Advanced level 2025 Littoral Regional Mock mathematics statistics 2
Advanced level 2025 Littoral Regional Mock mathematics statistics 2
1.
The polynomial p( x ) is defined by />(.1) =a.\ |0.v 2+ hx+ 8.
Given that (.v– 2) is a factor of both /;( x ) and // (.v ) , where p‘ ( x ) is the first derivative of />( v )
Find the values of the constants a and b
(i)
5 marks
x–
(ii) Show that for real values of v, — cannot take values between 0 and 4. 4 marks
x — I
2.
sin50– sin//
(i) Show that –=2eos0
sin40– sin20
| sii\50 — sin0 Hence, find the general solution of the equation sin40– sin20 |
5 mark* |
(ii) Given that / ( 0 ) =cos30– yfJsMO, express/ ( 0) in the form Kcos( 30+ A ) where /?> (). 0 “ < A 3 marks
3.
(i) The sum of the third and fifth terms of an arithmetic progression is six limes the first term while the sum of tl > v svcond
sixth and eighth terms of this sequence is 35.
Find:
(a) The first term and the common difference of the sequence.
(b) A formula for the if 1‘ term of this sequence.
4 marks
2 msirks
(ii) A mixed committee of 5 is to be selected from 13 elders comprising of the pastor, seven men and fi\ c w omen
Find the number of ways in which this can be done to include the pastor and more men than women. 4 marks
4.
3.v
(i) A real valued function / is defined by J‘ x+ 1 , A 6 R, x^ – I .
(a) show that/ ( x ) is injective 2 marks
(b) Evaluate the limits at the bounds of/ ( .v )
( c ) Sketch the curve of v=/ ( x ) , showing clearly the asymptotes and the behavior of the curve near
its asymptotes.
3 marks
5 marks
(ii) Two statements p and q are given by:
P‘Amad will write the mock
q:Amatf will pass thefinal exams
Write out the following statements in symbolic form:
(a) Amad will write the mock and Amad will pass the final exams.
(b) Amad will not write the mock or Amad will not pass the final
(c ) It is not true that if Amad will pass the final exams , then Amad did not write the mock .
exams.
3 mark
