A particle moves in a straight line. It passes through point O at  t = 0  with velocity  V = - 4 m/s. The acceleration a  m/s²  of the particle at time t seconds after passing through O is given by  a = 10t + 1

(a) Express the velocity V of the particle at time t seconds in terms of   t.                (3mks)

b) Find V when   t = 3                                             (1mk)

c) Determine the value of t when the particle is momentarily at rest          (3mks)

d) Calculate the distance covered by the particle between t = 2 and t = 4            (3mks)

Two variables x and V are known to satisfy the relation  V = Kxⁿ where k and n are constants. The table below shows data collected from an experiment.

(a) Write down the function V = Kxⁿ in linear form and make a suitable table of values correct to one decimal place.                              (3mks)

(b) Draw a suitable graph to represent the relation  V = Kxⁿ                       (3mks)

(c) Use your graph to determine the values of k and n                                        (4mks)

The data below shows the sample of age distribution of some of the people who reside in a Yoruba village in years.

(a) Complete the frequency distribution table above and hence

 i) Calculate the mean.                             (3mks)

 ii) Calculate the median.                               (2mks)

(b) Draw a frequency polygon from the given data on the grid below    (5mks)

Every Sunday Alex drives a distance of 80km on a bearing of 074⁰ to pick up his brother John to go to church.  The church is 75km from John’s house on a bearing of S50⁰E.  After church they drive a distance of 100km on a bearing of 260⁰ to check on their father before Alex drives to John’s home to drop him off then proceeds to his house

(a)  Using a scale of 1cm to represent 10km, show the relative positions of these places.       (4 mks)

 (b)       Use your diagram to determine:

           (i)        the true bearing of Alex’s home from their father’s house.   (1 mark)

          (ii)       the compass bearing of the father’s home from John’s home. (1 mark)

          (iii)      the distance between John’s home and the father’s home.    (2 marks)

           (iv)      the total distance Alex travels every Sunday.                        (2 marks)

OAB is a triangle in which OA= a, OB= b, M is a point on OA such that OM:MA=2:3 and N is another point on AB such that AN:NB = 1:2. Lines ON and MB intersect at X.

a)  Express the following vectors in terms of a and b

i) AB                                           (1mk)   

ii) ON                                           (1mk)

iii) BM                                            (1mk)

b) If OX=k ON and BX=h BM, express ON in two different ways. Hence or otherwise find the value of h and k   (6marks)

c) Determine the ratio OX: XN                                              (1mk)

In the figure below, EG is the diameter of the circle centre O. Points B, G, D, E and F are on the circumference of the circle. <BFD=50⁰ , <BEO=25⁰ and line ABC is a tangent to the circle at B

Giving reasons, calculate the size of

(a)  < CBD                                                  (2marks)

(b)  < BED                                                 (2marks)

(c) The reflex angle  BOD                          (2marks)

(d)  < EBA                               (2marks)

(e)  < BGD                               (2marks)

Two circles with centres O and Q and radii 8cm intersect at points A and B as shown below.

Given that the distance between O and Q is 12cm and that the line AB meets OQ at X, find:

            (a)       the length of the chord AB.             (3marks)

            (b)       the reflex angle AOB.                     (3marks)

            (c)       the area of the shaded region.              (4marks)

The vertices of a parallelogram are O (0,0), A(5,0),B(8,3) and C(3,3)

Plot on the same axes

i) Parallelogram O’A’B’C’, the image of OABC under reflection in the line x = 4            (4marks)

ii) Parallelogram O’’A’’B’’C’’ the image of O’A’B’C’ under a transformation described by the matrix   . Describe the transformation.                             (4marks)

iii) Parallelogram O’’’A’’’B’’’C’’’, the image of O’’A’’B’’C’’ under the enlargement, centre (0,0) and scale factor ¹/₂                                      (2marks)

A railway line and a road are parallel to each other on a flat and level section of land. A 5 metre long car moving at a speed of 110kmh^-1 starts overtaking a train which is 495 metres and moving at 80kmh^-1 .How long will it take the car to completely overtake the train?       (3marks)

Form three inequalities that satisfy the unshaded region R.                          (3mks)