The equation of a curve is given as y = 2x3 —9/2 x2 — 15x + 3.
(a) Find:
(i) the value of y when x = 2;
(ii) the equation of the tangent to the curve at x = 2.
(b) Determine the turning points of the curve.
An institution intended to buy a certain number of chairs for Ksh 16 200. The supplier agreed to offer a discount of Ksh 60 per chair which enabled the institution to get 3 more chairs.
Taking x as the originally intended number of chairs,
(a) Write an expressions in terms of x for:
(i) original price per chair;
(ii) price per chair after discount
(b) Determine:
(i) the number of chairs the institution originally intended to buy
(ii) price per chair after discount
(iii) the amount of money the institution would have saved per chair if it bought the intended number of chairs at a discount of 15%
Given that A =
and B =
find values of x for which AB is a singular matrix.
(b) Mambo bought 3 exercise books and 5 pens for a total of Ksh 165. 1f Mambo had bought 2 exercise books and 4 pens, he would have spent Ksh 45 less.
Taking x to represent the price of an exercise book and y to represent the price of a pen:
(i) Form two equations to represent the above information.
(ii) Use matrix method to find the price of an exercise book and that of a pen.
(iii) A teacher of a class of 36 students bought 2 exercise books and 1 pen for each student.
Calculate the total amount of money the teacher paid for the books and pens.
The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D.
(b) Use the scale drawing to determine:
(i) the bearing of A from D;
(ii) the distance BD in kilometres.
In the figure below (not drawn to scale), AB 11cm, BC = 8cm, AD = 3 cm, AC 5cm and A DAC is a right angle.
Calculate, correct to one decimal place:
(a) the length DC;
(b) the size of 4 ADC;
(0) the size of A ACB;
(d) the area of the quadrilateral ABCD
A solid S is made up of a cylindrical part and a conical part. The height of the solid is 4.5 m.
The common radius of the cylindrical part and the conical part is 0.9 m. The height of the conical part is 1.5 m.
(a). Calculate the volume. correct to 1 decimal place, of solid S.
(b). Calculate the total surface area of solid S.
A square base pillar of side 1.6 m has the same volume as solid S. Determine the height of the pillar, correct to 1 decimal place.
The masses, in kilograms, of patients who attended a clinic on a certain day were recorded follows.
38 52 46 48 60 59 62 73 49 54
49 41 57 58 69 72 60 58 42 41
79 62 58 67 54 60 65 61 48 47
69 59 70 52 63 58 59 49 51 44
67 49 51 58 54 59 39 59 54 52
(a) Starting with the class 35 — 39, make a frequency distribution table for the data.
(b) Calculate:
(i) the mean mass;
(ii)the median mass
(c) On the grid provided below draw a histogram to represent the data
Two lines L1: 2y — 3x 6 = 0 and L2: 3y + x — 20 =
0 intersect at a point A.
(a) Find the coordinates of A.
(b) A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y = mx + c, Where m and c are constants.
(c) Another line L4 is parallel to L1 and passes through (—l,3). Find the x and y intercepts of L 4
A construction company employs technicians and artisans. On a certain day 3 technicians and 2 artisans were hired and paid a total of Ksh 9000. On another day the firm hired 4 technicians and 1 artisan and paid a total of Ksh 9500‘ Calculate the cost of hiring 2 technicians and 5 artisans in a day
A triangle T With vertices A (2,4), B (6,2) and C (4,8) is mapped onto triangle T’ with vertices
A’(l0,0) , B'(8,—4) and C'(14,—2) by a rotation.
(a) On the grid provided draw triangle T and its image
(b) Determine the centre and angle of rotation that maps T onto T’.
