The table below shows some values of the function y = x² + 3

a) Complete the table above                (2marks)

b) Use the mid-ordinate rule with six strips to estimate the area bounded by the curve y = x² + 3, the y-axis, the x-axis and the line x = 6             (3marks)

c) Find the exact area in (b) above.         (3marks)

d) Calculate the percentage error in the approximated area from the exact area. (2 marks)

In the figure below OP = p, OQ = q, PQ = QR and OQ: QS = 3:1

a) Determine:-

 i. PQ                        (1 mark)

 ii. RS in terms of p and q                       (2 marks)

b) If RS:ST = 1:n and OP:PT = 1:m, determine:

i. ST in terms of p,q and m                 (1 mark)

ii. The values of m and n                       (4 marks)

iii. Show that R,S and T are collinear (2 marks)

From a watch tower M on a hill, N is 5km on a bearing of 078⁰ and a railway station 9km away on a bearing of 200⁰ .

a) Using a scale 1:100000, draw the relative positions of M, N and P. (4 marks)

b) Find;

i. The bearing of N from the railway station.     (1 mark)

ii. The distance between P and N    (2 marks)

iii. The shortest distance between M and the line PN. (3 marks)

In the figure below A,B,C and D are points on the circumference of the circle centre O. Line TDF is a tangent to the circle at D and BA produced meets the tangent at T. <ATD =38⁰ and <BAC = 28⁰.

Giving reasons in each case , find the size of:

(a) <AOD                                                               (2mks)

(b) <BDC                                                               (2mks)

(c) <ACB                                                               (2mks)

(d) <FDC                                                               (2mks)

(e) <ATD                                                               (2mks)

The figure below represents a wooden model. The model consists of a frustum part and a cylindrical part. The diameter of the cylindrical part is 28cm and the height is 40cm. the height of the frustum is 100cm.

If the vertical height of the cone from which the frustum was cut was 120cm, calculate:-

a) The larger radius of the frustum;                        (2marks)

b) The slant height of the frustum;                        (4marks)

c) The surface area of the model                          (4marks)

The vertices of a triangle PQR are P(-3,2), Q(-1,2) and R(-1,4)

a) On the grid provided draw triangle PQR. (1 mark)

b) Triangle PQR is reflected on line y = x + 1

i. Draw line y = x + 1 (2 marks)

ii. Draw triangle P’Q’R’ the image of triangle PQR under reflection in the line y = x + 1 (2 marks)

c) Draw triangle P”Q”R” the image of the triangle P’Q’R’ under a rotation of (-90⁰ ) about (0, 0). (2 marks)

d) Under translation   , triangle P”Q”R” is mapped onto triangle P’’’Q’’’R’’’.

 i. Find the coordinate of P’’’Q’’’R’’’ (2 marks)

ii. Draw triangle P’’’Q’’’R’’’ (1 mark)

A rectangular plot of land measures (3x + 9) m by (x - 3)m and has an area of 648m² .

a) Write an equation for the area of the plot in the form ax² + bx + c = 0         (2 marks)

b) Determine the dimensions of the plot.              (4marks)

c) Another similar plot has an area of 2592m² . Find the dimensions of the plot.         (4 marks)

The sides of a triangle are the ratio 3:5:6 and its perimeter is 56m. Calculate the angle between the shortest and longest sides.                 (3marks)

A line y + 6x + p = 0 passes through (4,-2) and is perpendicular to the line qy +4 x – 10 = 0. Determine the values of p and q.             (4 marks)

 Kemosi cycled from town A to town B at 10km/h and he returned at 12km/h. the total time taken was 1hr 50min. find the distance between the two towns.     (3 marks)