Find a quadratic equation whose roots are 25 3 and 25

Find a quadratic equation whose roots are 2.5 + 3 and 2.5 – 3, expressing it in the form
ax 2 + bx + c = 0 Where a, b and c are integers
13. Find the products of 17.3 and 13.8. Find also the percentage error in getting the product.
14. (a) Complete the table below for the equation :- y = x 2 + 3x – 6 for -6  x  4
(b) Using a scale 1cm to represent 2 units in both axes. Draw the graph of y = x 2 + 3x – 6
(c) Use your graph to solve:-
(i) X 2 + 3X = 6
(ii) X
2
+ 3X – 2 = 0
15. (a) Complete the table for the function: y = 2x
2
+ 3x + 1
x - 4 -3 -2 -1 0 1 2 3
2x 2 18 0 18
3x + 1 -7 0 10
y 11 1 6
(b) Use the table in (a) above to draw the graph : - y = 2x 2 + 3x + 1 for -4  x  3
(c) Use the graph in (b) to solve the equation :-
(i) 2x 2 + 4x – 3 = 0
(ii) x 2 + 3 x + 2 = 3
2
16. A youth group decided to raise Ksh 480,000 to buy a piece of land costing Ksh. 80,000 per
hectare. Before the actual payment was made, four of the members pulled out and each of those
remaining had to pay an additional Kshs. 20,000.
(a) If the original number of the group members was x , write down;
(i) An expression of how much each was to contribute originally.
(ii) An expression of how the remaining members were to contribute after the four pulled out.
(b) Determine the number of members who actually contributed towards the purchase of the
land.
(c) Calculate the ratio of the supposed original contribution to the new contribution.
(d) If the land was sub-divided equally, find the size of land each member got. (2 mk)
17. a) Draw the graph of y = 2 x 2 + x – 2 given the range -3 ≤ x ≤ 2
b) Use your graph above to solve
i) 2 x 2 + x – 2 =0
x -6 -5 -4 -3 -2 -1 0 1 2 3 4
y 12 -6 -6 22

ii) 2 x 2 + x – 3 =0
iii) 2 x 2 + x -5 =0
18. Three planes A , B and C leave an airport P simultaneously at 9.30a.m. Plane A flies on
a bearing of 070
o
from P at a speed of 400km/h. Plane B flies on a bearing of 290
o
at a
speed of 500km/h. Plane C flies on a bearing of 162
o
from P at a speed of 300km/h.
( Use scale drawing for this questio n)
(a) Show by scale drawing, the relative positions of the 3planes A, B and C three hours
after leaving airport P. (Use scale 1cm represents 200km)
(b) After 3 hours, B turns and head straight to the current position of A at the same
speed it had. Determine the scale drawing , the time it takes to reach this point, to
the nearest minute
(c) Determine the bearing and distance of B from C after the first 3 hours of flight after
leaving P
19. a) Use trapezoidal rule to find the area between the curve y = x 2 + 4x + 4, the x- axis and the
co-ordinates x = - 2 and x = 1. Take values of x at intervals of ½ unit.
b) Use integration to find the exact area. Hence find the percentage error in your approximation.
20. a) Use trapezoidal rule to find the area between the curve y = x
2
+ 4x + 4, the x- axis and the
co-ordinates x = - 2 and x = 1. Take values of x at intervals of ½ unit.
b) Use integration to find the exact area. Hence find the percentage error in your approximation.
21. Draw the graph of y = 2x 2 – 4x - 5 for x between -3 and 5 on the grid provided
(a) State the line of symmetry for the graph
(b) State the range of values for which 2x 2 – 4x – 5  0
(c) On the same set of axes, draw the graph of y=2x +3
(d) Determine the solutions to the equation: 2x
2
– 4x – 5 = 2x +3
22. Complete the table below for the equation y = 5 + 3x -2x 2 by filling in the blank space
X -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
Y -9 3 6 6 -4
(i) Use the values from the table above to draw the graph of y = 5 + 3x -2x 2 (3mks
(ii) Use the graph to:-
(a) Find the maximum point of the function 5 + 3x -2x 2
(b) Determine the range of values and give the integral values which satisfy
the inequality 5 + 3x -2x