide TS? (1mk)
 Using the equation of the curve y= ^{1}/_{2}x^{2}−2 for 0≤x≤8
 Complete the table below. (1mks)
x 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 y  Using trapezium rule with 8 strips, determine the area bounded by the curve, the lines x=0,x=8 and the xaxis. (2mks)
 Find the area in (b) above using the midordinate rule with 4 strips (2mks)
 Find the exact area by integration (3mks)
 What is the percentage error in using the midordinate rules? (2mks)
 Complete the table below. (1mks)
 The vertices of a triangle PQR are P(1,1), Q (4,1) and R(5,4).
 On the graph provided, plot the triangle PQR. (1mk)
 A transformation represented by a matrix T= (^{−1}_{0} ^{0}_{1}) maps triangle PQR onto P^{I}Q^{I}R^{I}. Draw and state the coordinates of P^{I}Q^{I}R^{I}. (3mks)
 Another transformation U= ( ^{1}_{0} ^{0}_{−1}) maps P^{I}Q^{I}R^{I} onto P^{II}Q^{II}R^{II}. Draw and state the coordinates of P^{II}Q^{II}R^{II}. (3mks)
 Describe a single transformation that maps PQR onto P^{II}Q^{II}R^{II} and find its matrix. (3mks)
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