Lengths of 100 mango leaves from a certain mango tree were measured t the nearest centimeter and   recorded as per the table below,

                                                                        Length in cm               No. of leaves

                                                                        10 to 12                                   3

                                                                        13 to 15                                   16

                                                                        16 to 18                                   36

                                                                        19 to 21                                   31

                                                                        22 to 24                                   14

(a) On the grid provided draw a cumulative frequency graph to represent this data.  (5mks)

            (b)  Use your graph to estimate

                 i) The median length of the leaves               (2mks)

                ii) The number of leaves whose lengths lie between 13cm and 17cm.      (3mks)

A classroom measures ( x + 2) m by ( x – 5)m. If the area of the classroom is 60m².  Find its length.       ( 3 mks )

A particle moves along a straight line such that its displacement s metres from a given

point is s = t³ – 5t² + 3t + 4 where t is time in seconds. Find:

(a) The displacement of the particle at t = 8.                                     ( 2 mks )

 (b) The velocity of the particle when t = 10.                                      (3 mks )

Two fair dice one a regular tetrahedron (4 faces) and the other a cube are thrown. The scores are added together.

(a) Complete the table below to show all possible outcomes.    (2 mks)

(b) Find the probability that:

i.  The sum is 6.                                             (1 mark)

ii.  The sum is 6 or 9.                                      (2 mks)

Given that  sin ⁽²/₃x+20⁰) - cos (⁵/₆x+10⁰) = 0. Without using a mathematical table or a calculator, determine tan (x+ 20⁰).      (3 mks)

Make a the subject of the formula:                             (3mks)

A circle centre is the point C(2,3) passes through a point P(a,b). A  point  M =   is the mid-point of the line  CP 

               a)     Calculate the coordinates of P.                            (1mk)

  b)  Determine the equation of the circle in the form x² +y² +ax +  by  +  c = 0                     (3mks)

A globe representing the earth has a radius of 0.5m.  point A(0⁰, 10⁰W), B (0⁰, 35⁰E), P(60⁰N, 110⁰E) and Q(60⁰N, 120⁰W) are marked on the globe.Find the length of arc AB, leaving your answer in term of      (3mks)

Use logarithms tables to 4 decimal places to evaluate:                         (4 mks)

The 4th , 5th, and 6th terms of a geometrical series are 9x² , 27x³ , 81x⁴ respectively. Determine :

a) The common ratio                                             (2mks)

b) The first three terms                                       (3mks)

c) The sum of the first ten terms                                         (3mks)

d) The ratio of the first term to the fifth term                    (2mks)