**SECTION I (50 Marks)**

**Answer all questions in this section**

- Use logarithms to evaluate; (4 marks)

- The equation of a line is -
^{3}/_{5}x + 3y = 6 . Find the- Gradient of the line. (1 mark)
- Equation of a line passing through point and perpendicular to the given line. (3 marks)

- A shirt whose marked price is sh. 800 is sold to a customer after allowing him a discount of 13%. If the trader makes a profit of 20%, find how much the trader paid for the shirt. (3 marks)

- Simplify (2 marks)

- The length and width of a rectangular signboard are (3x + 12)and (x-4) respectively. If the diagonal of the signboard is 200 cm, determine its area. (4 marks)

- Find the value of given that; Log (x-1) + 2 = log (3x + 2) + log 25 (3 marks)

- Use the expansion of (x-y)
^{5 }to evaluate correct to (9.8)^{5 }4 d.p. (3 marks)

- Evaluate (3 marks)

- Make y the subject of formula: (3 marks)

- In the figure below, ABCD is a cyclic quadrilateral. Point O is the centre of the circle. <ABO = 30
^{0 }and <ADO = 40^{0}.Calculate the size of angle BCD. (2 marks)

- Find the number of terms of the series 2 + 6 + 10 + 14 + 18.... that will give a sum of 800. (2 marks)

- A bag contains 10 balls of which 3 are red, 5 are white and 2 are green. Another bag contains 12 balls of which 4 are red, 3 are white and 5 are green. A bag is chosen at random and then a ball chosen at random from the bag. Find the probability that the bell chosen is red. (3 marks)

- The point (5,2) undergoes the transformation followed by a translation . Determine the coordinates of the image. (3 marks)

- The latitude and the longitude of two stations A and B are and Calculate the distance in nautical miles between A and B along latitude 47
^{0 }N. (3 marks)

- Using a ruler and a pair of compass only;
- Construct a parallelogram PQRS in which PQ = 6 cm, and QR = 4 cm and (3 marks)
- Determine the perpendicular distance between PQ and SR. (1 mark)

- The mass of a mixture A of beans and maize is 72 kg. The ratio of beans to maize is 3:5 respectively.
- Find the mass of maize in the mixture. (1 mark)
- A second mixture B of beans and maize of mass 98 kg is mixed with A. The final ratio of beans to maize is 8:9 respectively. Find the ratio of beans to maize in B. (3 marks)

**SECTION II (50 Marks)**

**Answer any five questions in this section**

- Given the simultaneous equations
- Write the simultaneous equations in matrix form. Hence solve the simultaneous equations. (6 marks)
- Find the distance of the point of the intersection of a line 5x + y = 19 and -x + 3y = 9 from the point (11,-2) (4 marks)

- A particle was moving along a straight line. The acceleration of the particle after t seconds was given by a = (9 - 3t)ms
^{-2}. The initial velocity of the particle was 7 m/s. Find:- The velocity (V) of the particle at any given time (t). (4 marks)
- The maximum velocity of the particle. (3 marks)
- The distance covered by the particle by the time it attained maximum velocity. (3 marks)

- The figure below represents a right pyramid with vertex V and a rectangular base PQRS. PQ = 16 cm and QR = 12 cm. M and O are the mid points of QR and PR respectively.

Find;- The length of the projection of line VP on the plane PQRS. (3 marks)
- The size of the angle between line VP and the plane PQRS. (3 marks)
- The size of the angle between the planes VQR and PQRS. (4 marks)

- Two towns A and B lie on the same latitude in the northern hemisphere. When it is 8:00 a.m. at A, the time at B is 11:00 a.m.
- Given that the longitude of A is E, find the longitude of B. (3 marks)
- A plane leaves A for B and takes hours to arrive at B travelling along a parallel of latitude at 850 km/h. Find
- The radius of the circle of latitude of towns A and B. (4 marks)
- The latitude of the two towns. (3 marks)

- The gradient function of a curve is given by the expression 2X+1. If the curve passes through the point (-4,6),
- Find;
- The equation of the curve. (3 marks)
- The values of x at which the curve cuts the x- axis. (3 marks)

- Determine the area enclosed by the curve and the x- axis. (4 marks)

- Find;

- The transformation A given by the matrix maps to and to
- Determine the matrix A giving a, b, c and d as fractions. (4 marks)
- Given that A represent a rotation through the origin, determine the angle of rotation. (3 marks)
- S is a rotation through 180
^{0}about the point (2, 3). Determine the image of (1, 0) under followed by A. (3 marks)

- The figure below shows a triangle ABC inscribed in a circle (not drawn to scale.) AB = 6 cm, BC = 9 cm and AC = 10 cm.

Calculate;- The radius of the circle. (6 marks)
- The area of the shaded parts. (4 marks)

- In an experiment involving two variables t and r, the following results were obtained.
t

1.0

1.5

2.0

2.5

3.0

3.5

r

1.50

1.45

1.30

1.25

1.05

1.00

- On the grid provided, draw the line of best fit for the data. (4 marks)

- The variables r and t are connected by the equation where
**a**and**k**are constants. Determine;- The values of
**a**and**k.**(3 marks) - The equation of the line of best fit. (1 mark)
- The value of t when. (2 marks)

- The values of

- On the grid provided, draw the line of best fit for the data. (4 marks)