KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
The distance covered by a moving particle through point O is given by the equation, s = t3 - 15t2 + 63t — 10.
Find: (a) distance covered when t = 2 (b) the distance covered during the 3rd second; (c) the time when the particle is momentarily at rest; (d) the acceleration when t = 5.
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Form 4 MathematicsA stone is thrown vertically upwards from a point O After t seconds, the stone is S metres from O Given that S= 29.4t – 4.9t2, Find the maximum height reached by the stone ( 3 marks) Form 1 MathematicsSuccessive moving averages of order 5 for the numbers 9,8.2, 6.7,5.4, 4.7 and k are A and B. Given that A – B = 0.6 find the value of k. Form 4 MathematicsForm 4 MathematicsThe gradient of a curve at point (x,y) is 4x – 3. the curve has a minimum value of – 1/8 (a) Find (i) The value of x at the minimum point ( 1 mark) (ii) The equation of the curve ( 4 marks) (b) P is a point on the curve in part (a) (ii) above. If the gradient of the curve at P is -7, find the coordinates of P ( 3 marks) Form 4 MathematicsThe table below gives some of the values of x for the function y = ½ x 2 + 2x + 1 in the interval 0≤ x ≤ 6. (a) Use the values in the table to draw the graph of the function ( 2 marks) (b) (i) Using the graph and the mid – ordinate rule with six (6) strips, estimate the area bounded by the curve, the x- axis, the y- axis and the line = 6 (ii) If the exact area of the region described in (b) (i) above is 78cm2, calculate the percentage error made when the mid – ordinate rule is used. Give the answer correct to two decimal places ( 2 marks) Form 4 Mathematics
The acceleration, a ms-2, of a particle is given by a =25 – 9t2, where t in seconds after the particle passes fixed point O.If the particle passes O, with velocity of 4 ms-1, find:
(a) An expression of velocity V, in terms of t ( 2 marks)
(b) The velocity of the particle when t = 2 seconds ( 2 marks) Form 4 Mathematics
A trader stocks two brands of rice A and B. The rice is packed in packets of the same size. The trader intends to order fresh supplies but his store can accommodate a maximum of 500 packets. He orders at least twice as many packets of A as of B.
He requires at least 50 packets of B and more than 250 packets of A. If he orders x packets of A and y packets of B, (a) Write the inequalities in terms of x and y which satisfy the above information. (b) On the grid provided represent the inequalities in part (a) above (c) The trader makes a profit of Ksh 12 on a packet of type A rice and Ksh 8 on a packet of type B rice. Determine the maximum profit the trader can make. Form 4 Mathematics
The figure below represents a cuboid ABCDEFGH in which AB = 16 cm, BC = 12 cm and CF = 6 cm.
(a) Name the projection of the line BE on the plane ABCD.
Calculate correct to 1 decimal place: (i) the size of the angle between AD and BF; (ii) the angle between line BE and the plane ABCD; (iii) the angle between planes HBCE and BCFG. (c) Point N is the midpoint of EF. Calculate the length BN, correct to 1 decimal place. Form 4 Mathematics
The vertices ofa rectangle ABCD are: A(0,2), B(0,4), C(4,4) and D(4,2). The vertices of its image under a transformation T are; A’(0,2) , B’(0,4) , C’(8,4) and D’(8,2).
On the grid provided, draw the rectangle ABCD and its image A’B’C’D’ under T. (ii) Describe fully the T. (iii) Determine the matrix of transformation. (b). On the same grid as in (a), draw the image of rectangle ABCD under a shear with line x =-2 invariant and A(0, 2) is mapped onto A”(0,0). Form 4 MathematicsForm 4 Mathematics
A basket ball team scored the points in 6 matches: 10, 12, 14, 16, 28 and 30. Using an assumed mean of l5. Determine the standard deviation correct to 2 decimal places.
Form 4 Mathematics
Determine the amplitude, period and the phase angle of the curve: y = 5/2 sin (4θ + 60°)
Form 4 Mathematics
An aircraft took off from a point P (65° S, 76° W) and flew due North to a point Q. The distance between P and Q is 5400 nm.
Determine the position of Q. Form 4 MathematicsForm 4 Mathematics
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. Form 4 Mathematics
(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. Form 4 MathematicsForm 4 Mathematics
A particle moves in a straight line. It passes though point O at t = O with velocity v= 5m/s. The acceleration a m/s2 of the particle at time t seconds after passing through O is given by a = 6t + 4
(a) Express the velocity v of the particle at time t seconds in terms of t (b) Calculate (i) The velocity of the particle when t = 3 (ii) The distance covered by the particle between t = 2 and t = 4 Form 3 MathematicsTriangle ABC is the image of triangle PQR under the transformation (b) Triangle ABC in part (a) above is to be enlarged scale factor 2 with centre at (11, -6) to map onto A’B’C. Construct and label triangle A’B’C’ on the grid above. (c) By construction find the coordinates of the centre and the angle of rotation which can be used to rotate triangle A’B’C’ onto triangle A” B” C”, shown on the grid above. Form 4 Mathematics
Use the mid ordinate rule with six strips to find the area bounded by the curve y = x2 + 1, the lines x = -4 , x = 8 and the x-axis.
Form 2 MathematicsForm 4 Mathematics
A quadrilateral with vertices at K (1, 1), L (4, 1), M (2, 3) and N (1, 3) is transformed by a matrix
a) Determine the coordinates of the image
(b)On the grid provided draw the object and the image. c)i)Describe fully the transformation which maps KLMN onto K’L’M’N ii) Determine the area of the image d) Find a matrix which maps K’L’M’N’ onto KLMN. Form 4 Mathematics
The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
a)Find i)The equation of the curve ii)The value of x at which the curve cuts the x – axis b) Determine the area enclosed by the curve and the x – axis Form 4 Mathematics
A tourist took 1 hour 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E, ). (Take the radius of the earth to be 6370km and π = 22/7)
(a) Find the average speed of the aircraft. (a) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E), The average speed of the second aircraft was 90% that of the first aircraft Determine the time, to the nearest minute, the aircraft took to travel from U to V. (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. |
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