Form 3 Mathematics
The table below shows values of x and some values of y for the curvey = x +3+3x^{2}+4x12 in the range 4 ≤ x ≤ 2.
a) Complete the table by filling in the missing values of y.
b) On the grid provided, draw the graph y=x^{3} + 3x^{2}+ 4x – 12 for 4 ≤ x ≤ 2.Use the scale. Horizontal axis 2cm for I unit and vertical axis 2cm for 5 units.
c) By drawing a suitable straight line on the same grid as the curve, solve the equation x^{3}+3x^{2}5x6=0 Form 1 Mathematics
Halima deposited Ksh. 109375 in a financial institution which paid simple interest at the rate of 8% p.a. At the end of 2 years, she withdrew all the money. She then invested the money in share. The value of the shares depreciated at 4% p.a. during the first year of investment. In the next 3 years, the value of the shares appreciated at the rate of 6% every four months
a) Calculate the amount Halima invested in shares. b) Calculate the value of Halima's shares. (i) At the end of the first year; (ii) At the end of the fourth year, to the nearest shilling. c) Calculate Halima„s gain from the share as a percentage. (ii) Find the values of x and y. (iii) Calculate the time taken before the policemen were unable to communicate. Form 4 MathematicsForm 2 Mathematics
Two policemen were together at a road junction. Each had a walkie talkie. The maximum distance at which one could communicate with the other was 2.5 km.
One of the policemen walked due East at 3.2 km/h while the other walked due North at 2.4 km/h the policeman who headed East traveled for x km while the one who headed North traveled for y km before they were unable to communicate. (a) Draw a sketch to represent the relative positions of the policemen. (b) (i) From the information above form two simultaneous equations in x and y. Form 2 MathematicsForm 4 Mathematics
a) complete the table below, giving the values correct to 2 decimal places.
b) On the grid provided, draw the graphs of y=sin 2x and y=3cosx2 for 0^{0} ≤ x ≤360^{0} on the same axes.
Use a scale of 1 cm to represent 30^{0} on the xaxis and 2cm to represent 1 unit on the yaxis. c) Use the graph in (b) above to solve the equation 3 Cos x – sin 2x = 2. d) State the amplitude of y=3cosx2. Form 3 Mathematics
Three variables p, q and r are such that p varies directly as q and inversely as the square of r.
(a) When p=9, q=12 and r = 2. Find p when q= 15 and r =5 (b) Express q in terms of p and r. (c) If p is increased by 10% and r is decreased by 10%, find; (i) A simplified expression for the change in q in terms of p and r (ii) The percentage change in q. Form 1 Mathematics
a) A trader deals in two types of rice; type A and with 50 bags of type B. If
he sells the mixture at a profit of 20%, calculate the selling price of one bag of the mixture. b) The trader now mixes type A with type B in the ratio x: y respectively. If the cost of the mixture is Ksh 383.50 per bag, find the ratio x: y. c) The trader mixes one bag of the mixture in part (a) with one bag of the mixture in part (b). Calculate the ratio of type A rice to type B rice in this mixture. Form 4 Mathematics
Find in radians, the values of x in the interval 0^{0}≤ x ≤ 2π^{0+} for which 2 cos 2x=1.
(Leave the answers in terms of π ) Form 4 Mathematics
A particle moves in a straight line from a fixed point. Its velocity Vms^{1} after t seconds is given by V=9t^{2} – 4t +1
Calculate the distance traveled by the particle during the third second. Form 4 MathematicsForm 3 Mathematics
The equation of a circle is given by 4x^{2} + 4y^{2}+ 8x+ 20y – 7 = 0. Determine the coordinates of the centre of the circle.
Form 4 Mathematics
Points A(2,2)and B(4,3) are mapped onto A‟(2,8) and b‟ (4,15) respectively by a transformation T.
Find the matrix of T. Form 2 MathematicsForm 4 Mathematics
An aero plane flies at an average speed of 500 knots due East from a point p (53.4^{0}e) to another point Q. It takes 2 ¼ hours to reach point Q. Calculate:
(i) The distance in nautical miles it traveled; (ii) The longitude of point Q to 2 decimal places Form 3 Mathematics
A student at a certain college has a 60% chance of passing an examination at the first attempt. Each time a student fails and repeats the examination his chances of passing are increased by 15%
Calculate the probability that a student in the college passes an examination at the second or at the third attempt. Form 3 Mathematics
The top of a table is a regular hexagon. Each side of the hexagon measures 50.0 cm. Find the maximum percentage error in calculating the perimeter of the top of the table.
Form 3 MathematicsForm 1 MathematicsForm 2 MathematicsForm 4 Mathematics
The distance s metres from a fixed point O, covered by a particle after t seconds is given by the equation;
S =t^{3} 6t^{2} + 9t + 5. a) Calculate the gradient to the curve at t=0.5 seconds b) Determine the values of s at the maximum and minimum turning points of the curve. c) On the space provided, sketch the curve of s= t^{3}6t^{2}+9t + 5. 
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