KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 Mathematics
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Form 4 MathematicsForm 4 Mathematics
(b) Okello bought 5 Physics books and 6 Mathematics books for a total of Ksh 2 440.
Ali bought 7 Physics books and 9 Mathematics books for a total of Ksh 3 560. (i) Form a matrix equation to represent the above information. (ii) Use matrix method to find the price of a Physics book and that of a Mathematics book. (c) A school bought 36 Physics books and 50 Mathematics books. A discount of 5% was allowed on each Physics book whereas a discount of 8% was allowed on each Mathematics book. Calculate the percentage discount on the cost of all the books bought. Form 4 Mathematics
The following distribution shows the masses to the nearest kilogram of 65 animals in a certain farm
Form 4 Mathematics
The equation of a circle is given by x2 + 4x +y2 – 5 = 0. Find the radius and the center of the circle.
Form 4 MathematicsForm 4 Mathematics
Triangle PQR shown on the grid has vertices p(5,5), Q(10, 10) and R(10,15)
a) Find the coordinates of the points p‟, Q‟ and R‟ and the images of P, Q and R respectively under transformation M whose matrix is
b) Given that M is a reflection;
i) draw triangle P‟Q‟R‟ and the mirror line of the reflection; ii) Determine the equation of the mirror line of the reflection c) Triangle P” Q” R” is the image of triangle P‟Q‟R‟ under reflection N is a reflection in the y-axis. i) draw triangle P”Q”R” ii) Determine a 2 x2 matrix equivalent to the transformation NM iii) Describe fully a single transformation that maps triangle PQR onto triangle P”Q”R” Form 4 Mathematics
The table below shows the number of goals scored in handball matches during a tournament.
Draw a cumulative frequency curve on the grid provided
b) Using the curve drawn in (a) above determine; i) The median; ii) The number of matches in which goals scored were not more than 37; iii) The inter-quartile range Form 4 MathematicsForm 4 Mathematics
Point P (400S, 450E) and point Q (400S, 600W) are on the surface of the Earth.
Calculate the shortest distance along a circle of latitude between the two points. Form 4 Mathematics
The diagram below shows a straight line intersecting the curve y = (x-1)2 + 4
At the points P and Q. The line also cuts x-axis at (7,0) and y axis at (0,7)
Form 4 MathematicsForm 4 MathematicsGiven the curve y = 2x3 + ½x2 – 4x + 1. Find the:
Form 4 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=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. 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. Form 4 MathematicsForm 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 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 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. Form 4 Mathematics
The figure below is a sketch of the curve whose equation is y=x2+x+5.
It cuts the line y=11 at points P and Q.
a) Find the area bounded by the curve = x2+x+5 and the line y=11 using the trapezium rule with 5 strips.
b) Calculate the difference in the area if the mid-ordinate rule with 5 ordinates was used instead of the trapezium rule. Form 4 MathematicsForm 4 MathematicsA triangle T whose vertices are A (2,3) B(5,3) and C (4,1) is mapped onto triangle T1 whose vertices are A1 (-4,3) B1 (-1,3) and C1 (x,y) by a transformation Find the: (i) Matrix M of the transformation (ii) Coordinates of C1 b) Triangle T2 is the image of triangle T1 under a reflection in the line y = x. Find a single matrix that maps T and T2 (8mks) |
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