Form 3 Mathematics
The table below shows values of x and some values of y for the curvey = x +3+3x2+-4x-12 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=x3 + 3x2+ -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 x3+3x2-5x-6=0
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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.
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Form 4 Mathematics
The table below shows the distribution of marks scored by 60 pupils in a test.
a) On the grid provided, draw an ogive that represents the above information
b) Use the graph to estimate the interquartile range of this information.
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Form 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.
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Form 2 Mathematics
In the figure below DA is a diameter of the circle ABCD centre O, radius 10cm. TCS is a tangent to the circle at C, AB=BC and angle DAC= 380
a) Find the size of the angle;
(i) ACS; (ii) BCA b) Calculate the length of: (i) AC (ii) AB
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Form 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=3cosx-2 for 00 ≤ x ≤3600 on the same axes.
Use a scale of 1 cm to represent 300 on the x-axis and 2cm to represent 1 unit on the y-axis. c) Use the graph in (b) above to solve the equation 3 Cos x – sin 2x = 2. d) State the amplitude of y=3cosx-2.
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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.
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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.
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Form 4 Mathematics
Find in radians, the values of x in the interval 00≤ x ≤ 2π0+ for which 2 cos 2x=1.
(Leave the answers in terms of π )
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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=9t2 – 4t +1
Calculate the distance traveled by the particle during the third second.
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Form 4 Mathematics
The figure below represents a triangular prism. The faces ABCD, ADEF and CBFE are rectangles.
AB=8cm, BC=14cm, BF=7cm and AF=7cm. 
Calculate the angle between faces BCEF and ABCD.
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Form 3 Mathematics
The equation of a circle is given by 4x2 + 4y2+- 8x+ 20y – 7 = 0. Determine the coordinates of the centre of the circle.
ANSWER
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.
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Form 2 Mathematics
In the figure below, angles BAC and ADC are equal. Angle ACD is a right angle. The ratio of the sides.
AC: BC =4: 3 
Given that the area of triangle ABC is 24 cm2+. Find the triangle ACD
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Form 4 Mathematics
An aero plane flies at an average speed of 500 knots due East from a point p (53.40e) 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
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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.
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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.
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Form 3 Mathematics
The position vectors of points A and B are;
A point P divides AB in AB it he ratio 2:3. Find the position Vector of point P.
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Form 1 Mathematics
Line AB given below is one side of triangle ABC. Using a ruler and a pair of compasses only;
(i) Complete the triangle ABC such that BC=5cm and angle ABC=45
(ii) On the same diagram construct a circle touching sides AC,BA produced and BC produced.
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Form 2 Mathematics
In this question, show all the steps in your calculations, giving the answer each stage. Use logarithms correct to decimal places, to evaluate.
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Form 4 Mathematics
The distance s metres from a fixed point O, covered by a particle after t seconds is given by the equation;
S =t3 -6t2 + 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= t3-6t2+9t + 5.
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