Form 4 Mathematics
The table below shows marks scored by 42 students in a test.
a) Starting with the mark of 25 and using equal class intervals of 10, make a frequency distribution table.
b) On the grid provided , draw the ogive for the data c) Using the graph in (b) above , estimate: (i) The median mark (ii) The upper quartile mark
answers
 Form 4 Mathematics
The equation of a curve is given by y = 5x − 1/2 x2
(a) On the grid provided, draw the curve of y = 5x − 1/2 x2 for 0 ≤ x ≤ 6 (b) By integration, find the area bounded by the curve, the line x =6 and the x-axis. (c) (i) On the same grid as in,(a).draw the line y = 2x. (ii) Determine the area bounded by the curve and the line y = 2 x.
answers
Form 3 Mathematics
Three quantities R, S, and T are such that varies directly as S and inversely as the square if T.
a) Given that R=480 when S=150 and T = 5, write an equation connecting R, S and T. b)(i)find the value of R when S = 360 and T = 1.5. (ii) Find the percentage change in R if S increases by 5% and T decreases by 20%.
answers
Form 4 Mathematics
(a) Complete the table below, giving the values correct to 1 decimal place.
b) On the grid provided, using the same scale and axes, draw the graphs of y = 2 sin (χ+20)0 and y = √3 cos χ for 00 ≤ χ ≤ 2400.
c) Use the graphs drawn in (b) above to determine: i) the value of χ for which 2sin (χ + 20) = √3 cos χ; ii)the difference in the amplitudes of y =2sin(χ + 20) and y =√3 cos χ.
answers
Form 4 Mathematics
The figure ABCDEF below represents a roof of a house. AB=DC=12 m, BC = AD = 6m, AE = BF = CF= DE = 5m and EF = 8m
(a) Calculate, correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD.
(b) calculate the angle between : (I) the planes ADE and ABCD (II) The line AE and the plane ABCD, correct to 1 decimal place; (III) The planes ABFE and DEFE, correct to 1 decimal place.
ANSWERS
Form 3 Mathematics
(a) Complete the table below for y = x3+4x2-5x-5
(b) On the grid provided, draw the graphs of y = x3 +4x2-5x-5 for -5 ≤ x ≤ 2
(c) (i) Use the graph to solve the equation x3 +4x2 – 5x – 5 = 0 (ii) By drawing a suitable straight line on the graph, solve the equation x3 + 4x2 – 5x -5 = - 4x – 1
answers
Form 3 Mathematics
In the figure below, PR is a diameter of the circle center O. Points P, Q, R and S are on the circumference of the circle. Angle PRQ = 72, QS = QP and line USV
is tangent to the circle at S. 
Giving reasons, Calculate the size of
(a) ˂ QPR (b) ˂ PQS (c) ˂ OQS (d) ˂ RTS (e) ˂ RSV
answers
Form 1 Mathematics
The hire purchase (H.P) price of a public address system was Kshs 276000. A deposit of Kshs 60000 was paid followed by 18 equal monthly installments.
The cash price of the public address system was 10% less than the H.P price. (a) Calculate (i) The monthly installments (ii) The cash price (b) A customer decided to buy the system in cash and was allowed a 5% discount on the cash price. He took a bank loan to buy the system in cash. The bank charged compound interest on the loan at the rate of 20% p.a. The loan was repaid in 2 years. Calculate the amount repaid to the bank by the end of the second year (c) Express as a percentage of the Hire Purchase price, the difference between the amount repaid to the bank and the Hire Purchase price
answers
Form 4 Mathematics
The vertices of triangle T are A(1, 2), B(4, 2) and C(3, 4). The vertices of triangle Tʹ, the image of T are Aʹ(1/2 ,1) , Bʹ(2,1) and Cʹ(3/2. 2).
answer
Form 4 Mathematics
The position of two towns are (20 S,300 E) and 20S, 37.4 0E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
answer
Form 3 Mathematics
The table below shows income tax rates in a certain year
In that year, a monthly personal tax relief of kshs 1056 was allowed .calculate the monthly income tax paid by an employee who earned salary of Ksh 32 500.
answers
Form 4 Mathematics
A point P moves inside a sector of a circle, centre O, and chord AB such that 2cm < OP ≤ 3cm and angle APB = 65 Draw the locus of P
answer
Form 1 Mathematics
Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage tap R can empty the full tank in 6 hours; taps A and R are opened for 5 hours then closed.
(a) Determine the fraction of the tank is still empty (b) Find how long it would take to fill the remaining fraction of the tank if all the three taps are opened
answer
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